text:
PEEK and POKE

In computing, PEEK and POKE are commands used in some high-level programming languages for accessing the contents of a specific memory cell referenced by its memory address. PEEK gets the byte located at the specified memory address. POKE sets the memory byte at the specified address. These commands originated with machine code monitors such as the DECsystem-10 monitor; these commands are particularly associated with the BASIC programming language, though some other languages such as Pascal and COMAL also have these commands. These commands are comparable in their roles to pointers in the C language and some other programming languages.

One of the earliest references to these commands in BASIC, if not the earliest, is in Altair BASIC. The PEEK and POKE commands were conceived in early personal computing systems to serve a variety of purposes, especially for modifying special memory-mapped hardware registers to control particular functions of the computer such as the input/output peripherals. Alternatively programmers might use these commands to copy software or even to circumvent the intent of a particular piece of software (e.g. manipulate a game program to allow the user to cheat). Today it is unusual to control computer memory at such a low level using a high-level language like BASIC. As such the notions of PEEK and POKE commands are generally seen as antiquated.

The terms peek and poke are sometimes used colloquially in computer programming to refer to memory access in general.

Statement syntax
The PEEK function and POKE commands are usually invoked as follows, either in direct mode (entered and executed at the BASIC prompt) or in indirect mode (as part of a program): The address and value parameters may contain expressions, as long as the evaluated expressions correspond to valid memory addresses or values, respectively. A valid address in this context is an address within the computer's address space, while a valid value is (typically) an unsigned value between zero and the maximum unsigned number that the minimum addressable unit (memory cell) may hold.

Memory cells and hardware registers
The address locations that are POKEd or PEEKed at may refer either to ordinary memory cells or to memory-mapped hardware registers of I/O units or support chips such as sound chips and video graphics chips, or even to memory-mapped registers of the CPU itself (which makes software implementations of powerful machine code monitors and debugging/simulation tools possible). As an example of a POKE-driven support chip control scheme, the following POKE command is directed at a specific register of the Commodore 64's built-in VIC-II graphics chip, which will make the screen border turn black:

A similar example from the Atari 8-bit computers tells the ANTIC display driver to turn all text upside-down:

The difference between machines, and the importance and utility of the hard-wired memory locations, meant that "memory maps" of various machines were important documents. An example is Mapping the Atari, which starts at location zero and mapped out the entire 64 kB memory of the Atari 8-bit systems location by location.

PEEK and POKE in other BASICs
North Star Computers, a vendor from the early 1980s, offered their own dialect of BASIC with their NSDOS operating system. Concerned about possible legal issues, they renamed the commands  and. There were also BASIC dialects that used the reserved words  and   instead.

BBC BASIC, used on the BBC Micro and other Acorn Computers machines, did not feature the keywords PEEK and POKE but used the question mark symbol (?), known as query in BBC BASIC, for both operations, as a function and command. For example:

32-bit values could be POKEd and PEEKed using the exclamation mark symbol (!), known as pling, with the least significant byte first (little-endian). In addition, the address could be offset by specifying either query or pling after the address and following it with the offset:

Strings of text could be PEEKed and POKEd in a similar way using the Dollar sign ($). The end of the string is marked with the Carriage return character (&0D in ASCII); when read back, this terminating character is not returned. Offsets cannot be used with the dollar sign.

16 and 32-bit versions
As most early home computers used 8-bit processors, PEEK or POKE values are between 0 and 255. Setting or reading a 16-bit value on such machines requires two commands, such as PEEK(A)+256*PEEK(A+1) to read a 16-bit integer at address A, and POKE A,V followed by POKE A+1,V/256 to store a 16-bit integer V at address A.

Some BASICs, even on 8-bit machines, have commands for reading and writing 16-bit values from memory. BASIC XL for the Atari 8-bit computers uses a "D" (for "double") prefix:  and. The East-German "Kleincomputer" KC85/1 and KC87 calls them  and.

The Sinclair QL has  and   for 16-bit values and   and   for 32-bit values. ST BASIC for the Atari ST uses the traditional names but allows defining 8/16/32 bit memory segments and addresses that determine the size.

A Linux command line  utility has been developed mainly for ARM based single board computers. is a Linux command line tool to read from and write to system memory. Its main use is to talk to hardware peripherals from userland: to read or manipulate state, and to dump registers.

POKEs as cheats
In the context of games for many 8-bit computers, users could load games into memory and, before launching them, modify specific memory addresses in order to cheat, getting an unlimited number of lives, immunity, invisibility, etc. Such modifications were performed using POKE statements. The Commodore 64, ZX Spectrum and Amstrad CPC also allowed players with one of the relevant cartridges (such as Action Replay or Multiface) to freeze the running program, enter POKEs, and resume.

For example, in Knight Lore for the ZX Spectrum, immunity can be achieved with the following command: In this case, the value 201 corresponds to a RET instruction, so that the game returns from a subroutine early before triggering collision detection.

Magazines such as Your Sinclair published lists of such POKEs for games. Such codes were generally identified by reverse-engineering the machine code to locate the memory address containing the desired value that related to, for example, the number of lives, detection of collisions, etc.

Using a 'POKE' cheat is more difficult in modern games, as many include anti-cheat or copy-protection measures that inhibit modification of the game's memory space. Modern operating systems enforce virtual memory protection schemes to deny external program access to non-shared memory (for example, separate page tables for each application, hence inaccessible memory spaces).

Generic usage of POKE
"POKE" is sometimes used to refer to any direct manipulation of the contents of memory, rather than just via BASIC, particularly among people who learned computing on the 8-bit microcomputers of the late 1970s and early 1980s. BASIC was often the only language available on those machines (on home computers, usually present in ROM), and therefore the obvious, and simplest, way to program in machine language was to use BASIC to POKE the opcode values into memory. Doing much low-level coding like this usually came from lack of access to an assembler.

An example of the generic usage of POKE and PEEK is in Visual Basic for Windows, where DDE can be achieved with the LinkPoke keyword.

title: PEEK and POKE


text:
Maurice André

Maurice André (21 May 1933 – 25 February 2012) was a French trumpeter, active in the classical music field.

He was professor of trumpet at the Conservatoire National Supérieur de Musique in Paris where he introduced the teaching of the piccolo trumpet including the Baroque repertoire on trumpet. André has inspired many innovations on his instrument and he contributed to the popularization of the trumpet.

Biography
André was born in Alès in the Cévennes, into a mining family. He himself worked in the mine from the age of 14 to the age of 18. His father was an amateur musician; André studied trumpet with a friend of his father, who suggested that André be sent to the conservatory. In order to gain free admission to the conservatory, he joined a military band. After only six months at the conservatory, he won his first prize.

At the conservatory, André's professor, Raymond Sabarich, reprimanded him for not having worked hard enough and told him to return when he could excel in his playing. A few weeks later, he returned to play all fourteen etudes found in the back of Arban's book to a very high standard. Sabarich later said that "it was then that Maurice Andre became Maurice Andre." Maurice André won the Geneva International Music Competition in 1955, together with Theo Mertens, and the ARD International Music Competition in Munich in 1963. He was made an honorary member of the Delta chapter of Phi Mu Alpha Sinfonia at Ithaca College in New York in 1970.

André rose to international prominence in the 1960s and 1970s with a series of recordings of baroque works on piccolo trumpet for Erato and other labels. He also performed many transcriptions of works for oboe, flute, and even voice and string instruments. André had over 300 audio recordings to his name, from the mid-1950s to his death.

André had three children: Lionel (1959–1988), trumpeter and music teacher; Nicolas, who plays the trumpet; and Béatrice, who plays the oboe. All three performed with their father in concert. He also made several recordings with his brother Raymond (b. 1941).

One of André's students, Guy Touvron, wrote a biography entitled Maurice André: Une trompette pour la renommée (Maurice André: A Trumpet for Fame), which was published in 2003.

André spent the last few years of his life in retirement in southern France. He died at the age of 78 in a hospital in Bayonne on 25 February 2012. He is buried in the cemetery of the village of Saint-André-Capcèze (in the Lozère).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Maurice André


text:
Severn Tunnel

The Severn Tunnel (Twnnel Hafren) is a railway tunnel in the United Kingdom, linking South Gloucestershire in the west of England to Monmouthshire in south Wales under the estuary of the River Severn. It was constructed by the Great Western Railway (GWR) between 1873 and 1886 for the purpose of dramatically shortening the journey times of their trains, passenger and goods alike, between South Wales and Western England. It has often been regarded as the crowning achievement of GWR's chief engineer Sir John Hawkshaw.

Prior to the tunnel's construction, lengthy detours were necessary for all traffic between South Wales and Western England, which either used ship or a lengthy diversion upriver via Gloucester. Recognising the value of such a tunnel, the GWR sought its development, tasking Hawkshaw with its design and later contracting the civil engineer Thomas A. Walker to undertake its construction, which commenced in March 1873. Work proceeded smoothly until October 1879, at which point significant flooding of the tunnel occurred from what is now known as “The Great Spring”. Through strenuous and innovative efforts, the flooding was contained and work was able to continue, albeit with a great emphasis on drainage. Structurally completed during 1885, the first passenger train was run through the tunnel on 1 December 1886, nearly 14 years after the commencement of work.

Following its opening, the tunnel quickly formed a key element of the main trunk railway line between southern England and South Wales. Amongst other services, the GWR operated a car shuttle train service through the tunnel for many decades. However, the tunnel has also presented especially difficult conditions, both operationally and in terms of infrastructure and structural maintenance. On average, around 50 million litres of water per day infiltrates the tunnel, necessitating the permanent operation of several large pumping engines. Originally, during much of the steam era, a large number of pilot and banking locomotives were required to assist heavy trains traverse the challenging gradients of the tunnel, which were deployed from nearby marshalling yards.

The tunnel is 7,008 m long, although only 3,621 m of its length are under the river. It was the longest underwater tunnel in the world until 1987 — when Japan’s Seikan Tunnel linking the islands of Honshu and Hokkaido took the title — and, for more than 100 years, it was the longest mainline railway tunnel within the UK. It was finally exceeded in this capacity during 2007 with the opening of the two major tunnels of High Speed 1, forming a part of the Channel Tunnel Rail Link. In 2016, overhead line equipment (OHLE) was installed in the tunnel to allow the passage of electric traction; this work was undertaken as one element of the wider 21st-century modernisation of the Great Western main line.

General
The Severn Tunnel forms a critical part of the trunk railway line between southern England and South Wales, and carries an intensive passenger train service as well as significant levels of goods traffic. As of 2012, an average of 200 trains per day use the tunnel. The whole length of the tunnel is controlled as a single signal section, which has the consequence of limiting the headway of successive trains.

There is a continuous drainage culvert between the tracks to lead ground water away to the lowest point of the tunnel, under Sudbrook Pumping Station, where it is pumped to the surface. The hazard of ignited petroleum running into the culvert in the event of derailment of a tank wagon means special arrangements have to be made to prevent occupation of the tunnel by passenger trains while hazardous liquid loads are being worked through. Evacuation arrangements are in place to enable the escape of passengers and staff in the event of serious accident in the tunnel.

There is restricted personnel access to the tunnel at Sudbrook Pumping Station, where an iron ladder descends in the shaft of the water pumping main; the ventilation air is pumped in at this point also. The GWR original ventilation arrangement was to extract air at Sudbrook, but the exhaust gases from steam train operation led to premature corrosion of the fan mechanism. When the Cornish pumping engines were replaced in the 1960s, the draughting was reversed so that atmospheric air is pumped into the tunnel exhausting at the tunnel mouths.

On average, it has been determined that around 50,000,000 litre per day of fresh (spring) water are typically being pumped from the tunnel; this is normally released directly into the adjacent River Severn. Attempts have also been made to try to determine the sources of the water which feeds the "Great Spring".

The especially difficult conditions for infrastructure maintenance in the tunnel, as well as the physical condition of the tunnel structure, require a higher than normal degree of maintenance attention. Access and personal safety difficulties mean that significant work tasks can only be performed during temporary line closure, during which trains are normally diverted via Gloucester. It is claimed that the tunnel would be full of water within 26 minutes if the pumps were switched off and backup measures failed, while Network Rail has also observed that the corrosive atmosphere of the tunnel, produced from a combination of moisture and diesel fumes from passing trains, results in so much corrosion that the steel rails need to be replaced every six years.

Construction
Prior to the building of the tunnel, the railway journey between the Bristol area and South Wales involved a ferry journey between New Passage and Portskewett or a long detour via Gloucester. Officials within the Great Western Railway (GWR) Company soon realised that the rail journey time between the two locations could be significantly shortened by construction of a tunnel directly underneath the River Severn. As such, during the early 1870s, GWR's chief engineer, Sir John Hawkshaw, developed his design for this tunnel. On 27 June 1872, the company obtained an Act of Parliament which authorised the construction of the envisioned railway tunnel as a replacement for the ferry between Portskewett, Monmouthshire and New Passage, Gloucestershire.

On 18 March 1873, construction activity commenced using labourers employed directly by the GWR; this initial work was focused on the sinking of a shaft, possessing a diameter of 4.6 m at Sudbrook and a smaller drainage heading near the Pennant Measures. The rate of early work on the tunnel was slow and gradual, but without major incident. By August 1877, only the shaft and a 1.5 km heading had been completed; accordingly, that same year, new contracts were issued for the digging of additional shafts at both sides of the Severn as well as new headings along the tunnel's intended route.

As the civil engineer Thomas A. Walker, who was appointed as the contractor for the tunnel's construction, notes in his book, the GWR had expected the critical part of the work to be the tunnelling under the deep-water channel of the Shoots. However, the most substantial difficulties of the venture were encountered during October 1879, when, with only 130 yards (119 m) separating the main tunnel heading being driven from the Monmouthshire side and the shorter Gloucestershire heading, the workings were inundated. The incoming water was fresh, not from the Severn but from the Welsh side, and the source became known as "The Great Spring".

Walker was entrusted by Hawkshaw to proceed with efforts to rescue and then complete the tunnel following the 1879 flooding. To achieve this required holding the Great Spring in check, which in turn was accomplished via the installation of greatly-increased pumping facilities, while a diver also had to be sent down a shaft and 300 m along the tunnel heading to close a watertight door in the workings, sealing off the waters. During November 1880, this troublesome task was finally achieved by the lead diver, Alexander Lambert, who was equipped with Henry Fleuss' newly developed self-contained rebreather apparatus, avoiding the need for the trailing hose of standard diving dress. However, work in the area of the Great Spring was unable to continue until January 1881, at which point the Great Spring was temporarily sealed off.

On 26 September 1881, the two headings met, marking a key milestone in the tunnel's construction, efforts transferred to addressing the tunnel's final structure along with the long deep cuttings at either end. During October 1883, work was again disrupted by further flooding originating from the Great Spring, which was further compounded by the appearance of a spring tide only a week later; again, Lambert and other divers managed to save the day and seal the works. It was recognised that water ingress problems were to continue, thus a heading was driven at a gradient of 1 in 500 from the original Sudbrook shaft, continuing until it reached the fissure through which the Great Spring flowed. By diverting the water into the new heading, the walled-in section of the tunnel could be more easily drained and finished.

There were additional mishaps which afflicted the construction site; at one point, there was an unintentional breakthrough of the bed of a pool, known as the "Salmon Pool", on the English side of the tunnel. It had been originally assumed that the continuous brickwork lining of the tunnel would withstand the groundwater pressure, thus the drainage sluice valve on the side heading was closed and all but one of the pumps were taken from the site. However, on 20 December 1885, the pressure rose so high (up to 395 kN per sq m) that a number of bricks were discovered to have been pushed out of the lining. To address this, the sluice valve was opened gradually, allowing the pressure to subside but necessitating the long-term operation of additional pumping engines. In the intervening period, the Severn Railway Bridge, a competing means for railway traffic to traverse the Severn, spanning between Sharpness and Lydney, was also being built, eventually being opened to traffic during 1879.

On 22 October 1884, work commenced on the laying of the double tracks throughout the tunnel. On 18 April 1885, the final brick was placed in the tunnel's lining. It possessed a horseshoe-shaped cross-section, complete with a concave floor, having a height of 6.1 meters above the rails along with a maximum width of 7.9 m. An enclosed drainage channel, in the form of an upturned semi-circular tunnel, is built onto the tunnel invert, 1.4 m below the rails and having a height of 533 mm. According to Railway Industry publication Rail Engineer, it is believed that around 76.4 million bricks were used in the tunnel's construction. The brickwork is between 686 mm and 914 mm thick. Around the deepest part of the tunnel, the roof is only a maximum of 15.2 m beneath the river bed.

During mid-1885, the Severn Tunnel was completed from a structural standing. To mark this accomplishment, on 5 September 1885, a special passenger train carrying numerous company officials and VIPs, including Sir Daniel Gooch, the then-chairman of the GWR Company, travelled through the tunnel. The first goods train passed through it on 9 January 1886. However, regular services would have to wait until the permanent pumping systems were complete. On 17 November 1886, the tunnel works were inspected by Colonel F. H. Rich, the Government Inspector, a necessary step in advance of its opening to any passenger traffic. Colonel Rich approved the works; thus, the tunnel was opened to regular goods trains during September 1886; the first passenger train followed on 1 December 1886, by which point nearly 14 years had passed since work on the tunnel had started.

Operations
At the newly built Severn Tunnel Junction station, the GWR built a major marshalling yard, which: distributed east and north, sending coal from the South Wales Valleys towards London and the Midlands; created mainline and localised mixed-traffic freight from goods shipped in from the Midlands, the Southwest and along the Thames Valley, both westwards into Wales and vice versa.

Due to the access gradients, throughout the steam era, assistance was required for the passage of all heavy trains through the Severn Tunnel, which entailed (eastwards, from Severn Tunnel Junction): 3+1/2 mile of 1-in-90 down to the middle of the tunnel; a further 3+1/2 mile at 1-in-100 up to Pilning; a short level then 3+1/2 mile more at 1-in-100 to Patchway. This meant that the associated locomotive shed at Severn Tunnel Junction (86E), had a large number of pilot and banking locomotives to assist heavy trains through the tunnel. Under typical operations, pilot locomotives usually worked eastwards and were detached at Pilning, and would then work westwards piloting a second train back to the marshalling yard. During the latter days of steam under British Rail, these locomotives were mainly a group of latter-built GWR 5101 Class 2-6-2T locomotives, the bulk of which now form the core preserved stock of that class today.

A number of fixed Cornish engines, powered by Lancashire boilers, were used to permanently pump out the Great Spring and other sources of water from the tunnel. These were still in regular use until the 1960s, at which point they were replaced by electrically powered pumps. These pumps and their control systems have since been replaced during the 1990s by privately owned railway infrastructure company Railtrack. During the 1930s, the availability of the reliable fresh water supply from the Great Spring was a significant contributing factor in favour of the selection of an adjacent site to be established as the Royal Navy Propellant Factory, Caerwent. Water was also supplied for paper manufacture to a mill at Sudbrook; this facility has since been closed.

On 7 December 1991, the Severn Tunnel rail accident occurred, involving an InterCity 125 that was struck from behind by a Class 155. The subsequent accident investigation, while unable to reach a firm conclusion on the cause, indicated that the axle counters used for detecting train movements in the tunnel may have been accidentally reset.

The Second Severn Crossing, which was built during the 1990s, crosses over the tunnel via a "ground level bridge" on the English side, near the Salmon Pool. This bridge is supported in such a way that no load is imposed on the tunnel. During that bridge's construction, the opportunity was taken to renew the concrete cap above the tunnel in the Salmon Pool.

In 2002, two Class 121s were overhauled by LNWR, Crewe for use as a Network Rail emergency train that was stabled near Severn Tunnel Junction station. They were removed in 2008 having never been used.

Car transport
During 1924, the Great Western Railway started a car shuttle train service using the tunnel, which would transport cars on rail trucks through the tunnel between Pilning and Severn Tunnel Junction. The service functioned as a rail-based alternative to the Aust Ferry, which was operated under an erratic timetable determined by the tides, or lengthy road journeys via Gloucester. The rail shuttle service was continued after the end of World War II, but was ultimately made redundant by the opening of the Severn Bridge in 1966, leading to its discontinuation shortly thereafter.

Electrification
As part of the 21st-century modernisation of the Great Western Main Line, the tunnel was prepared for electrification. While the structure provided good clearances and was therefore relatively easy to electrify, there was also a detracting factor in the form of the continuous seepage of water through the tunnel roof in some areas, which provided a key engineering challenge. The options of using either conventional tunnel electrification equipment or a covered solid beam technology were considered; supported by studies, it was decided to use the solid beam approach. Accordingly, along the length of the tunnel's roof, an aluminium conductor rail was installed to hold an un-tensioned copper contact cable; this rail is held in place using roughly 7000 high-grade stainless steel fixtures, which should be resistant to the hostile tunnel environment. Reportedly, the rigid rail is more robust, requires less maintenance, and is more compact than traditional overhead wires, and has been used in several other tunnels along the GWML.

In order to install the overhead electrification equipment, a six-week closure of the Severn Tunnel was necessary, which commenced on 12 September 2016. During that time, alternative means of travel were either a longer train journey via Gloucester, or a bus service between Severn Tunnel Junction and Bristol Parkway stations. Also during that time, and until late 2017, there were direct flights between Cardiff and London City Airport. Following the completion of this work, which involved the installation of 14 km of copper contact wires using 1,700 vertical drop tubes and 857 anchoring points at a rough cost of £10 million to perform, the tunnel was reopened to regular traffic on 22 October 2016. However, less than two years later, another three-week closure of the tunnel was enacted after it was discovered that some of the recently installed overhead electrification equipment had already started to rust. To combat corrosion, aluminium wire was used, the first of its type in the United Kingdom. Electric trains began operating through the tunnel in June 2020.

title: Severn Tunnel


text:
List of governors of New Mexico

The governor of New Mexico is the head of government of New Mexico and the commander-in-chief of the state's military forces. The governor has a duty to enforce state laws, the power to either approve or veto bills passed by the New Mexico Legislature, to convene the legislature at any time, and to grant pardons.

Twenty-eight individuals have held the office of governor of New Mexico since the state's admission to the Union in 1912, two of whom—Edwin L. Mechem and Bruce King—served three non-consecutive terms. King holds the record as New Mexico's longest-serving governor, with 12 years of service. William C. McDonald, the first governor, took office on January 15, 1912. The first woman to serve as Governor was Republican Susana Martinez, who served from 2011-2019. The current officeholder is Michelle Lujan Grisham, who took office on January 1, 2019, as the first elected female Democratic governor of the state.

List of governors
On August 18, 1846, American forces led by Stephen W. Kearny captured Santa Fe, capital of the Mexican territory of Santa Fe de Nuevo México. A code of laws known as the Kearny Code was established on September 22, 1846. The region remained under military control until formally annexed by the United States on July 4, 1848. Following Kearny's departure for California on September 26, the chief military officer in the territory was Col. Sterling Price until October 11, 1848; Lt. Col. John M. Washington until October 23, 1849; and Col. John Munroe until the territory was organized.

Kearny appointed Charles Bent as governor before he left for California; Bent would be assassinated during the Taos Revolt on January 19, 1847. Col. Price appointed Donaciano Vigil as acting governor. A statehood convention chose Henry Connelly as governor on June 20, 1850, but this was never recognized by the federal government.

Territory of New Mexico
New Mexico Territory was organized on December 13, 1850. It would remain a territory for 62 years.

State of New Mexico
The state of New Mexico was admitted to the Union on January 6, 1912.

The state constitution of 1912 called for the election of a governor and lieutenant governor every four years. The term was changed to two years by a 1914 amendment, and lengthened back to four years in 1970. Governors originally could not succeed themselves; this was changed in 1914 to allow governors to succeed themselves once before having to take a term off. With the lengthening of the term to four years in 1970, this was changed back to prohibiting them from succeeding themselves, but in 1986 it was lengthened back to two terms. A 1962 amendment made it so that the governor and lieutenant governor are elected on a ticket (election). In the event of a vacancy in the office of governor, the lieutenant governor becomes governor.

title: List of governors of New Mexico


text:
List of governors of Washington

The governor of Washington is the head of government of Washington and commander-in-chief of the state's military forces. The officeholder has a duty to enforce state laws, the power to either approve or veto bills passed by the Washington Legislature and line-item veto power to cancel specific provisions in spending bills. The Washington governor may also convene the legislature on "extraordinary occasions".

Washington Territory had 14 territorial governors from its organization in 1853 until the formation of the state of Washington in 1889. Territorial governors were appointed by the president of the United States. Elisha P. Ferry had the longest term of eight years and went on to become the state's first governor. William H. Wallace was appointed governor but never took office due to being elected as the territory's congressional delegate. George Edward Cole was appointed governor and took office, but his appointment was never ratified by the U.S. Senate and he was replaced as governor after four months.

Twenty-two individuals have held the office of Governor of Washington since the state's admission to the Union, with Arthur B. Langlie serving non-consecutive terms. Populist Party candidate John Rankin Rogers is the only non-Democratic or Republican nominee to win office. The most recent governor to be from Eastern Washington was Clarence D. Martin, elected in 1932. The current governor is Democrat Jay Inslee, who took office on January 16, 2013, and was reelected in 2016 and 2020; his term will expire on January 15, 2025, as Inslee announced on May 1, 2023, that he will not be seeking re-election to an unprecedented fourth term in 2024. Washington has had the longest current streak of Democratic governors in the nation, with the last Republican to hold the office being John Spellman in 1985.

With the re-election of Inslee in 2020, Langlie, Daniel J. Evans and Inslee are the only three Washington governors to be elected to three terms with 12 years respectively.

Territory of Washington
Washington Territory was organized on March 2, 1853, from the northern half of Oregon Territory.

State of Washington
Washington was admitted to the Union on November 11, 1889. The term for governor is four years, commencing on the second Monday in the January following the election. If the office of governor is vacant or the governor is unable to discharge their duties, the lieutenant governor assumes the duties of governor, though still officially retains the office of lieutenant governor. If both the offices of governor and lieutenant governor are unable to fulfill their duties, the secretary of state is next in line, and then the treasurer. There is no limit to the number of terms a governor may serve. The office of lieutenant governor is not elected on the same ticket as the governor.

title: List of governors of Washington


text:
TwixT

TwixT is a two-player strategy board game, an early entrant in the 1960s 3M bookshelf game series. It became one of the most popular and enduring games in the series. It is a connection game where players alternate turns placing pegs and links on a pegboard in an attempt to link their opposite sides. While TwixT itself is simple, the game also requires strategy, so young children can play it, but it also appeals to adults. The game has been discontinued except in Germany and Japan.

History
TwixT was invented as a paper and pencil game in 1957 by Alex Randolph, a game designer. When Alex was commissioned along with Sid Sackson by 3M in 1961 to start a games division, the game was issued as a boardgame, one of the first 3M bookshelf games. Avalon Hill took over publication in 1976 when 3M sold its game division. Avalon's parent company was acquired by Hasbro in 1998, and the game was discontinued. The game is no longer produced in the United States, but a succession of German companies has produced the game since the 1970s under license from Avalon. TwixT was short-listed for the first Spiel des Jahres in 1979, and was inducted into the Academy of Adventure Gaming Arts & Design's Hall of Fame, along with Randolph, in 2011.

Rules
Twixt is played on a board comprising a 24×24 square grid of holes (minus 4 corner holes). The game has two types of playing pieces, pegs, which fit into the holes, and links, which fit into the top of the peg pieces and are used to connect to peg pieces. In the 3M edition, players are Red and Black; different sets may use different colors. The topmost and bottommost rows of holes belong to the lighter color; the leftmost and rightmost rows to the darker color.

 * The players take turns placing pegs of their respective colors on the board, one peg per turn.
 * The player with the lighter color makes the first move.
 * A player may not place a peg on their opponent's border rows.
 * To counteract first-move advantage, the pie rule is suggested. After the first peg is placed, the second player has the option to swap sides. This is typically indicated by turning the pieces box end for end, or swapping boxes if they are separate. If the second player chooses not to swap immediately after the first peg is placed, then sides may not be swapped later in that game. (This "one-move equalization" was added by Randolph after 3M published his game. It is present in the Schmidt Spiele edition and all later editions.)
 * After placing a peg, a player may link one or more pairs of pegs on the board of their colour. The links can only connect two pegs a knight's move away from each other, and cannot cross another link; they block other links, most importantly those of the opponent. As part of the player's move, they may remove their own links (but not those of the opponent) in order to rearrange the sequence of links on the board. A variant for pencil and paper play allows a connection to cross the player's links but not those of the opponent.
 * The object is to make a continuous chain of linked pegs connecting the player's border rows. If neither player can achieve this, the game is a draw.

Computational complexity for general rectangular boards
TwixT has been proven to be PSPACE-complete for determining the game value, via a reduction from Hex. TwixT has also been shown to be NP-complete regarding whether a single set of vertices can support a connecting path, via a reduction from 3-satisfiability. These proofs are indicative of a complex strategy: the game has not been solved, no winning strategy has been discovered, nor is the outcome of the game with perfect play known.

Related games
On the 24×24 grid, tactical considerations tend to predominate. The opening phase is over quickly, and the rest of the game is spent attempting to tactically execute the plan. Hex, which has a very similar game object, may have more predictable tactics, but strategical considerations are much more important. In this sense, Hex is more like Go than TwixT, since a single move is generally less committal, and consequences may take longer to play out.

Variants

One variant is Twixt PP (Paper and Pencil). The rules are almost identical to standard TwixT, except links are never removed and a player's own links are allowed to cross each other. A winning path might loop across itself but crossed links are not connected to each other at the intersection. The paper and pencil rules may reduce the number of draws (which are already rare). Whether it reduces the complexity of the game or not is highly debatable.

This rules difference has no effect in terms of game outcome most of the time. For those rare situations where it does, most of those cases are where a draw under standard rules is a decisive game under PP rules. The image shows a contrived position where black is to move. Black wins under PP rules but loses under standard rules.

Row handicapping can be used to equalize the game for players of different strengths. The simplest handicap is to allow the weaker player to move first (i.e. eliminate the pie rule). Beyond that, one dimension of the grid is reduced so the weaker player has a shorter distance to span.

The game may be played on different size grids. The 12×12 board shown here leads to a very short game. On the standard board, tactics dominate; larger boards introduce deeper strategic considerations. Since most commercial sets use boards which are made from four "quadrants" which either clip together or are hinged, a 36×36 grid could be assembled from three standard sets of the same size. In Europe, there briefly appeared a TwixT knock-off called "Imuri" which used a 30×30 grid. The board had no holes, and lines were drawn to indicate where the links could be placed. This edition was removed from shelves for copyright infringement.

Mark Thompson's variant Diagonal TwixT has the same rules as standard TwixT, but the border lines run at a 45-degree angle to the grid. David Bush's version has the border lines running parallel to link paths. These variants result in different tactical patterns.

Competition
The official world championships were held as part of the Mind Sports Olympiad in 1997, 1998 and 1999. Since 2000 TwixT has had a major international tournament as part of the MSO but there has been no official World Championships. Between 2011 and 2022, the TwixT event at the MSO has again become the World Championships. The list of winners is given below.

List of MSO champions

• 1997: 🇺🇸 Alex Randolph

• 1998: 🇩🇪 Klaus Hussmanns

• 1999: 🇩🇪 Klaus Hussmanns

• 2000: 🇩🇪 Klaus Hussmanns

• 2001: 🇩🇪 Klaus Hussmanns

• 2002: 🇩🇪 Peter Henke

• 2003: 🇩🇪 Klaus Hussmanns

• 2004: 🇸🇪 Carl J. Ragnarsson

• 2005: 🇺🇸 David Bush

• 2006: 🇺🇸 David Bush

• 2007: 🏴 Bharat Thakrar

• 2008: 🏴 Bharat Thakrar

• 2009: 🇺🇸 David Bush

• 2010: 🏴 Bharat Thakrar

• 2011: 🏴 David M. Pearce

• 2012: 🇫🇷 Florian Jamain

• 2013: 🇳🇴 Jan Kristian Haugland

• 2014: 🇫🇷 Florian Jamain

• 2015: 🇫🇷 Florian Jamain

• 2016: 🇫🇷 Florian Jamain

• 2017: 🇫🇷 Florian Jamain

• 2018: 🇫🇷 Florian Jamain

• 2019: 🇮🇹 Cosimo Cardellicchio

• 2020: 🇺🇸 David Bush

• 2021: 🇫🇷 Florian Jamain

• 2022: 🇫🇷 Florian Jamain

Reception
Games magazine included TwixT in their "Top 100 Games of 1980", describing it as "much more subtle and interesting than the old Bridg-It, with which it should not be confused".

Games magazine included TwixT in their "Top 100 Games of 1981", noting that "The best offense, oddly enough, is a good defense."

Games magazine included TwixT in their "Top 100 Games of 1982", noting that "Subtlety and finesse will win every time against straightforward aggression in this game of great depth and varied tactics."

Reviews

 * Jeux & Stratégie #6
 * Games & Puzzles #18
 * The Playboy Winner's Guide to Board Games
 * Family Games: The 100 Best

title: TwixT


text:
Bank and Monument stations

Bank and Monument are two interlinked stations in the City of London that form a public transport complex served by five lines of the London Underground as well as the Docklands Light Railway (DLR).

Bank station, named after the Bank of England, opened in 1900 at Bank Junction and is served by the Central, Northern and Waterloo & City lines, and the DLR. Monument station, named after the Monument to the Great Fire of London, opened in 1884 and is served by the District and Circle lines. The stations have been linked as an interchange since 1933.

The station complex is one of the busiest on the London Underground network. The station complex was rated the Underground's worst station in passenger surveys, and a substantial upgrade and expansion was completed in 2023 after 7 years of construction. The station has 27 escalators, the most of any station on the Underground. The stations are in fare zone 1.

History
The Bank–Monument station complex was created by building links between several nearby stations constructed by different companies. The first station was opened by the Metropolitan Inner Circle Completion Railway.

Metropolitan Inner Circle Completion Railway, 1884
The Metropolitan Railway (MR) and District Railway (DR) had, by 1876, built most of the Inner Circle (now the Circle line), reaching and  respectively. The companies were in dispute over the completion of the route as the DR was struggling financially and the MR was concerned that completion would affect its revenues through increased competition from the DR in the City area. City financiers keen to see the line completed established the Metropolitan Inner Circle Completion Railway in 1874 to link Mansion House to Aldgate. Forced into action, the MR bought out the company and with the DR began construction of the final section of the Inner Circle in 1879. The new section of railway included two new stations: Tower of London and another located close to the Monument.

The station at Monument opened with the name "Eastcheap" on 6 October 1884, after the nearby street, and was renamed "The Monument" on 1 November 1884. Initially, trains from both companies served the station on the Inner Circle service but other operational patterns have been used. In 1909, a new entrance was completed to a design by architect George Campbell Sherrin, which included a new entrance incorporating commercial space where the booking hall had previously been located. The Inner Circle service achieved a separate identity as the Circle line in 1949 although its trains were still provided by the District or Metropolitan lines.

Waterloo & City Railway, 1898
The Waterloo & City Railway was built by the London and South Western Railway (L&SWR) to link its terminus at Waterloo to the City. The station, with platforms under Queen Victoria Street and close to Mansion House, opened on 8 August 1898 as "City".

The Waterloo and City line platforms were renamed "Bank" on 28 October 1940. In September 1960, the steeply sloping passages to the platforms were supplemented with the "Travolator", one of the few sets of moving walkways on the whole underground system. Advertising at the Waterloo & City line station often takes the form of large painted murals on the walls and ceilings of the sloped exits, forming one of the largest advertisements on the Underground.

As the W&CR was owned by the L&SWR, a mainline railway, it became part of British Rail; it was only transferred to Underground operation in 1994.

City & South London Railway, 1900
The first station to be known as Bank opened on 25 February 1900, when the City & South London Railway (C&SLR, now part of the Northern line) opened its extension from to. The earlier terminus of the line,, on a different tunnel alignment was closed at the same time.

The C&SLR had obtained permission to demolish the 18th-century church of St Mary Woolnoth on the corner of Lombard Street and build a station (originally proposed to be named "Lombard Street") on the site. After public protest, the company changed its plans to build only a sub-surface ticket hall and lift entrance in the crypt of the church. This necessitated moving the bodies elsewhere, strengthening the crypt with a steel framework and underpinning the church's foundations. Unusually for stations later converted to escalators, the original lift access from the ticket hall is still in use.

Central London Railway, 1900
The opening of the eastern terminus of the Central London Railway (CLR, now the Central line) at Bank followed on 30 July 1900.

As with the C&SLR, the high cost of property in the City, coupled with the presence of the Royal Exchange, the Bank of England, and Mansion House, meant that the station had to be built entirely underground. Permission was granted by the City of London Corporation for the station to be sited beneath the busy junction of roads meeting at this point on condition that public subways were provided to act as pedestrian road crossings. To avoid undermining the road above, the station's lifts were installed in separate lift shafts rather than paired two-per-shaft as usual.

To avoid wayleave payments to property owners and to lessen possible claims for damage during construction and operation, the CLR tunnels were directly under public streets. This caused the platforms under Threadneedle Street and Poultry to be so curved that one end of the platform cannot be seen from the other. East of Bank station the Central line tunnels have sharp curves to avoid the vaults of the Bank of England itself. Due to the close proximity of the CLR, W&CR and C&SLR stations, and the non-competing directions of their services, their ticket halls were soon connected, but connection between the CLR and C&SLR platforms were made only when escalators were installed in 1924. The Central London Railway station itself was reconstructed during the major rebuilding of the Bank of England in 1925. The booking hall underneath Bank junction was redecorated and a new subway entrance built into the corner of the Bank of England itself.

Monument link, 1933
The southern end of the C&SLR (by then part of the Edgware-Highgate-Morden line) platforms was close to those of Monument station and, on 18 September 1933, a connecting escalator link was opened, connecting the two stations directly for the first time.

World War II
During the Blitz, the station was used as a bomb shelter. On 11 January 1941 during World War II the Central line ticket hall of Bank station suffered a direct hit from a German bomb. The roadway collapsed into the subways and station concourse, killing 56 people.

Docklands Light Railway and station refurbishment, 1990s
In 1991, the Docklands Light Railway was extended to Bank station, following criticism of the original, poorly connected terminus at Tower Gateway. The new platforms were built parallel to but deeper than those of the Northern line, with connections at one end to the Central line and Monument Station at the other. As part of the construction of the extension, a new link between the Waterloo & City and the Central line was excavated – uncovering part of one of the Greathead tunnelling shields used for the Waterloo and City line. This shield forms part of the new passageway, and passengers pass through when transferring between the two lines. As with all other DLR stations, the DLR platforms are accessible, however the route is indirect with the use of three different passenger lifts required to reach the DLR.

In January 1994, a statue of James Henry Greathead was erected outside the station, next to the Royal Exchange. It was unveiled by the Lord Mayor of London and is positioned on a plinth which hides a ventilation shaft for the Underground. The rest of the station was comprehensively refurbished, with decorative tiling panels based on the City's coat of arms, new lighting and replacement of escalators. This work was completed in 1997, partially funded by the City of London Corporation.

New Bloomberg entrance, 2010s
In the late 2010s, a new entrance was constructed at Bloomberg's new London headquarters on Walbrook, near station, providing direct access to the Waterloo & City line via four new escalators and two lifts – providing step free access to that line for the first time. First announced in 2008, construction began in November 2015 following delays due to the financial crisis. The new entrance was opened on 30 November 2018, and was officially opened by Mayor of London Sadiq Khan and former Mayor of New York Michael Bloomberg in December 2018.

The new entrance incorporates etched glass panels by artist John Hutton, depicting 66 figures based on the ancient Roman history of the area, including the Roman Temple of Mithras. The artwork was originally completed in 1962 on Bucklersbury House, the post war office building previously located on the site.

Station upgrade and expansion
Between 2003 and 2014, demand at the Bank–Monument station complex rose by over 50% to 337,000 customers per day. The station complex was also rated the Underground's worst station in passenger surveys.

According to Transport for London (TfL), "areas of the station are close to 'saturation' point, where day to day demand overwhelms capacity". Unlike other congested stations such as Oxford Circus, passengers cannot be held back at station entrances during peak times to avoid overwhelming the station, as around half of passengers are interchanging between lines. The high demand on the station is exacerbated by the narrow passageways, pinch points, spiral staircases and indirect routes between lines. Some parts of the station operate "one way", with staff directing passengers on longer routes to increase the capacity of the station.

Given these issues, the station complex was substantially upgraded between 2016 and 2023, increasing capacity by 40%, at a cost of around £700million. The overall project – incorporating twelve new escalators, two new lifts and two moving walkways – included:

Owing to the severe curvature of the Central line platforms, there is a substantial gap between the train and the platform. Because of this, no step-free access was currently proposed for the Central line, as the cost would be prohibitive and it would be difficult for passengers to use.
 * A new southbound platform for the Northern line and conversion of the existing southbound platform to passenger circulation space.
 * New direct passenger tunnel with moving walkways connecting the Northern line and Central line.
 * New escalators between the Northern line and the DLR
 * A new station entrance and ticket hall on Cannon Street, just east of St Mary Abchurch, with new escalators and step free access to the Northern line and DLR.
 * Modernising the station to comply with contemporary fire and evacuation standards.

TfL described the construction of the project as "intricate and complicated", with over 30 listed buildings in the historic City of London located above the tunnels. The new southbound Northern line tunnel was dug from a worksite on King William Street, using the underground spaces left over from the closed King William Street tube station. Former running tunnels have previously been used as circulation space at Angel and London Bridge stations.

As part of the development of the scheme, TfL worked with potential bidders to improve the design of the station from TfL's original design. The design proposed in the winning bid by Dragados was 9.7% cheaper than the original design (saving TfL £60million), took ten months less time to construct than the original design (the proposed closure of the Northern line was also five weeks shorter), and the layout of the station was more efficient. This improved the benefit–cost ratio by 45%, from 2.4:1 to 3.5:1.

Progress
Following consultations in the early 2010s, and a Transport and Works Act Order in 2015, construction of the new Northern line tunnel began in April 2016, and was estimated to take six years. By July 2019, the project had reached the halfway stage. By October 2020, the majority of tunnelling work, around 1.3 km, had been completed, with around 200,000 tonnes of material excavated from beneath the City. By July 2021, installation of escalators was underway, as well as preparation work to connect to the new Northern line tunnels in 2022. From January until mid May 2022, the Northern line through Bank was closed – this was required to allow the existing line to be connected to the new running tunnels, convert the previous southbound platform to a new passenger concourse, as well as final fit-out and integration works throughout the expanded station complex. On 15 May 2022, the new Northern line southbound platform and concourse was opened, the first part of the station expansion open to the public. On 13 October 2022, new escalators connecting the DLR and the Northern line opened. On 28 October 2022, a moving walkway between the Central and Northern lines was opened. These new connections cut the time taken to interchange between lines, as well as expanding the capacity of the station. On 27 February 2023, the project was completed with the opening of the new Cannon Street entrance, as well as lifts providing step free access to the Northern line and the DLR. The station has 27 escalators, the most of any station on the Underground.

Ticket halls and entrances
Following the opening of the Cannon Street entrance in 2023, the station complex has sixteen entrances and five ticket halls, the most of any station on the Underground.

 * Bullring (Central line) ticket hall, located underneath Bank Junction.
 * Lombard Street (Northern line) ticket hall, located under Lombard Street.
 * Monument ticket hall, located under Monument Street adjacent to the Monument to the Great Fire of London, serving the District & Circle lines.
 * Walbrook ticket hall, at Bloomberg London, serving the Waterloo & City line.
 * Cannon Street ticket hall, on Cannon Street located just east of St Mary Abchurch.

Notable events
On 11 January 1941, during the Blitz, 56 people were killed and 69 were seriously injured when a German bomb hit the booking hall, with the blast travelling down the stairs and escalators to the platforms. The crater, measuring 120 x, was covered with a Bailey bridge for the traffic to pass over. The station itself was closed for two months.

On 7 September 2003, Bank station was used for a disaster training exercise, Exercise Osiris, billed as "the most realistic live disaster exercise of its kind". The event, lasting several hours and involving about 500 police, fire brigade, ambulance and London Underground personnel, was intended to prepare the emergency services for mass decontamination in the event of a chemical, biological, radiological or nuclear attack.

Connections
A large number of London Buses routes serve the station complex day and night.

title: Bank and Monument stations


text:
Plymouth Brethren

The Plymouth Brethren or Assemblies of Brethren are a low church and Nonconformist Christian movement whose history can be traced back to Dublin, Ireland, in the mid to late 1820s, where it originated from Anglicanism. The group emphasizes sola scriptura, the belief that the Bible is the only authority for church doctrine and practice. Plymouth Brethren generally see themselves as a network of like-minded free churches, not as a Christian denomination.

Origins in Ireland
The Brethren movement began in Dublin, Ireland, where several groups of Christians met informally to celebrate the Eucharist together, the first meeting being in 1825. The central figures were Anthony Norris Groves, a dentist studying theology at Trinity College; Edward Cronin, studying medicine, John Nelson Darby, a curate in County Wicklow; and John Gifford Bellett, a lawyer who brought them together. They did not have any liturgy, order of service, or even any ministers; in their view, since their guide was "the Bible alone" they sought to do it according to their own interpretation of the biblical text.

Early theology
An important early stimulus was the study of prophecy, which was the subject of a number of annual meetings at Powerscourt House in County Wicklow starting in 1831. Lady Powerscourt had attended Henry Drummond's prophecy conferences at Albury Park, and Darby was espousing the same pre-tribulational view in 1831 as Edward Irving. Many people came to these meetings who became important in the English movement, including Benjamin Wills Newton and George Müller.

The two main but conflicting aspirations of the movement were to create a holy and pure fellowship on the one hand, and to allow all Christians into fellowship on the other. Believers in the movement felt that the established Church of England had abandoned or distorted many of the ancient traditions of Christendom, following decades of dissent and the expansion of Methodism and political revolutions in the United States and France. People in the movement wanted simply to meet together in the name of the Lord Jesus Christ without reference to denominational differences.

Establishment in England
The first meeting in England was held in December 1831 in Plymouth, Devon. It was organised primarily by George Wigram, Benjamin Wills Newton, and John Nelson Darby. The movement soon spread throughout the United Kingdom, and the assembly in Plymouth had more than 1,000 people in fellowship in 1845.

They became known as "the brethren from Plymouth" and were soon simply called "Plymouth Brethren". The term Darbyites is also used, especially when describing the Exclusive branch which has a more pronounced influence from Darby. Many within the movement refuse to accept any name other than "Christian".

Schism
In 1845, Darby returned from an extended visit to Switzerland where he had achieved considerable success establishing churches. He returned to Plymouth where Newton was in control, and he disagreed with some details in a book that Newton had published concerning the tribulation that was coming. He also objected to Newton's place as an elder in the Plymouth meeting. But several attempts to settle the quarrel in the presence of other brethren failed to produce any clear result. Two years later, Darby attacked Newton over a lecture that Newton had given on the 6th Psalm, and an exchange of tracts followed. Newton retracted some of his statements, but he eventually left Plymouth and established another chapel in London.

Darby had instituted a second meeting at Plymouth, and in 1848 he complained of the Bristol Bethesda assembly, in which George Müller was prominent; he was concerned because they had accepted a member from Ebrington Street, Newton's original chapel. Bethesda investigated the individual but defended their decision, and Darby was not satisfied. He issued a circular on 26 August 1848, cutting off Bethesda and all assemblies who received anyone who went there. This defined the essential characteristic of "exclusivism" which he pursued for the rest of his life.

Two movements: Exclusive Brethren and Open Brethren
From 1848, the Brethren continued as two separate main movements: the Exclusive Brethren led by Darby, and the Open Brethren led by Müller and others. Darby visited Exclusive assemblies in America seven times between 1862 and 1877. Itinerant preachers from Scotland and Ireland established most of the early Open Brethren assemblies in America in the second half of the 19th century.

The Exclusive Brethren experienced many subsequent splits, scatterings, and recombinations. The Open Brethren also suffered a split concerning the autonomy of assemblies, which occurred at different times in different parts of the world. Nevertheless, both continued to expand their congregations. In the United States between 1916 and 1919, Exclusive Brethren membership increased 33% to 3,896, while Open Brethren membership increased 25% to 5,928. The census also recorded three smaller movements with sizeable congregations.

Open Brethren
The best-known and oldest distinction between Open assemblies is in the nature of relationships among their local churches. Open Brethren assemblies function as networks of like-minded independent local churches. Brethren generally feel an obligation to recognize and adhere to the disciplinary actions of other associated assemblies. Conversely, Open assemblies aware of that disciplining would not automatically feel a binding obligation to support it, treating each case on its own merit. Reasons for being put under discipline by both the Open and Exclusive Brethren include disseminating gross Scriptural or doctrinal error or being involved in unscriptural behavior. Being accused of illegal financial dealings may also result in being put under discipline.

Another less clear difference between assemblies lies in their approaches to collaborating with other Christians. Many Open Brethren will hold gospel meetings, youth events, or other activities in partnership with non-Brethren Evangelical Christian churches. More conservative Brethren tend to not support activities outside their own meetings.

IBCM
International Brethren Conferences on Mission (IBCM) were founded in 1993 in Singapore by unions of churches from various countries. According to an IBCM Network census released in 2020, they claimed 40,000 churches and 2,700,000 members in 155 countries.

Exclusive Brethren
Exclusive Brethren have remained attached to Darby's doctrine. They are more interdependent, more conservative with a propensity for a dress code, very attached to the spontaneity of worship and preaching. They form several more or less compartmentalized circles of communion, from the most moderate to the narrowest. The movement has a Protestant theology and recognizes infant baptism. Around 40,000 worldwide in 2012, "close" brothers are often referred to as Darbyists, but rarely refer to themselves as such.

Plymouth Brethren Christian Church
The term Exclusive Brethren is most commonly used in the media to describe one separatist group known as Taylor-Hales Brethren, who now call themselves the Plymouth Brethren Christian Church (PBCC), which claims 50,000 members worldwide in 2023, known for a particularly isolationist interpretation of separation from evil and definition of what constitutes fellowship. In their view, fellowship includes dining out, business and professional partnerships, membership of clubs, etc., rather than just the act of Communion (Lord's Supper), so these activities are done only with other members. There are several unquantified but sizable branches unaffiliated with the Raven-Taylor-Hales group (since initial divisions in the 1880's, and more recent secessions in the 1960's-1970's) that prefer being referred to as Closed or Careful rather than Exclusive brethren to avoid any connection with the more strident group.

Brethren labels and distinctions
Terminology which sometimes confuses Brethren and non-Brethren alike is the distinction between the Open assemblies, usually called "Chapels", and the Closed assemblies (non-Exclusive), called "Gospel Halls." Contrary to common misconceptions, those traditionally known as the "Closed Brethren" are not a part of the Exclusive Brethren, but are rather a very conservative subset of the Open Brethren. The Gospel Halls regard reception to the assembly as a serious matter. One is not received to the Lord's Supper but to the fellowship of the assembly. This is important because the Lord's Supper is for believers, not unbelievers.

Some chapels, on the other hand, will allow practically anyone to participate who walks in and says that s/he is a Christian, based on the newcomer's profession of faith. Such assemblies are said to have an "open table" approach to strangers. Gospel Hall Brethren, on the other hand, generally believe that only those formally recognised as part of that or an equivalent assembly should break bread. Most Closed and some Open Brethren hold that association with evil defiles and that sharing the Communion meal can bring that association.

Their support text is from 1 Corinthians 15:33, "Do not be deceived: evil communications corrupt good manners." Among other distinctions, the Gospel Halls would generally not use musical instruments in their services, whereas many Chapels use them and may have singing groups, choirs, "worship teams" of musicians, etc. The Gospel Halls tend to be more conservative in dress; women do not wear trousers often, although they can and there is no scriptural objection in doing so, but most do not wear them in meetings and always have their heads covered, while in most Chapels women may wear whatever they wish, though modesty in dress serves as a guideline, and many continue the tradition of wearing a head covering taught in 1 Corinthians 11:2-13. Open Brethren churches are all independent, self-governing, local congregations with no central headquarters, although there are a number of seminaries, missions agencies, and publications that are widely supported by Brethren churches and which help to maintain a high degree of communication among them.

Henry K. Carroll performed an analysis of United States census data in 1912 to assign Roman numerals to various Brethren groups. For example, Brethren III is also known as the Lowe Brethren and the Elberfeld Brethren. Carroll's initial findings listed four sub-groups, identified as Brethren I-IV, but he expanded the number to six and then to eight; Arthur Carl Piepkorn expanded the number to ten. Those who have attempted to trace the realignments of the Plymouth Brethren include Ian McDowell and Massimo Introvigne. The complexity of the Brethren's history is evident in charts by McDowell and Ian McKay.

Definition
Both Open and Exclusive Brethren have historically been known as "Plymouth Brethren." That is still largely the case in some areas, such as North America. In some other parts of the world such as Australia and New Zealand, most Open Brethren shun the "Plymouth" label. This is mostly because of widespread negative media coverage of the Plymouth Brethren Christian Church, the most hardline branch of the Exclusive Brethren (and the only numerically significant Exclusive group in either country), which most Open Brethren consider to be a cult with which they do not wish to be misidentified.

Leadership
One of the most defining elements of the Brethren is the rejection of the concept of clergy. Their view is that all Christians are ordained by God to serve and therefore all are ministers, in keeping with the doctrine of the priesthood of all believers. The Brethren embrace the most extensive form of that idea, in that there is no ordained or unordained person or group employed to function as minister(s) or pastors. Brethren assemblies are led by the local church elders within any fellowship.

Historically, there is no office of pastor in most Brethren churches, because they believe that the term pastor (ποιμην, poimen in Greek) as it is used in Ephesians 4:11 describes one of the gifts given to the church, rather than a specific office. In the words of Darby, these gifts in Ephesians 4:11 are "ministrations for gathering together and for edification established by Christ as Head of the body by means of gifts with which He endows persons as His choice." Therefore, there is no formal ordination process for those who preach, teach, or lead within their meetings. Men who become elders, or those who become deacons and overseers within the fellowship, have been recognized by others within the individual assemblies and have been given the blessing of performing leadership tasks by the elders.

An elder should be able and ready to teach when his assembly sees the "call of God" on his life to assume the office of elder. Brethren elders conduct many other duties that would typically be performed by the clergy in other Christian groups, including counselling those who have decided to be baptized, performing baptisms, visiting the sick, and giving spiritual counsel in general. Normally, sermons are given either by the elders or by men who regularly attend the Sunday meetings—but, again, only men whom the elders recognize as having the "call of God" on their lives for that particular ministry. Visiting speakers, however, are usually paid their travel costs and provided for with Sunday meals following the meetings.

Open and Exclusive Brethren differ in how they interpret the concept of no clergy. The Open Brethren believe in a plurality of elders (,; ; Philippians 1:1), men meeting the Biblical qualifications found in and. This position is also taken in some Baptist churches, especially Reformed Baptists, and by the Churches of Christ. It is understood that elders are appointed by the Holy Spirit (Acts 20:28) and are recognised as meeting the qualifications by the assembly and by previously existing elders. Generally, the elders themselves will look out for men who meet the biblical qualifications, and invite them to join them as elders. In some Open assemblies, elders are elected democratically, but this is a fairly recent development and is still relatively uncommon.

Officially naming and recognizing eldership is common to Open Brethren (cf. ), whereas many Exclusive Brethren assemblies believe that recognizing a man as an elder is too close to having clergy, and therefore a group of leading brothers, none of whom has an official title of any kind, attempts to present issues to the entire group for it to decide upon, believing that the whole group must decide, not merely a body of elders. Traditionally, only men are allowed to speak (and, in some cases, attend) these decision-making meetings, although not all assemblies follow that rule today.

The term elder is based on the same Scriptures that are used to identify bishops and overseers in other Christian circles, and some Exclusive Brethren claim that the system of recognition of elders by the assembly means that the Open Brethren cannot claim full adherence to the doctrine of the priesthood of all believers. Open Brethren consider, however, that this reveals a mistaken understanding of the priesthood of all believers which, in the Assemblies, has to do with the ability to directly offer worship to God and His Christ at the Lord's Supper, whether silently or audibly, without any human mediator being necessary—which is in accordance with, where it is stated that Christ Jesus Himself is the sole Mediator between God and men (men being used here generically of mankind, and not referring simply and solely to males).

The Plymouth Brethren Christian Church, the most hardline of all the Exclusive Brethren groups, has developed into a de facto hierarchical body which operates under the headship of an Elect Vessel, currently Bruce Hales of Australia.

In place of an ordained ministry, an itinerant preacher often receives a "commendation" to the work of preaching and teaching that demonstrates the blessing and support of the assembly of origin. In most English-speaking countries, such preachers have traditionally been called full-time workers, labouring brothers, or on the Lord's work; in India, they are usually called Evangelists and very often are identified with Evg. in front of their name.

A given assembly may have any number of full-time workers, or none at all. In the last twenty years, many Open Assemblies in Australia, America, and New Zealand, and some elsewhere, have begun calling their full-time workers pastors, but this is not seen as ordaining clergy and does not connote a transfer of any special spiritual authority. In such assemblies, the pastor is simply one of several elders, and differs from his fellow-elders only in being salaried to serve full-time. Depending on the assembly, he may or may not take a larger share of the responsibility for preaching than his fellow elders.

UK government COVID-19 contracts
Dozens of companies with connections to the Exclusive Brethren, now known as the Plymouth Brethren Christian Church, were awarded £2.2 billion in UK government COVID-19 contracts from the Department of Health and Social Care. This included providing personal protective equipment (PPE). Several former members of the church have connections with the ruling Conservative Party, and Members of Parliament previously lobbied for the church to be given UK charitable status by the Charity Commission.

Missionary work
The Plymouth Brethren have been active in foreign missionary work, principally in Central Africa, India and Latin America. Brethren are found throughout the English-speaking world and in most European countries. The movement spread to the US in the 1860s.

Notable Brethren
This list consists of mostly nineteenth-century figures who were associated with the Brethren movement before the 1848 schism. They are the leading historical figures common to both the Open and Exclusive Brethren. Two exceptions are H.A. Ironside and Watchman Nee, twentieth-century preachers who spent time associated with both the Open and Exclusive Brethren. See the respective articles for other more recent figures who have functioned primarily or entirely in either the Open Brethren or Exclusive Brethren:

 * Robert Anderson – senior officer of Scotland Yard and Christian author; was a member of the Plymouth Brethren, first with Darby then with the Open Brethren party, before returning to his Presbyterian roots
 * John Gifford Bellet – research fellow in classics at Trinity College, Cambridge.
 * André Bergeron – French trade union leader
 * George Beurling – Canadian WWII fighter pilot
 * Robert Mackenzie Beverley – one of the most influential figures to abandon the Quakers and join the Brethren during the Beaconite controversy
 * John Bodkin Adams – British general practitioner, convicted fraudster, and suspected serial killer.
 * Lancelot Brenton – translator of the Greek-English edition of the Septuagint
 * F. F. Bruce – British biblical scholar, author of 40 books and commentaries. (Open Brethren)
 * Robert Chapman – prominent among the Plymouth Brethren in the 19th century
 * William Coltman - Victoria Cross recipient, most decorated stretcher bearer of World War I.
 * Henry Craik – worked with George Müller in Bristol at Gideon and Bethesda Chapels from 1832
 * Edward Cronin – pioneer of homeopathy and one of the original Dublin brethren
 * Anthony Crosland – British Labour Party MP and Foreign Secretary from 1976 to 1977; grandson of F. E. Raven (Raven Exclusive Brethren).
 * Aleister Crowley – British occultist, was raised in the movement until his father's death.
 * John Nelson Darby – international preacher, writer, translator, hymn writer, and "father of dispensationalism"
 * James George Deck – evangelist and missionary to New Zealand; officially associated with the Exclusives but refused to cut his ties to the Open Brethren.
 * Jim Elliot – one of five missionaries killed while participating in Operation Auca
 * Garrison Keillor - author and radio personality, left PB assemblies of his childhood
 * Ken Follett – British novelist
 * Emily Bowes Gosse – painter, illustrator, and author of religious tracts
 * Philip Henry Gosse – naturalist and marine biologist
 * Edmund Gosse – the son of Phillip and Emily Gosse who wrote Father and Son, about his relationship with his father and the religion.
 * Anthony Norris Groves – missionary to Baghdad and India
 * Stuart Wesley Keene Hine – missionary and hymn-writer, translator and author of How Great Thou Art
 * John Eliot Howard – chemist and quinologist
 * Luke Howard – chemist and meteorologist, the "namer of clouds"
 * Harry Ironside – Bible teacher, preacher, and author; pastor of the Moody Church in Chicago (1930–1948); associated at different times with both the Open and Exclusive Brethren
 * William Kelly – prominent leader of the Exclusive Brethren in the late 19th century
 * Charles Henry Mackintosh – 19th-century author of Christian books who published as C.H.M.
 * George Müller – founder of the Bristol Orphanage and a stated teacher in Bethesda Chapel, Bristol
 * Watchman Nee – leader in the "Little Flock" movement in China after being "put out" by Exclusive Brethren for "breaking bread with sectarians"
 * Thomas Newberry – translator of the Newberry Reference Bible, which uses a system of symbols to explain verb tenses
 * Francis William Newman – younger brother of Cardinal John Henry Newman; excommunicated for denying the Divinity of Christ
 * Benjamin Wills Newton – early leader of the assembly in Plymouth; branded as a heretic by John Darby and his followers
 * John Parnell, 2nd Baron Congleton – missionary to Mesopotamia
 * G. H. Pember – English theologian who lived in the 19th century; wrote the book Earth's Earliest Ages
 * Joseph M. Scriven – writer of the words to the hymn "What A Friend We Have In Jesus"
 * Hudson Taylor – founder of the China Inland Mission
 * Samuel Prideaux Tregelles – English biblical scholar and theologian
 * William Edwy Vine – author of Vine's Expository Dictionary of Old and New Testament Words and numerous commentaries
 * George Wigram – wrote a Greek and English Concordance to the New Testament and The Englishman's Hebrew and Chaldee Concordance of the Old Testament
 * Orde Wingate – British commando
 * Orde Wingate – British commando

title: Plymouth Brethren


text:
List of governors of Idaho

The governor of Idaho is the head of government of Idaho and commander-in-chief of the state's military forces. The officeholder has the duty to see state laws are executed, power to either approve or veto bills passed by the Idaho Legislature. The current governor of Idaho is Brad Little, a Republican, who took office on January 7, 2019.

Thirty-one individuals have held the office of governor of Idaho since the state's admission to the Union in 1890, two of whom served non-consecutive terms. The state's first governor, George L. Shoup, had the shortest term, of three months; Cecil Andrus had the longest, of 14 years.

Territory of Idaho
Idaho Territory was created from Dakota Territory, Nebraska Territory, and Washington Territory on March 4, 1863.

There were sixteen territorial governors appointed by the president of the United States from the territory's organization in 1863 until the formation of the state of Idaho in 1890. Due to the long distance from Washington, D.C. to Boise, there was often a lengthy gap between a governor being appointed and his arrival in the territory; four resigned before even arriving.

State of Idaho
Idaho was admitted to the Union on July 3, 1890. The terms for governor and lieutenant governor are 4 years, commencing on the first Monday in the January following the election. Prior to 1946, the offices were elected to terms of two years. If the office of governor is vacant or the governor is out of state or unable to discharge his duties, the lieutenant governor acts as governor until such time as the disability is removed. If both the offices of governor and lieutenant governor are vacant or both those officers are unable to fulfill their duties, the President pro tempore of the Idaho Senate is next in line, and then the Speaker of the Idaho House of Representatives. After the change to four-year terms, self-succession (re-election) was not initially allowed; newly elected Governor Robert E. Smylie, formerly the state's attorney general, successfully lobbied the 1955 legislature to propose an amendment to the state constitution to allow gubernatorial re-election, which was approved by voters in the 1956 general election. There is no limit to the number of terms a governor may serve. The governor and the lieutenant governor are elected at the same time but not on the same ticket.

title: List of governors of Idaho


text:
List of governors of Wyoming

The governor of Wyoming is the head of government of Wyoming, and the commander-in-chief of the U.S. state's military department.

The gubernatorial term has been set at four years since statehood. Originally, a governor could be elected any number of times. Since a 1992 referendum, governors have been limited to eight years in office during any 16-year period—effectively limiting them to two consecutive terms.

title: List of governors of Wyoming


text:
Zollernalbkreis

The Zollernalbkreis is a Landkreis (district) in the middle of Baden-Württemberg, Germany. The district is located in the Swabian Alb, and contains the second highest elevation of this range, the 1011 m high Oberhohenberg. In the south-east the district nearly reaches to the river Danube.

The district was created on January 1, 1973, when the two previous districts Balingen and Hechingen were merged.

Neighboring districts are (from north clockwise) Tübingen, Reutlingen, Sigmaringen, Tuttlingen, Rottweil and Freudenstadt.

Coat of arms
The coat of arms shows the black-and-white checkered symbol of Hohenzollern in the left half, and the triple black deer antler on the yellow ground as the symbol of Württemberg. Almost all of the district's area belonged to these two states historically.

Language
In the area of Zollernalbkreis, Swabian German is spoken. In former times, Yiddish, Pleißne and Romani was also spoken. The Pleißne was spoken by hawkers selling items such as baskets, brushes, and whips, and belongs to Rotwelsch. It was used as a code.

Smuggler
Within the Heuberg Training Area there is the legendary Dreibannmarke, also called the "Bahn", a 17th-century border, which today marks the border between three different municipalities, formerly in the three states of Württemberg, Baden, and Hohenzollern. The meadow at the Dreibannmarke served as a stopping place for traveling merchants, wagons and craftsmen. With care it is possible to identify traces of the border. After the inauguration of the firing ranges, a meadow in Meßstetten was allocated as a camping site at the edge of the restricted area. Until 1835 merchandise was smuggled over the customs borders guarded by local hunters. Hans Ungnad von Weißenwolff, Freiherr von Sonneck, Hans III.(1493–1564) Bible printer and smuggler in Bad Urach Coffee smuggler Haux had was killed on 21 July 1831 in Pfaffental.

Ébénistes
Ébénistes make case furniture, either veneered or painted. Frommern was the world capital of furniture in the time of Wirtschaftswunder. In Frommern a line of high polished industrial production take up the ideas of the royal Hofebenist. In the Haus der Volkskunstof the Schwäbischer Albverein the traditional Himmelbett is use as a hotel bed.

Mining
Sandstone, limestone, black coal and sand have been the primary products mined. The Goldhöhle mine was in Erlaheim near Mildersbach, Schwefelkies, in Geislingen. It later collapsed. In former times iron ore was mined on the Heuberg. Fidel Eppler was the name of the mine inspector. The buttress wood was bought in Truchtelfingen and used by Lautlingen miners at the Hörnle area. In Oberdigisheim Geppert in 1738 SHW-Ludwigsthal produced iron ore. From an old 3.5 km mine in an ooidal iron ore seam (Doggererzflöz) in Weilheim is wood in the Tuttlinger Fruchtkasten. Steel was produced in Tuttlingen by the Schwäbische Hüttenwerke in Ludwigstal, which produces now iron brakes. In Meßstetten-Michelfeld sand was found in an old arm of Danube. Christian Kiesinger (1876–1969) father of Kurt Georg Kiesinger had a factory. Ooidal iron ore (Bohnerz aus Eisenroggenstein) was found. After the Franco-Prussian War the mining was stopped. In Germany coal mining stopped 2018.

black stone was mined for Operation Desert (German fuel project). Black coal is mined from the Posidonia Shale. Jet work (to make black jewellery which was very fashionable), was called Beinschnitzen.

title: Zollernalbkreis


text:
James T. Conway

James Terry Conway (born December 26, 1947) is a retired United States Marine Corps four-star general who served as the 34th Commandant of the Marine Corps. Among his previous postings were Director of Operations (J-3) on the Joint Chiefs of Staff, Commanding General of 1st Marine Division and I Marine Expeditionary Force, taking part in the 2003 invasion of Iraq and the First Battle of Fallujah.

Early life and education
Conway was born in Walnut Ridge, Arkansas. He graduated from Roosevelt High School in St. Louis, Missouri, and then attended Southeast Missouri State University, where he was a member of the Sigma Phi Epsilon fraternity, graduating in 1969 with a Bachelor of Science degree in psychology. Conway is a graduate of the Infantry Officers Advanced Course, the Marine Corps Command and Staff College, and the Air War College. He was commissioned as an infantry officer in 1970.

Marine career
Conway's first assignment was command of a rifle platoon with 3rd Battalion 1st Marines, based at Camp Pendleton. He also served as the battalion's 106mm recoilless rifle platoon commander. Later, he served as Marine detachment executive officer aboard the aircraft carrier USS Kitty Hawk (CV-63) and as commanding officer of the Sea School at Marine Corps Recruit Depot San Diego.

After graduating with honors from the Army's Infantry Officers Advanced Course, Conway commanded two companies in the 2nd Marine Regiment's Operations and Security section. As a field grade officer, he commanded two companies of students and taught tactics at The Basic School. He then went on to serve as operations officer for the 31st Marine Amphibious Unit, with sea duty in the western Pacific and in contingency operations off Beirut, Lebanon.

Returning to the United States, Conway was assigned as Senior Aide to the Chairman of the Joint Chiefs of Staff for two years. After graduating from Marine Corps Command and Staff College with honors, he took command of 3rd Battalion 2nd Marines through its eight-month deployment to Southwest Asia during the Gulf War.

After the war, he was promoted to colonel and assigned command of The Basic School. In 1992–1993, he attended MIT Seminar XXI. Promoted to brigadier general in December 1995, he again was assigned to the Joint Chiefs and later served as president of the Marine Corps University. After being promoted to major general, he served as commander of the 1st Marine Division and as Deputy Commanding General of Marine Forces Central. He was promoted to lieutenant general and assumed command of I Marine Expeditionary Force (I MEF) on November 16, 2002. He commanded I MEF during two combat tours in Iraq, with 60,000 troops under his command, including Marines, soldiers, sailors, and British forces. In the book The Iraq War, Conway was described as, "big, buff, well read and well educated ... he represented all that was best about the new United States Marine Corps, which General Al Gray as the commandant had set up."

US Marines of the 1st Marine Expeditionary Force under Conway's command constructed the military base "Camp Alpha" on top of ancient Babylonian ruins following the invasion. Though a US Military spokesman claimed that the project was discussed with the "head of the Babylon museum", the construction of the base drew intense criticism from archaeologists, who contend that it caused irreparable damage to one of the most important sites in the world.

On June 13, 2006, Conway was nominated by President George W. Bush to become the 34th Commandant of the Marine Corps; the nomination was confirmed by the Senate on August 2, 2006. On November 13, Conway was promoted to the rank of general at Marine Barracks, Washington, D.C., and became the 34th Commandant of the Marine Corps. He was the first Commandant in nearly 40 years to have not served in the Vietnam War.

On June 11, 2009, Conway spoke at the National Press Club about the importance of maintaining the Amphibious assault ships to lift two Marine Expeditionary Brigades and the time "at home" away from the current wars to train for amphibious assault.

Conway was reported to have had "major reservations" about the repeal of "don't ask, don't tell", in contrast to the Pentagon opinion that the younger rank and file of the military did not have such reservations about serving with openly gay service members. Conway, along with Chief of Naval Operations, Admiral Gary Roughead, and Chief of Staff of the United States Army, General George Casey, supported running a one-year study on the effects of a possible repeal. Conway said that if gay Marines are allowed to serve openly, he might need to change the policy that requires unmarried Marines to share rooms. The policy was repealed on December 22, 2010, after his tenure as Commandant had ended.

On October 22, 2010, Conway turned the position of Commandant over to General James F. Amos, his Assistant Commandant, at a ceremony at Marine Barracks, Washington, D.C., Defense Secretary Robert Gates presented Conway with his third Defense Distinguished Service Medal during the change-in-command. He then retired on November 1.

Personal life
Conway is married to Anette Conway and together they have three children, two sons, currently serving in the Marine Corps, and a daughter.

Post-retirement, Conway has held many different positions including a board member seat for Textron, Colt Firearms, General Dynamics, and the Center for Naval Analysis, and xG technologies. He sits on the Board of Directors for Warriors & Quiet Waters and is a member of the board of trustees for the Marine Corps University Foundation.

Conway served as an adjunct faculty member of Georgetown University.

Awards and decorations
Conway has been decorated for service, to include:

 * He also holds 7 expert awards in both rifle and pistol marksmanship badges. In 2010, Conway was the recipient of the distinguished "Keeper of the Flame" award.

title: James T. Conway


text:
Rule of inference

In philosophy of logic and logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).

For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion.

Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary ω-rule.

Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers.

Standard form
In formal logic (and many related areas), rules of inference are usually given in the following standard form:

Premise#1 Premise#2 ...  Premise#n Conclusion

This expression states that whenever in the course of some logical derivation the given premises have been obtained, the specified conclusion can be taken for granted as well. The exact formal language that is used to describe both premises and conclusions depends on the actual context of the derivations. In a simple case, one may use logical formulae, such as in:

 * $$A \to B$$
 * $$\underline{A \quad \quad \quad}\,\!$$
 * $$B\!$$

This is the modus ponens rule of propositional logic. Rules of inference are often formulated as schemata employing metavariables. In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions) to form an infinite set of inference rules.

A proof system is formed from a set of rules chained together to form proofs, also called derivations. Any derivation has only one final conclusion, which is the statement proved or derived. If premises are left unsatisfied in the derivation, then the derivation is a proof of a hypothetical statement: "if the premises hold, then the conclusion holds."

Example: Hilbert systems for two propositional logics
In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables. For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation ($$\vdash$$) instead of a vertical presentation of rules. In this notation,

$$\begin{array}{c} \text{Premise } 1 \\ \text{Premise } 2 \\ \hline \text{Conclusion} \end{array}$$

is written as $$(\text{Premise } 1), (\text{Premise } 2) \vdash (\text{Conclusion})$$.

The formal language for classical propositional logic can be expressed using just negation (¬), implication (→) and propositional symbols. A well-known axiomatization, comprising three axiom schemata and one inference rule (modus ponens), is:

(CA1) ⊢ A → (B → A) (CA2) ⊢ (A → (B → C)) → ((A → B) → (A → C)) (CA3) ⊢ (¬A → ¬B) → (B → A) (MP) A, A → B ⊢ B

It may seem redundant to have two notions of inference in this case, ⊢ and →. In classical propositional logic, they indeed coincide; the deduction theorem states that A ⊢ B if and only if ⊢ A → B. There is however a distinction worth emphasizing even in this case: the first notation describes a deduction, that is an activity of passing from sentences to sentences, whereas A → B is simply a formula made with a logical connective, implication in this case. Without an inference rule (like modus ponens in this case), there is no deduction or inference. This point is illustrated in Lewis Carroll's dialogue called "What the Tortoise Said to Achilles", as well as later attempts by Bertrand Russell and Peter Winch to resolve the paradox introduced in the dialogue. For some non-classical logics, the deduction theorem does not hold. For example, the three-valued logic of Łukasiewicz can be axiomatized as:

(CA1) ⊢ A → (B → A) (LA2) ⊢ (A → B) → ((B → C) → (A → C)) (CA3) ⊢ (¬A → ¬B) → (B → A) (LA4) ⊢ ((A → ¬A) → A) → A (MP) A, A → B ⊢ B

This sequence differs from classical logic by the change in axiom 2 and the addition of axiom 4. The classical deduction theorem does not hold for this logic, however a modified form does hold, namely A ⊢ B if and only if ⊢ A → (A → B).

Admissibility and derivability
In a set of rules, an inference rule could be redundant in the sense that it is admissible or derivable. A derivable rule is one whose conclusion can be derived from its premises using the other rules. An admissible rule is one whose conclusion holds whenever the premises hold. All derivable rules are admissible. To appreciate the difference, consider the following set of rules for defining the natural numbers (the judgment $$n\,\,\mathsf{nat}$$ asserts the fact that $$n$$ is a natural number):

 * $$\begin{matrix}

\begin{array}{c}\\ \hline{\mathbf{0} \,\,\mathsf{nat}}\end{array} & \begin{array}{c}{n \,\,\mathsf{nat}} \\ \hline {\mathbf{s(}n\mathbf{)} \,\,\mathsf{nat}} \end{array} \end{matrix}$$

The first rule states that 0 is a natural number, and the second states that s(n) is a natural number if n is. In this proof system, the following rule, demonstrating that the second successor of a natural number is also a natural number, is derivable:

 * $$\begin{array}{c}

{n \,\,\mathsf{nat}} \\ \hline {\mathbf{s(s(}n\mathbf{))} \,\,\mathsf{nat}} \end{array}$$

Its derivation is the composition of two uses of the successor rule above. The following rule for asserting the existence of a predecessor for any nonzero number is merely admissible:

 * $$\begin{array}{c}

{\mathbf{s(}n\mathbf{)} \,\,\mathsf{nat}} \\ \hline {n \,\,\mathsf{nat}} \end{array}$$

This is a true fact of natural numbers, as can be proven by induction. (To prove that this rule is admissible, assume a derivation of the premise and induct on it to produce a derivation of $$n \,\,\mathsf{nat}$$.) However, it is not derivable, because it depends on the structure of the derivation of the premise. Because of this, derivability is stable under additions to the proof system, whereas admissibility is not. To see the difference, suppose the following nonsense rule were added to the proof system:

 * $$\begin{array}{c}\\\hline {\mathbf{s(-3)} \,\,\mathsf{nat}} \end{array}$$

In this new system, the double-successor rule is still derivable. However, the rule for finding the predecessor is no longer admissible, because there is no way to derive $$\mathbf{-3} \,\,\mathsf{nat}$$. The brittleness of admissibility comes from the way it is proved: since the proof can induct on the structure of the derivations of the premises, extensions to the system add new cases to this proof, which may no longer hold.

Admissible rules can be thought of as theorems of a proof system. For instance, in a sequent calculus where cut elimination holds, the cut rule is admissible.

title: Rule of inference