Member, IEEE Najett Neji

Member, IEEE Raul De Lacerda

Member, IEEE Alain Azoulay

Member, IEEE Thierry Letertre
email: thierry.letertre@supelec.fr

Olivier Outtier
email: olivier.outtier@aviation-civile.gouv.fr

Survey on the Future Aeronautical Communication System and its development for continental communications

Keywords: Aeronautical communications, Future Communication System (FCS), L-band Digital Aeronautical, Electromagnetic Interference (EMI), Electromagnetic Compatibility (EMC)

We present in this survey new technologies proposed for the evolution of the aeronautical communication infrastructure. Motivated by studies that estimate a growth of the air traffic flow, a joint Euro-American project was launched in 2004 to provide solutions adapted to the future aeronautical scenario (air-air communication, traffic optimization...). This project is entitled aeronautical Future Communication System (FCS) and is composed by researchers, industrials and aeronautical authorities from many countries around the world. Inside the scope of this project, it has been developed a system called L-band Digital Aeronautical Communication System (L-DACS) to face the saturation of the current continental aeronautical communication system that operates in the VHF band. Since 2007, the L-DACS is being developed and two candidates were pre-selected: L-DACS1 and L-DACS2. In this work, we discuss about the FCS and the particularities of both pre-selected L-DACS candidates, comparing their benefits with the current aeronautical system. Some insights about their physical and medium access layers are also detailed and the project status is presented. Finally, the last part of this

I. INTRODUCTION

In 2002, the need to improve the aeronautical communication system for air traffic management and air traffic control was recognized by the International Civil Aviation Organization (ICAO). This official organization affiliated to the United Nations was created in April 1947 [1] and comprises nowadays more than 180 country members. The ICAO is an important actor for the standardization of airspace control. Among other missions, the organization is responsible for the definition of the technology used for aeronautical communications and manages the aeronautical radio frequency spectrum [2].

The continental aeronautical communication is mainly ensured by the combination of two systems deployed in the Very High Frequency (VHF) aeronautical band (from 118 to 137 MHz).

One of them is an analogue system developed for voice transmissions that has been in use for more than half a century [3]. The second one is a digital system recently introduced that enables data transmission [START_REF] Sajatovic | Future Aeronautical Communications Concepts and Their Impact on ATM Procedures[END_REF]. Despite this latter evolution, current aeronautical communication systems seem to be insufficient to accommodate the traffic increase of the coming years. According to aviation authorities [START_REF]European Organization for the Safety of Air Navigation[END_REF], the air traffic is estimated to grow 3% per year. Thus, the traffic load in early 2030 should be more than twice when compared to the load in 2005. Based on these estimations, the current system will suffer from severe congestion in some regions around the globe. For this reason and taking into account the evolution of wireless communication technologies, new requirements such as high data rate links, automatization procedures and air-toair communication have been considered [START_REF]Future Communications Study Operational Concepts and Requirements Team[END_REF], [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF] to the evolution of the continental aeronautical communication. Some improvements for the legacy systems were proposed [START_REF] Van Den Boogaard | Agenda Item 2: Future air/ground data link systems -The IATA position on the use of 8.33 kHz (contribution)[END_REF]- [START_REF] Cosovic | Physical Layer Design for a Broadband Overlay System in the VHF band[END_REF] but none of them could provide a long term solution (beyond 2020).

In this context, a joint Euro-American project was launched in 2004 in support to October 19, 2011 DRAFT ICAO discussions to develop a Future Communication System that will complete the existing technology and provide a suitable solution based on the new aeronautical requirements. The development of the Future Communication System is now part of two programs: the Next Generation Air Transportation System (NextGen) [START_REF]Next Generation Air Transportation System -Integrated plan[END_REF], [START_REF]NextGen Commitments and FY09 Work Plan[END_REF] lead by the US Federal Aviation Administration (FAA) and the Single European Sky ATM Research (SESAR) [START_REF]State of progress with the project to implement the new generation European air traffic management system (SESAR)[END_REF]. It involves a large number of research teams as well as industrial partners and aeronautical authorities from many countries. So far, numerous technologies have been considered to the Future Communication System (FCS) infrastructure and evaluated in agreement with the aeronautical requirements [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF]- [START_REF]Technology Assessment for the Future Aeronautical Communications System[END_REF]. These evaluations allowed the identification of potential solutions [START_REF] Gilbert | FCS Technology Investigation -Conclusions and Recommendations[END_REF]- [START_REF] Fistas | Future Communication Study -Action Plan 17: Final Conclusions and Recommendations Report[END_REF] but no single technology could outperform all the other options with respect to the chosen criteria [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF].

The L-band Digital Aeronautical Communication System (L-DACS) is the system in the FCS for L-band continental communications. Different from the current systems operating in the VHF aeronautical band, L-DACS is foreseen to provide interesting additional features such as a higher data rate. The band 960-1164 MHz was allocated to the Aeronautical Mobile (Route) Service (AM(R)S) in the Radio Regulations of the International Telecommunication Union (ITU) to enable the introduction of L-band aeronautical safety communication system. Some studies have been carried out to identify the L-DACS technologies that will support this service. Two proposals have been pre-selected. The first candidate named L-DACS1 [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D2[END_REF],

derived from IEEE 802.16 wireless system, is an evolution of the Broadband Aeronautical Multi-carrier Communication (B-AMC) standard [START_REF] Frequentis | B-AMC Operating Concept and Deployment Scenarios -Delivrable 2.2[END_REF] and the Telecommunications Industry Association Standard 902 (TIA-902) [START_REF]European Organization for the Safety of Air Navigation[END_REF], also known as the Public Safety Communications Standard APCO Project 34 (P34). The second candidate called L-DACS2 [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF], derived from the Global System for Mobile communications (GSM), is based on the All-purpose Multi-channel Aviation Communication System standard (AMACS) [START_REF]Future Communications Infrastructure -Technology Investigations: Description of AMACS[END_REF] and the L-band Data Link (LDL). The candidate systems fulfill most of the requirements expressed by the aeronautical community but are quite different and the final choice between the two L-DACS options should be made by the ICAO at the end of 2013, depending on the SESAR workplan.

Before the L-DACS technology choice, in-depth studies are required to compare the capabilities of both proposals. Current L-DACS investigations are focused on developing specifications [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D2[END_REF], [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF] and prototypes [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D3 -Design specifications for L-DACS1 prototype[END_REF], [START_REF] Fistas | L-DACS2 Transmitter and Receiver prototype equipment specifications: Deliverable D3[END_REF] for both transmitters and receivers, as well as testing their performance in relevant aeronautical environments through Electromagnetic Compatibility October 19, 2011 DRAFT (EMC) studies. Indeed, the EMC of L-DACS with all systems operating in the L-band or in adjacent bands is very important due to flight safety [START_REF]AM(R)S sharing feasibility in the 960-1164 MHz band -Preliminary draft new report ITU-R M[END_REF].

These studies carried until now were crucial but not sufficient to select the L-DACS technology.

Independently of the final decision, the L-DACS system must actually overcome numerous challenges for further stages in its development process. The L-DACS solution should accommodate continuously the air traffic growth and must be developed in a multinational cooperative context.

In addition, for sake of viability, L-DACS must be standardized world-wide and its deployment should have a small impact on the aircraft building process.

Hence, this paper aims to present the L-DACS candidates and describe their advantages and limitations when compared with the legacy VHF system. This paper is organized as follows.

Section II presents the current continental communication system used by aviation in the VHF for the data system, such as the VHF Digital Link (VDL) [START_REF] Schnell | B-VHF-An overlay system concept for future ATC communications in the VHF band[END_REF] and the Aircraft Communication Addressing and Reporting System (ACARS) [START_REF] Sajatovic | Future Aeronautical Communications Concepts and Their Impact on ATM Procedures[END_REF]. Nowadays, with the feature to transmit voice and data messages simultaneously, the pilots are better assisted to conduct their flights.

Even with the recent evolution of the aeronautical VHF technology, current VHF systems are reaching their capacity limits and would not accommodate the increase of the air traffic around the world [START_REF]Future Aeronautical Mobile Communications Scenario -Report on Agenda Item 2[END_REF]. According to the forecasts [START_REF]European Organization for the Safety of Air Navigation[END_REF], after 2011 the traffic will increase at least by a factor of by 3% per year, which means that the current system will suffer from severe congestion in some regions around the globe due to high traffic load [START_REF] Schnell | B-VHF-An overlay system concept for future ATC communications in the VHF band[END_REF]. In these conditions, as the air traffic volume increases, more airplanes will require one or several VHF radio frequencies for communications. Due to susceptibility of VHF analogue technology to background noise and interference, the quality of communication is likely to degrade below acceptable limits if the frequency congestion is not carefully managed. The technology, in use for decades, was conceived to provide voice services and it cannot be adapted to data link applications. Current other technologies have relatively low data rates and this also limits the possibilities of implementing new sets of services and features on such systems.

From the technological perspective, telecommunication systems are evolving and high-datarate links are fundamental to provide advanced services that would be very useful for air control safety. Higher-data-rate solutions would enable additional features that would provide better safety systems and support automatic communication, pilot assistance and air traffic optimization.

For these reasons, technology improvement is fundamental to be able to provide a long-term solution to the air traffic growth presented in the Communications Operating Concepts and Requirements (COCR) reports [START_REF]Future Communications Study Operational Concepts and Requirements Team[END_REF], [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF].

Some solutions have been considered and studied so far. The first idea is to increase the network capacity by reducing transmission channel bandwidths [START_REF] Van Den Boogaard | Agenda Item 2: Future air/ground data link systems -The IATA position on the use of 8.33 kHz (contribution)[END_REF]. However, in case of digital systems, this induces degradation on system data rate. The second approach is to develop an overlay technology in the VHF aeronautical band, i.e. a technology which shares the same frequency band with legacy VHF systems [START_REF] Sajatovic | B-VHF Functional Principles and Architecture[END_REF]- [START_REF] Cosovic | Physical Layer Design for a Broadband Overlay System in the VHF band[END_REF]. The problem with this method is the high interference levels that can be generated over the current system and endanger its reliability.

These two options may not meet the long term aeronautical requirements, given the congestion of the VHF band. According to [START_REF] Hakegard | Spectral Efficient COMmunications for future Aeronautical Services (SECOMAS)[END_REF], these potential improvements may have been sufficient

only for short and medium terms. Therefore, in the prospect to find a long term solution to cope October 19, 2011 DRAFT with VHF band saturation, they have not been retained.

In this very specific context, the aeronautical community has indicated a preference for a new data communication system that will be able to coexist with the VHF system and will be adapted to the new traffic requirements. The idea lies on the preparation of the aeronautical communication to accommodate the traffic growth in the long term based on new communication technologies [START_REF] Hakegard | Spectral Efficient COMmunications for future Aeronautical Services (SECOMAS)[END_REF]. The future system is foreseen to support capacity demand for both voice and data beyond the traffic estimations for the future years and it is expected to provide air/air and air/ground communications.

The initial spectrum requirements were initially calculated in 2003 by LS-TELECOM (in cooperation with EUROCONTROL) [START_REF] Schütz | Radio Frequency Spectrum Requirement Calculations for Future Aeronautical Mobile(Route) System[END_REF], assuming an exemplary system using CDMA technology (because at that moment, the system technology was not yet known). These requirements were updated in 2006 in the COCR document [START_REF]Future Communications Study Operational Concepts and Requirements Team[END_REF] where the exact capacity per user was calculated through evaluation scenarios. Other requirements (such as latency, integrity per service...) were also formulated in the finalized COCR version published in 2007 [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF].

As the aeronautical authorities forecast that the use of data communications will increase, the FCS will allow greater information exchange between aircraft and ground systems to achieve better Air Traffic Management (ATM). For example, some autonomous operations should take place in some parts of the airspace. Based on these requirements, the amount of communication traffic that the FCS is expected to support was calculated in the COCR [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF] for several representative operational volumes like the Terminal Manoeuvring Area (TMA) or the continental en-route (ENR) area. It should be noticed that these technical requirements were provided from operational requirements independent from any specific technology and that the traffic growth was taken into account using prediction tools [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF].

For the FCS development project, emphasis has been put in data-communications, and digital voice will be considered in next steps.

In addition, to support the different services within this future data-link system, a research program named NEtWorking the SKY (NEWSKY) was developed from February 2007 to October 2009 [START_REF]NEWSKY project website[END_REF], [START_REF] Bauer | A Thorough Investigation of Mobile IPv6 for the Aeronautical Environment[END_REF] and aimed to define an IP based network architecture [START_REF] Ayaz | Architecture of an IP-based Aeronautical Network[END_REF], [START_REF]Architecture of an IP-based Aeronautical Network to Integrate Satellite and Terrestrial Data Links[END_REF] to ensure both safety-related and non-safety-related services.

A. Overview

The Future Communication Study seeks for a solution in the long term considering among other reasons, that the technology improvements in the VHF band will be insufficient. Therefore, both programs focus on the introduction of new technologies to the FCI, based on three main phases. The first phase aims at identifying the most promising technologies to support this infrastructure by the assessment of a wide range of potential technologies: cellular system standards, IEEE wireless standards, public safety radio technologies, aviation specific technologies and military radio systems [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF]. The second phase consists of the development of the identified technologies, from technology transition concepts to implementation strategies. Finally, the third phase is to build the new infrastructure at a wide scale not only in Europe and the US but also all over the world.

The first phase (i.e. technology assessment) of the FCS development was completed in

2007 and, for the moment, the second phase is in progress. We detail in the following paragraphs the methodology and results of that first development phase. (around fifty) [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF]. Two categories are identified: the technical criteria and the viability criteria.

The technical criteria are related to system performance and the viability criteria address cost and risk elements associated to its implementation. The list of the eleven retained criteria can be found in [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF].

The technologies are first screened considering only essential criteria, which are very important because without them, a technology can never be deployed. For instance, many aeronautical systems are already in operation both on the ground and in aircraft. Therefore, to ensure the flight safety, the functioning of existing equipments should not be altered by the deployment of a new system. In addition, the target technology is foreseen to be used in many countries in the world, which means that the future system must be open to international standardization.

From the screening process, the emerging technologies are then evaluated by applying all the criteria weighted to their relative importance. In [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF], two weighting approaches are proposed.

In the first approach, a qualitative ranking of the criteria is performed and organized into three classes: important (not specifically addressed), very important (addressed for the viability of the technology) or most important (addressed for the applicability of the technology). In the second approach, criteria ranking based on Analytical Hierarchy Process (AHP) is performed based on some desirable features from technology attributes.

From 2004 to 2007, EUROCONTROL and the FAA performed a cooperative work to assess the different existing technologies. The activities were coordinated and presented to the ICAO Aeronautical Communication Panel (ACP) for international acceptance [START_REF] Gilbert | FCS Technology Investigation -Conclusions and Recommendations[END_REF]- [START_REF] Fistas | Future Communication Study -Action Plan 17: Final Conclusions and Recommendations Report[END_REF].

According to the first evaluation results [START_REF] Schnell | Future Communications Infrastructure -Step 1 -version 1.0[END_REF], [START_REF] Gilbert | FCS Phase I -Technology Assessment for the Future Aeronautical Communication System[END_REF], the FCI will use complementary tech- The screening results emphasize a significant overlap between the European and the American technology shortlists for all the domains (see [START_REF] Gilbert | FCS Phase II -Identification of Technologies for Provision of Future Aeronautical Communications[END_REF], [START_REF] Schnell | Future Communications Infrastructure -Step 2: Technology Assessment Results -version 1.0[END_REF]). The technologies were classified into two general categories: technologies in continental airspace and technologies in specific flight domain (oceanic/remote airspace and airport surface).

One single candidate was retained in the shortlist for airport surface Consequently, the application of all the criteria to discriminate among other technologies was meaningless [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF].

The application of all the criteria was also useless for the two satellite systems/concepts identified for oceanic/remote airspace [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF] because, as mentioned in [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF], the "timeframe of the COCR operational concept is beyond the service horizon of current satellite systems".

Therefore, research activities are being currently made to develop a "follow-on or custom satellite solution" (i.e. custom-designed satellite implementation specifically designed for aeronautical communications) fulfilling the aeronautical requirements.

The whole-criteria studies were indeed focused on the proposed solutions for the continental domain. The evaluation results for both qualitative and AHP weighting methods are given in [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF]. CDMA functional elements is required to satisfy aeronautical requirements). Furthermore, it was recognized that a future satellite solution may be able to support continental environments possibly complementing terrestrial systems.

From these results, the European and American teams developed the same technology recommendations for the different flight domains in [START_REF] Gilbert | FCS Technology Investigation -Conclusions and Recommendations[END_REF]- [START_REF] Fistas | Future Communication Study -Action Plan 17: Final Conclusions and Recommendations Report[END_REF]:

• Airport surface: Aeronautical Mobile Airport Communications System (AeroMACS) based on IEEE 802.16e standard in the C-band,

• Oceanic and desert communications: Next Generation Satellite system in the AMS(R)S band,

• Continental communications: In addition to systems in the VHF band, data-link system in the L-band, possibly complemented by Next Generation Satellite Systems.

Using the technology assessment results, a first joint roadmap (see Fig.

B. The current status: L-DACS investigations

The L-band data-link system identified in the FCS to support the FCI in continental areas is named the L-DACS. Different from the existing VHF systems, L-DACS includes features such as a higher data rate and it also complies with most of the air traffic requirements expressed by the aeronautical community [START_REF]Future Communications Study Operational Concepts and Requirements Team[END_REF], [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF]. In parallel, some additional studies have been carried out to determine the most suitable technologies to support L-DACS services in this frequency band. Using the technology assessment process results and for sake of a harmonized technology, the EUROCONTROL has initiated the development of two candidate systems named L-DACS1 [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D2[END_REF] and L-DACS2 [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF].

Among other needs

The development of L-DACS candidates involves researchers, industrial partners and aviation authorities from many countries in the world. In addition, the L-DACS development activities follow a precise roadmap including a conception phase, a development phase and a deployment phase (see [START_REF] Fistas | Future Aeronautical Communication System -FCI[END_REF]). It should now be updated taking into account the development activities advancement in the recent months and it is also likely to be updated again in the coming years.

Currently, in depth-studies are being performed to choose the final L-DACS technology to be developed and implemented in the FCI. In the two next sections of this paper, we first present the origins and the main characteristics of the two pre-selected candidates, and then we provide a better insight on the studies that have been carried out from 2007 to now.

IV. THE TWO L-DACS CANDIDATE SYSTEMS

In this section, we focus on the description of the main characteristics of the two L-DACS candidates. We mention the benefits of L-DACS compared to current VHF technologies and we address the Physical (PHY) and the Medium Access Control (MAC) layers of the Open System Interconnection (OSI) reference model. We emphasize that although some significant similarities exist, the L-DACS candidate systems are quite different.

Let us first detail the technologies behind each L-DACS proposal. L-DACS1 [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D2[END_REF] is derived from the IEEE 802. [START_REF]Next Generation Air Transportation System -Integrated plan[END_REF] wireless standard, which is one of the most widely deployed wireless technologies [START_REF] Kuran | A survey on emerging broadband wireless access technologies[END_REF]. One of the original standards of L-DACS1 is the B-AMC standard [START_REF] Frequentis | B-AMC Operating Concept and Deployment Scenarios -Delivrable 2.2[END_REF] developed in Europe and based on the Broadband VHF (B-VHF) system [START_REF] Haindl | B-VHF, A multi-carrier broadband communications concept for air traffic management in the VHF band[END_REF]. The other is the October 19, 2011 DRAFT P34, developed in the US and based on the TIA-902 [START_REF]European Organization for the Safety of Air Navigation[END_REF]. L-DACS2 [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF] is inspired from the commercial GSM standard, which is the most popular standard for mobile telephone systems in the world. L-DACS2 is originated from two standards: the AMACS [START_REF]Future Communications Infrastructure -Technology Investigations: Description of AMACS[END_REF] developed in Europe and the LDL developed in the US.

Both L-DACS candidates take advantage from the most promising existing technologies. While L-DACS1 relies on modern modulation techniques and advanced network protocols used in the existing commercial standards, L-DACS2 capitalizes on experience from aviation specific standards using protocols that provide high quality-of-service communications.

Having the possibility to employ the same type of antennas already in use by other aeronautical systems is also among the potential strengths of L-DACS. The system will provide high quality of service communication in each coverage volume and for each flight domain, based on robust modulations and coding schemes [START_REF] Kuran | A survey on emerging broadband wireless access technologies[END_REF]- [START_REF]Technical Specification Group GSM/EDGE Radio Access Network; Modulation, 3rd Generation Partnership Project[END_REF].

A. PHY layer characteristics

1) The similarities: First of all, both candidates will employ conventional aeronautical Lband antennas. Indeed, these antennas are also used by aeronautical radionavigation systems already in operation, which means that their use will decrease the costs of the L-DACS deployment. Such antennas are omnidirectional in the azimuthal plane and their radiation patterns depend strongly on the elevation angle, referenced at the horizontal plane.

The typical airborne antenna gains are given by [START_REF]Methodology for assessing the maximum aggregate equivalent power flux-density at an aeronautical radionavigation service station from all radionavigation-satellite service systems operating in the 1164-1215 MHz band[END_REF] for elevation angles between -90 and 90 degrees. The airborne antenna maximum gain is 5.4 dBi according to [START_REF]Protection criterion for the aeronautical radionavigation service with respect to aggregate emissions from space stations in the radionavigation[END_REF]. In addition, the expected ground antenna gains are determined by [START_REF]Reference radiation patterns of omnidirectional, sectoral and other antennas in point-to-multipoint systems for use in sharing studies in the frequency range from 1 GHz to about 70 GHz[END_REF] for elevation angles between -90 and 90 degrees and the maximum ground antenna gain is 8 dBi. In addition, both L-DACS candidates have comparable operational ranges in Nautical Miles (NM).

2 I). Moreover, based on their specifications, L-DACS devices are not expected to use the same effective bandwidth and power to transmit their respective signals (see Table I).

For sake of protection against electromagnetic radiations to other systems, L-DACS1 and L-DACS2 masks limit the unwanted power to ensure that out of band and spurious transmission levels (see Fig. 2) remain lower than thresholds specified by [START_REF]Unwanted emissions in the spurious domain[END_REF]. Due to different transmit powers and bandwidths, transmission masks are specific for each candidate system.

Divergences between L-DACS1 and L-DACS2 are noticed not only in the transmit mode but also in their receiving functions. Actually, the specifications of L-DACS candidates also present some differences in the receivers' parameters (see Table I). Both L-DACS receiving masks have not been defined yet and that they will be determined based on experiments in further steps of the L-DACS development. However, a first approximation can be to consider that the receiving mask and the transmitting mask would be similar.

So far, we detailed the main divergences between L-DACS1 and L-DACS2 with respect to system-parameters. We also mention herein a principal distinction addressing the duplexing technique, which qualifies how L-DACS terminals access to the transmission channels. While detailed in [START_REF] Sumiya | Agenda Item 2:Future Communication Infrastructure, progress update and recommendations,Status of Air-Ground Datalink Study in ENRI/Japan[END_REF], [START_REF] Nagaoka | Long-term Vision of ENRI's Research and Development[END_REF].

In addition, specific test-beds are being created to evaluate these prototypes. This step is necessary to demonstrate the suitability of L-DACS performance in the presence of interference from existing systems as well as their spectrum compatibility. This aspect is known as the EMC of L-DACS with legacy systems. For the moment, test-beds for L-DACS transmitters are in the planning phase.

C. L-DACS1 and L-DACS2 performance

To test the performance of the L-DACS candidate systems in relevant aeronautical environments with respect to requirements [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF], the main outputs to be checked are the continuity, the integrity, the availability, the latency, the expiration time, the peak number of users per L-DACS cell and the throughput for each user.

Many studies are being currently performed to assess L-DACS capabilities through different interference scenarios and application/traffic scenarios. The output of interference simulations (such as BER) is also used as an input for capacity and performance simulations. The EMC analysis is important to complete the selection of the L-DACS solution and includes studies in both ground and onboard environments. Knowing that each aeronautical system includes an onboard equipment and a ground equipment, many interference scenarios should be considered for EMC investigations, as detailed in Fig. 4.

EMC studies determine if an interfering transmitter and a victim receiver can coexist in the same electromagnetic environment. More precisely, the EMC is achieved if the victim receiver performance remains acceptable in the worst case situation, where the equipment is likely to receive the highest interference level from its potential interferers. The number of interferers is large because the future aeronautical network is foreseen to manage the communication among a large number of airplanes [START_REF]Communications Operating Concept and Requirements for the Future Radio System[END_REF]. To deal with EMC in such environments, a generic approach is proposed and it consists of five successive steps:

• Identify the interference scenario, the victim receiver and the potential interferers,

• Characterize each interferer by its transmitting parameters (power, central frequency, bandwidth, antenna radiation pattern, cable losses and spectral mask), October 19, 2011 DRAFT

• Characterize the victim receiver by its receiving parameters (central frequency, bandwidth, antenna radiation pattern, cable losses, blocking mask, sensitivity and system range),

• Define the interference path (relative position between the victim receiver and each potential interferer in space and frequency) and the propagation model,

• Compute the resulting interference level at the victim receiver and compare it to its maximum acceptable level with respect to its performance requirements.

Based on this methodology, number of tests [START_REF] Micallef | FCI Technology Investigations: L band Compatibility Criteria and Interference Scenarios Study -Deliverable C1: Compatibility criteria and test specification for DME[END_REF]- [START_REF]2: Compatibility criteria and test specification for UAT[END_REF] are being carried out to evaluate the L-DACS performance through various interference scenarios detailed in [START_REF] Micallef | FCI Technology Investigations: L band Compatibility Criteria and Interference Scenarios Study -Deliverables S1-S7: L-Band Interference Scenarios[END_REF], with different aeronautical and telecommunication systems which are operating either in the L-band or in the adjacent bands. We present in the following subsections the issues that have been raised to perform such studies.

1) How to model the environment?: Two different approaches to model the aerospace environment may be adopted. The first approach comprises static [START_REF]AM(R)S sharing feasibility in the 960-1164 MHz band -Preliminary draft new report ITU-R M[END_REF], [START_REF]Report 146: Compatibility studies between GSM MCBTS and other services (TRR, RSBN/PRMG, HC-SDMA, GSM[END_REF]- [START_REF]Report 42: Compatibility between UMTS and existing and planned aeronautical systems above 960 MHz[END_REF] and statistic [START_REF]Report on co-frequency co-coverage Sharing Issues between two CDMA Systems[END_REF] models which have been used so far for first and second generation systems for mobile communications.

The interference level is computed for example through Monte-Carlo simulations. However, taking into account the airplanes safety issues, these methods may not cover the worst case situations of some scenarios mentioned in Fig. 4. The second approach [START_REF] Neji | Radioelectric Compatibility of the Future Aeronautical Communication System[END_REF] is proposed to analyze these particular situations. It consists of building a deterministic model to represent the aeronautical environment, based on number of parameters such as aeronautical regulatory constraints, the minimal distance separation between any two airplanes or any two base stations for example. The paper [START_REF]Interference Analysis for the Future Aeronautical Communication System[END_REF] gives a case study in the air to air scenario. Resulting models strongly depend on radiation patterns of both transmitting and the receiving antennas.

Modeling the environment is more complicated for the co-site scenario, which is the most EMC critical situation because of equipments proximity. One should take into account relative positions of the different devices as well as the effects of the airplane's structure. A tool is being proposed for this particular case in [START_REF] Yalc ¸in | Conception d'un outil d'analyse de compatibilité radioélectrique pour évaluer la performance des systèmes "multi formes d'onde[END_REF] and could be further investigated.

2) How to mitigate the interference?: In addition to transmitting and receiving spectral masks, the interference mitigation is necessary to reduce L-DACS unwanted radiations over other L-band and adjacent equipments, and also to protect L-DACS from unwanted signals of legacy systems. The L-DACS1 and L-DACS2 specifications mentioned several techniques for interference suppression, which can be categorized into three different classes.

October 19, 2011 DRAFT

The first class includes techniques proposed for L-DACS1 transmitters and adapted to the OFDM modulation. They are described more in details in [START_REF] Brandes | Suppression of Mutual Interference in OFDM Based Overlay Systems[END_REF], [START_REF] Schnell | Interference Mitigation for Broadband L-DACS[END_REF]. Some of them are used in the time domain whereas the others are employed in the frequency domain:

• The time windowing consists of multiplying each OFDM symbol by a raised cosine window.

• The Multiple Choice Sequences means transmitting several versions of the OFDM symbol and choosing the one with the lowest out-of-band power (see Fig. 2).

• The Cancelation Carriers technique is to add some carriers which do not transmit data on the right and left of the OFDM symbol.

• The Sub-Carrier Weighting principle is to weight each subcarrier transmitting data by a factor between g min and g max .

The second class comprises filtering tools that have been proposed for L-DACS1 receivers.

They are explained more explicitly in [START_REF] Schnell | Interference Mitigation for Broadband L-DACS[END_REF] and are the following:

• Combination of two digital filters: this technique reduces the narrowband interference. The first one (time domain) is placed before the OFDM demodulator and the second (frequency domain) is after this block.

• Soft erasure decoding: this technique suppresses the received symbols with a very low Signal to Interference plus Noise Ratio (below a fixed threshold).

The third class of techniques represents some filtering methods for L-DACS2 receivers. The system specifications [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF] emphasize two main types of filtering:

• Notch filtering: this technique suppresses narrowband pulse signals.

• Hybrid filtering: this technique detects L-DACS2 pulses (in the time domain) and applies the notch filtering around its estimated carrier. This filter is already used for satellite systems.

3) How to achieve a satisfying EMC?: The first EMC investigations on L-DACS systems have been carried out in the frequency domain. The addressed problem is the frequency sharing between L-DACS and legacy systems. As detailed in [START_REF]AM(R)S sharing feasibility in the 960-1164 MHz band -Preliminary draft new report ITU-R M[END_REF], [START_REF]Report on co-frequency co-coverage Sharing Issues between two CDMA Systems[END_REF], [START_REF]Guidelines for AM(R)S sharing studies in the 960-1 164 MHz band[END_REF], the idea is to analyze the highest generated interference density with respect to the spacing between the interferers and the victim receiver central frequencies. The obtained results so far indicate that both L-DACS candidate waveforms could cause potential interference on existing radionavigation systems. In such a situation, i.e. when the achieved EMC level is insufficient, many solutions are being studied.

October 19, 2011 DRAFT A first option is mentioned in [START_REF] Neji | Radioelectric Compatibility of the Future Aeronautical Communication System[END_REF], which proposes an additional spatial and/or frequency separation between the victim receiver and its potential strongest interferers. To protect the victim receiver from interfering radiations, it is possible either to increase the distance between the victim receiver and the interferers or to reduce the number of in-band interferers, i.e.

transmitters whose frequency channels overlap with the victim receiver bandwidth.

As the degrees of freedom related to this option is limited (because of the finite allocated spectrum and the increasing density of airplanes), another solution is currently under study in [START_REF] Neji | Effect of the aeronautical L-DACS2 radio-frequency signals on the DME system performance[END_REF] and [START_REF]How the aeronautical L-DACS2 radio-frequency signals modulation affects the DME system performance[END_REF]. According to the specifications of both L-DACS candidates and legacy L-band systems, each Radio Frequency (RF) transmission is pulsed (so, not continuous) and each device uses the RF channel during a limited period of time, called the channel occupation rate. Hence, in this approach, Electromagnetic Interference (EMI) studies are being performed taking into account the different systems time domain characteristics. When the interferer and the victim receiver are functioning during distinct time intervals, the probability of interference is likely to decrease comparing to the frequency-domain case.

A good EMC level is achieved once guaranteed that during a given time slot, only one device transmits/receives signals, or if the performance degradation due to interference is sufficiently low. Actually, this condition may be not satisfied especially for the co-site interference scenario.

As a large number of systems are implemented within the same airplane, the collision probability among onboard-generated signals becomes higher and higher. To overcome these undesired effects, the L-DACS specifications mention the possibility to study the implementation of a common suppression bus, which interconnects the airborne L-DACS equipment with onboard other avionics elements. This bus could be activated if a system which could damage other systems or provoke undesired operation, transmits. During this activation, the other onboard equipment transmissions and / or receptions can be blocked. This technique is already proposed for several onboard systems, namely the Universal Access Transceiver (UAT) [START_REF]Manual on the Universal Access Transceiver (UAT)[END_REF] and the Traffic Collision Avoidance System (TCAS) [START_REF] Vesel | Integrity Monitor for TCAS Mutual Suppression[END_REF] but no general operating mode of the device is currently provided. Based on these elements, studies are being carried out to assess the potential use of the suppression bus in onboard environments [START_REF] Micallef | FCI Technology Investigations: L band Compatibility Criteria and Interference Scenarios Study -Deliverable C7: Assessment on the potential use of the onboard suppression bus for L-DACS operation[END_REF].

October 19, 2011 DRAFT

VI. L-DACS CHALLENGES

The L-DACS is being designed to fulfill all of the new aeronautical requirements and provide better mechanisms to assist the pilot and increase flight safety. However, this system has to meet number of challenges before its deployment and some aspects of its development still need to be more analyzed before its implementation. In the previous section, we focused on EMC / EMI investigations, which is one of the most important areas to be studied to ease the L-DACS development. We recall this aspect in this section and we present several other main challenges for further stages of the L-DACS development.

A. Standardization

The L-DACS system, being a part of the proposed FCI, is expected to be a global system for aeronautical safety continental communications. As a result, it is expected that L-DACS will be globally deployed in the long term. For this reason, an important multinational cooperation will be necessary and international standards and recommended practices will also have to be developed by the ICAO for this communication system.

B. EMC Conformity

As far as standardization is considered, one of the key questions to be addressed is the EMC of L-DACS with existing systems in both ground and airborne environments. The task is particularly important because any disfunction in the communication can threaten the flight safety. Not only must the candidate systems be able to operate in the presence of interference from other equipments, but they must also cause the minimum possible interference to legacy systems. Some of these systems in the 960-1215 MHz band are illustrated in Fig. 5.

Most of them are other aeronautical systems but they also include telecommunication as well as satellite systems (these two latter are using adjacent frequency bands to the L-DACS spectrum).

In the following, we give a brief description of each system herein mentioned.

• The Distance Measuring Equipment (DME) [82] which evaluates the slant range between an airplane and a ground beacon by measuring the return ticket of gaussian shaped pulse pairs,

• The Tactical Air Navigation (TACAN) which is similar to the DME, October 19, 2011 DRAFT

• The UAT [83] which exchanges data related to the traffic state and weather conditions,

• The Secondary Surveillance Radar (SSR) [START_REF]Surveillance and Collision Avoidance Systems[END_REF] which identifies airplanes and provides information about the flight's speed, altitude and state,

• The other non-ICAO ARNS which refer to national radionavigation systems,

• The GSM in the 900 MHz band, which is a second generation system for mobile telephony that is standardized by the European Telecommunications Standards Institute (ETSI) and is used in Europe, Africa, Mideast and Asia,

• The Universal Mobile Telecommunications System (UMTS) in the 900 MHz band, which is a European third generation system for mobile telephony that is standardized by the Third Generation Partnership Project (3GPP). Other broadband electronic communication means may be deployed in the future.

• The Global Positioning System (GPS) L5 [START_REF] Bastide | Analysis of the Feasibility and Interests of Galileo E5a/E5b and GPS L5 Signals for Use with Civil Aviation[END_REF] which is a worldwide localization system that uses satellite signals, characterized by the Radio Technical Commission for Aeronautics (RTCA) DO-292 working group,

• The Galileo E5a and E5b signals [START_REF] Bastide | Analysis of the Feasibility and Interests of Galileo E5a/E5b and GPS L5 Signals for Use with Civil Aviation[END_REF] which are new types of signals similar to the GPS L5 signal and standardized by the European Organization for Civil Aviation Equipment (EUROCAE) Working Group 62 commission.

• The Joint Tactical Information Distribution System (JTIDS) and and the Multifunctional Information Distribution System (MIDS) [START_REF]Results of studies of the AM(R)S allocation in the band 960-1 164 MHz and of the AMS(R)S allocation in the band 5 030-5 091 MHz to support control and non-payload communications links for unmanned aircraft systems[END_REF] which are radiocommunication systems authorized by some administrations.

All these systems have different performances and independent functioning modes. Moreover, many among these systems (and others in other frequency bands like VHF) are foreseen to operate in the same airplane. Therefore, the EMC conformity becomes more and more complex.

C. Radio Resource Optimization

Once the EMC step is achieved, it is important to find the optimal way to manage the total allocated spectrum to AM(R)S. The radio resources allocation is related to the transmission peak/average power, the transmission channel bandwidth and the channel occupation rate, that is the percentage of time during which a user is allowed to transmit its messages. Indeed, the network capacity (being herein the number of airplanes simultaneously connected to the particular L-DACS ground station) could be maximized by optimizing the frequency planning October 19, 2011 DRAFT as well as L-DACS protocols, and by minimizing interference levels between users through a control of the airplane transmitted power. However, this latter may have to be balanced with the fact that having more airplanes in the same network may increase interference phenomena.

Hence, a trade-off between the interference minimization and the capacity maximization should be found for the radio resource optimization.

D. Air Traffic Growth

As mentioned in the Section II, the design of L-DACS candidates and their associated requirements are based on the air traffic forecast for the next decades, depending upon statistical studies performed by aeronautical authorities throughout the world. L-DACS1 and L-DACS2 are then considered as a long term best-performer solution for L-band continental communications.

Therefore, they should be able to fulfil this long term communication demand.

VII. CONCLUSION

In this survey, we showed that the future aeronautical communication system will have to

  band and the motivations and objectives of the FCS are discussed. Then, we provide an overview of the achieved steps of the joint Euro-American project for the development of the Future Communications Infrastructure (FCI) in Section III. After that, Section IV focuses on the description of the L-DACS candidates. After giving the principal reasons behind choosing L-DACS, we give a deeper insight on both L-DACS proposals through a comparative study regarding the physical and the medium access control layers. Section V provides an overview of the main research axes leading the current investigations on the L-DACS candidate systems. Finally, we present some challenges that L-DACS has to overcome for the future development and implementation stages.II. WHY A NEW SYSTEM FOR AERONAUTICAL MOBILE COMMUNICATIONS?Civil air traffic control communications and air traffic management communications in continental areas are mainly supported by the combination of two narrowband communication systems that operate on the aeronautical portion of the VHF band, between 118 MHz and 137 MHz. Both systems are based on the communication between the ground and the aircrafts and are used by civil aviation. The first and main system that guarantees the air traffic control communication is an analog-based system that employs a Double Side-Band Amplitude Modulation (DSB-AM). This system allows voice communication and it is being used for more than 70 years. In the 1990s, a new system was introduced to provide data transmission and to allow air-ground message exchanges for the purpose of air traffic management. Different technologies are employedOctober 19, 2011 DRAFT

  list of investigated technologies comprises cellular telephony derivatives (including 3G technologies like W-CDMA and UMTS), IEEE 802 wireless derivatives, Public Safety and Specialized Mobile Radios, Custom Narrowband VHF solutions, Custom Broadband, military and APC telephony. For the technology assessment, eleven criteria based on the COCR are used to compare the capabilities of all the existing technologies

  nologies across multiple frequency bands to provide the data and voice communication. The requirements depend on the aeronautical flight domains (airport surface, oceanic/remote airspace and continental/terrestrial airspace) and the most suitable frequency bands to each flight domain were identified depending on propagation conditions: • Airport surface communications: C-band due to the limited propagation distance and high October 19, 2011 DRAFT data rate, supported by an AM(R)S allocation in the Radio Regulation of the ITU limited to the ground, • Continental communications (Airport area, TMA and En Route airspaces): in addition to the VHF band, the L-Band due to the potential spectrum availability and the suitable Lband propagation characteristics [19], supported by an AM(R)S allocation in the Radio Regulation of the ITU, • Oceanic and remote communications: L-band supported by an Aeronautical Mobile Satellite (Route) Service allocation in the Radio Regulation of the ITU, for aeronautical beyond line of sight systems.

  [START_REF] Gilbert | Future Communication Study Technology Investigation -Conclusions and Recommendations[END_REF],[START_REF] Gilbert | FCS Phase II -Identification of Technologies for Provision of Future Aeronautical Communications[END_REF],[START_REF] Lommaert | IEEE802.16 System Profile Analysis for FCI's Airport Surface Operation[END_REF],[START_REF] Barba | Aero Wimax[END_REF]. In fact, the candidate technologies for this flight domain are required to provide high-datarate communications within limited-range[START_REF] Gilbert | FCS Phase II -Identification of Technologies for Provision of Future Aeronautical Communications[END_REF] and the IEEE 802.16 has been recognized as the technology with the best performance for airport surface and terminal domains.

For

  this flight domain, all the emerged technologies from the assessment process were datalink candidates, and their performance were evaluated in the L-band [20]. Among these technologies, the Wideband Code Division Multiple Access (W-CDMA) technology was not selected due to its impracticality to deploy (according to [20], a full complement of W-October 19, 2011 DRAFT

  1) was developed to structure the implementation and evolution of aeronautical mobile communications with respect to traffic requirements. The FCI technologies for specific flight domains are identified whereas further studies are needed to determine the best technology to be used for continental communications. Indeed, for this flight domain, the L-band is a challenging environment because of the current spectral occupation by numerous aeronautical systems and other systems in the immediate adjacent bands. That is why it is very important to focus on the potential usage of the L-band for the FCI.

  , L-DACS has to cover very long distances (nearly 400 km) and to support very high mobility (up to 1080 km/h) [50]. L-DACS performance requirements are evaluated based on information from [7] for the different operational volumes (such as TMA and ENR). In particular, this evaluation includes Peak Instantaneous Aircrafts Counts (P IACs) per volume, Maximum airspeed in Knots T rue Air Speed (KT AS) per October 19, 2011 DRAFT volume and most stringent capacity requirements in kbps (exact values can be found in [50]). In November 2007, the World Radiocommunications Conference (WRC) organized by the ITU decided a new AM(R)S allocation in a part of the L-Band (from 960 to 1164 MHz), primarily allocated to the Aeronautical Radionavigation Service (ARNS) [51]. This allocation has been made to support the L-DACS development in this band.

)

  The differences: L-DACS1 and L-DACS2 have different required system performance in terms of residual Bit Error Rate (BER), inferred from [26], [29] (see Table I). It should be noticed that the residual BER represents the BER after applying error correction codes to received signals. In addition, both L-DACS systems are foreseen to operate in distinct frequency bands. The L-DACS1 proposed frequency band would cover some parts of the 960 -1009 MHz spectrum for ground transmissions and some parts of the 1048 -1164 MHz band for mobile transmissions, knowing that the separation between the transmitting and receiving October 19, 2011 DRAFT center frequencies is initially proposed to be set to 63 MHz. However, the expected spectrum for L-DACS2 would be 960.5 -975 MHz, considering at present a minimum 0.5 MHz guard band for sake of reducing the mutual interference with mobile telephony signals coming from base stations, which occupy the 925 -960 MHz band. Not only frequency ranges but also modulation schemes are different. L-DACS1 is based on an Orthogonal Frequency Division Multiplexing (OFDM) modulation with Quadratic Phase Shift Keying (QPSK) mapped symbols, whereas L-DACS2 is characterized by a differential Gaussian Minimum Shift Keying (GMSK) modulation on binary symbols (see Table

L 72 ms

 72 -DACS1 employs a Frequency Division Duplex (FDD), L-DACS2 uses a Time Division Duplex (TDD). In the first case, the Ground Station (GS) and the Mobile Station (MS) can transmit simultaneously but using different carrier frequencies, whereas in the second case, the GS and the MS can use the same frequency channel to transmit but during disjoint time intervals. From these definitions, we show in the next subsection the effect of this parameter on the organization of the L-DACS communication. October 19, 2011 DRAFT B. MAC layer characteristics 1) The similarities: The L-DACS communication is basically ensured by exchange of messages between a GS and a MS in its operational coverage. Information coming from the GS are transmitted via the Forward Link (FL) and those from the MS via the Reverse Link (RL). The communication is ensured by a succession of frames, a frame being a unit for information transmission between a GS and each MS in its coverage. For both candidates, the evolution of the communication between a MS and a GS can be represented by six successive steps. The first three steps are executed only once, during the cell entry, whereas the remaining steps will be repeated several times, during the aircraft dwell time within the cell. In the first step, a MS listens to the framing message broadcasted by the GS to all covered MSs and containing its configuration information. In the second step, the MS requests a connection to the GS. In the third step, the GS acknowledges this request, gives a local address and allocates an available slot to the connected MS. In the fourth step, the MS formulates to the GS the needed resources to transmit its message. More precisely, if a connected MS does not transmit data, it transmits regularly a Keep Alive (KA) message in these parts. In the fifth step, the GS acknowledges the MS demand and indicates the position of the requested resources (if available) in the frame, to be used for this MS transmission. If the available resource is insufficient, the remaining slots will be allocated in the next transmission unit. In the sixth step, the MS transmits its RL message using the resource allocated by the GS. For both L-DACS proposals, the communication with the current GS may end due to two events. In the first situation, the MS initiates a handover process to communicate with the GS of a neighboring cell or initiates a disconnection of the L-DACS network. In the second situation, the MS does not transmit data and the GS does not receive a KA message. 2) The differences: Because of L-DACS candidate systems duplexing technique divergence, their MAC layers are differently structured. Indeed, while the FL and RL are operating simultaneously for L-DACS1, the L-DACS2 communication is based on alternation between RL and FL messages. For L-DACS1, the communication is organized into October 19, 2011 DRAFT 240 ms Superframes (SF) as mentioned in [26] and whose beginning and end are aligned in the FL and RL directions from the view of the GS. However, the L-DACS2 communication is organized into one-second successive frames [29]. Because of the L-DACS candidates system duplexing technique divergence, their frames are differently structured (see Fig. 6 for L-DACS1 and Fig. 7 for L-DACS2). On the one hand, a SF in the FL direction is composed by a 6.72 ms Brodacast (BC) frame followed by four 58.32 ms Multiframes (MF). The parallel SF in the RL direction is formed by a 6.Random Access (RA) frame then four 58.32 ms MF. The BC part gives information about the serving and adjacent GSs and the RA part is used to connect to the serving GS. In addition, each MF in the FL direction is divided into nine frames: the four first frames are for payload data, then the variable-size block of Common Control (CC) starts from the fifth frame, and the remaining frames are for payload data. Moreover, an MF in the RL direction is organized into small segments called tiles. Each tile belongs to either a Dedicated Control (DC) segment (for signalization) or a Data segment. According to the L-DACS1 specifications [26], a given MS is allowed to use only one RA subframe and only one DC tile per SF. The GS sends in the CC of the first MF the identifier of the DC tile allocated to the MS. On the other hand, the L-DACS2 frame is divided into five sections. The sections UP1 and UP2 are used only by the GS and the remaining sections (LoG2, CoS1 and CoS2) are employed only by the MS. The beginning of the UP1 section contains information about the serving GS. The LoG2 section is used to connect to the serving GS. When a MS is already connected to the GS, the GS transmits in UP1 the CoS1 slot that will be reserved to that MS (for signalization) and indicates in UP2 the allocated resources. The L-DACS2 frame is composed by 150 equal size transmission units named basic slots distributed over the five sections of the frame. To avoid overlapping between RL and FL messages, each slot contains a radio-frequency transmission element called burst and a guard time. Within a one-second frame, a MS is allowed to use one LoG2 slot, one CoS1 slot and between one and ten CoS2 slots to transmit data (see [29]) and a GS must use one UP1 slot and one UP2 slot to transmit messages to a given MS. Based on the information given so far, we have shown the differences between the two L-DACS proposals. Each technology has its own advantages and drawbacks and it is difficult to October 19, 2011 DRAFT airborne installations. In parallel, the Japanese ENRI started in April 2009 a research program on L-DACS aiming to develop an L-DACS transceiver using Software-Defined-Radio tools as

provide many interesting services

  for both pilots and controllers and to cope with the VHF spectrum congestion, meeting new requirements formulated by aeronautical authorities, and introducing new applications and concepts in aviation. We emphasized that the future communication infrastructure will use various technologies across different frequency bands to support both data and voice demand for the upcoming years. In particular, we emphasize that the L-DACS system has been chosen for continental communication. The L-DACS development motivated researchers, industrial partners and aeronautical instances from different continents around the world. According to technology assessment results, no existing technology could provide optimal performance with respect to the evaluation criteria, and consequently two options have been currently preselected to support this system. The two L-DACS proposals are very different, in particular at PHY and MAC layers, but both are promising as they fulfill aeronautical requirements and take advantage from the best existing technologies. Before the final L-DACS choice, in-depth studies are being performed to develop L-DACS1/2 prototypes and to assess their performance through evaluation scenarios as well as interference scenarios. More particularly their coexistence with all the numerous systems that have been already operating in the aeronautical L-band October 19, 2011 DRAFT and its adjacent bands is important. Some other aspects of its development should also be more analyzed before L-DACS implementation. Therefore, joint efforts are being made to develop L-DACS, address its different development issues and overcome eventual risks of its deployment. The subsequent work is to select the final L-DACS solution and continue on the road of L-DACS development through multinational cooperation.

Fig. 1 .Fig. 3 .Fig. 4 .Fig. 6 .Fig. 7 .

 13467 Fig. 1. The aeronautical communications evolution roadmap in Europe and the United States (source [25])

formulated in the COCR [7]. The development of the future communication system

	III. FCI DEVELOPMENT ACTIVITIES FROM 2004 TO 2009
	Recognizing that there is an insufficient spectrum in the VHF band to support future aeronauti-
	cal communications needs, EUROCONTROL and the US FAA coordinated a joint development
	activity in 2004 in support of ICAO discussions. This initiative is known as the Future Com-
	munications Study and was started with a Cooperative Research Agreement named Action Plan
	17 (AP-17). The objective was to identify the adapted technologies to support the FCI in the
	timeframe of 2020 and beyond and that fulfill the aviation needs
	October 19, 2011	DRAFT

is now a part of two parallel research programs looking for (among other issues) a general solution allowing a long term communication infrastructure in the different regions of the world. One of these programs is named NextGen

[START_REF]Next Generation Air Transportation System -Integrated plan[END_REF]

,

[START_REF]NextGen Commitments and FY09 Work Plan[END_REF]

. It is lead by the US FAA and supported by the National Aeronautics and Space Administration (NASA). The other program is called SESAR

[START_REF]State of progress with the project to implement the new generation European air traffic management system (SESAR)[END_REF]

. It is supported by EUROCONTROL, the European Union (EU), Air Navigation Service Providers (ANSPs) as well as institutional and industrial partners. More recently (in 2008), a Japanese team from the Electronic Navigation Research Institute (ENRI) started developing research activities in parallel to the two programs

[START_REF] Sumiya | Agenda Item 2:Future Communication Infrastructure, progress update and recommendations,Status of Air-Ground Datalink Study in ENRI/Japan[END_REF]

,

[START_REF] Nagaoka | Long-term Vision of ENRI's Research and Development[END_REF]

.

October 19, 2011 DRAFT

discriminate between them. For this reason, more detailed studies are needed to evaluate them to make the final choice. A scope of such studies is provided in the next section. Definition documents of both L-DACS systems [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D2[END_REF], [START_REF] Fistas | L-DACS2 System Definition Proposal: Delivrable D2[END_REF] give detailed description of each candidate and identify the most relevant parameters to take into account. Information about PHY and MAC layers in time and frequency domains have been provided in the previous section of this paper. These specifications may be updated after prototypes' development and tests. The L-DACS1 specifications have been updated within the early task of SESAR working activities.

B. L-DACS1 and L-DACS2 prototypes

Based on identified parameters, transmitter and receiver prototypes are being defined. These prototypes, which are also key parts of the L-DACS development, must be in line with the systems specifications. So far, EUROCONTROL has developed in documents [START_REF] Sajatovic | L-DACS1 System Definition Proposal: Delivrable D3 -Design specifications for L-DACS1 prototype[END_REF] (respectively [START_REF] Fistas | L-DACS2 Transmitter and Receiver prototype equipment specifications: Deliverable D3[END_REF]) transmitter and receiver prototype specifications for L-DACS1 (respectively L-DACS2) for both ground and


Michele Abrusci

Christian Retoré

Some proof-theoretical remarks on quantification in ordinary language

This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's operator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to natural language, in particular with quantified noun phrases as individual terms. We also define guidelines for the design of the proof rules corresponding to generalised quantifiers.

Résumé Cet article dresse un rapide panorama de l'approche commune de la quantification généralisée ou non en linguistique formelle et en philosophie du langage. Nous montrons que ce cadre général est va parfois à l'encontre des données linguistiques, et nous donnons quelques indications pour une approche différente basée sur la théorie de la démonstration, qui sur bien des points s'avre plus proche de la langue. Nous soulignons l'importance des opérateurs tau et epsilon de Hilbert qui rendent respectivement compte de la qualification universelle et existentielle. En effet ces opérateurs permettent de construire des des représentations sémantiques qui suivent la lange avec, en particulier des groupes nominaux quantifiées qui soient des termes individuels. Nous donnons aussi des principes pour définir des rgles de déduction qui correspondent aux quantificateurs généralisés.

1 Foreword: empirical data on quantification Although quantification in logic, in linguistics and in philosophy of language are much studied we think that the dominant model theoretic approach partly leaves out linguistic reality. [START_REF] Peters | Quantifiers in Language and Logic[END_REF][START_REF] Steedman | Taking Scope: The Natural Semantics of Quantifiers[END_REF][START_REF] Szabolcsi | Quantification. Research Surveys in Linguistics[END_REF][START_REF] Gabbay | Quantification in Nonclassical Logic[END_REF] Quantifiers are quite common in ordinary language and even more in speciality languages like sciences, in particular mathematics... unfortunately for the linguists, the more difficult quantifiers are the most common in natural language. Indeed, as we shall see besides the classical quantifiers of mathematics for all ∀ and there exists ∃, natural language makes use of many other quantifiers, some of which are only implicitly stated. Consider for instance the plural definite determiner the it can be used as universal quantification as in The children fell asleep, and it can be used as most was in The Brits love France1 which does not mean that the Brits all do, but more likely that a large part of them do, or even that a short majority does as in France may have elected François Hollande, but she really needs a Napoleon Bonaparte. Let us first say a linguistically oriented word on the usual quantifiers, namely for all and there exists.

The existential quantifier is omnipresent in natural language. As soon as one speaks about something, this "something" is existentially quantified as in A man enters. He whistles. (us) The introduction of new referents, that are existentially quantified, and that are the beginning of anaphoric chains are an important par of the structure of a discourse. For instance, observe that the scope of the existential quantifier extends to the next sentence -this has been a reason to for introducing various dynamic logics. The behaviour of existential quantifiers actually lead to a formalism which is structured by existential quantification, namely Discourse Representation Theory, which construct logical formula in a way that better matches the linear progression of sentences. It is often opposed to compositional semantics, since DRT proceeds top down from larger units to the smallest, words, but there by now exist compositional formulations of DRT. So existential quantifiers are really present in discourse and conversation, and they contribute to the structure and coherence of a discourse. [START_REF] Kamp | From Discourse to Logic[END_REF] The universal quantifier, as it is use in mathematics, is rather rare in ordinary conversation, as corpora study shows, an exception being the reference to a group that can be inferred from the context like in They all went to bed.. The negative formulation is more frequent no one, nothing etc. and if no one came it means that every one did not come.

When speaking about natural language it is often assumed that the individuals that is being referred to by quantification is finite.2 This is not the case. Firstly we meets such expression in mathematical discussions, but also various cases:

(1) He wrapped up by explaining the dark future for the Universe when all the stars go away.

(2) All atoms are made from the same bits, which are called subatomic particles

(3) Just about all sentences in the English language fall into ten patterns determined by the presence and functions of nouns, verbs, adjectives, and adverbs.

(4) All ideas are welcome.

The most that we discussed above is also quite common and also applies to infinite collection of objects:

(5) In basic math, we're taught multiplication tables. We learn that most numbers are the answer to at least two different multiplication problems, some numbers are the answer to several, and then... ( 6) Any module of known β is weak. Most numbers have even β and most of them are not antisymmetric. [START_REF] Kneale | The development of logic[END_REF] The number one reason why most people fail at dieting is simple: they can't stick to it.

(8) Since most numbers are not prime, it would waste time to check every number.

(9) ... thus, in the limit most numbers are not prime.

The human processing of quantifiers is quite difficult, in particular their alternation. There are experiments comforting this viewpoint, see e.g. [START_REF] Szymanik | Comprehension of simple quantifiers: Empirical evaluation of a computational model[END_REF]. But, on the other hand, one finds rarely but sometimes Henkin quantifiers in natural language, like Every member of the lab knows a member of every village sports club. What do people mean when using such quantifiers that would require a lifetime verification? This is a mystery, we know that our study, as well as others, via a confronting the formal model with what we hear or with psycholinguistics experiments may give some hints on the complexity of the human processing.

These few introductory word should have convinced the reader that quantification is an important and common phenomenon in natural langue, although mathematical logic ignores it (an important exception being Hilbert, as we shall see), and although natural language processing consider it as rare and irrelevant (an exception being categorial grammar). So we agree with semanticists: quantification is an important question connecting logic, linguistics and philosophy.

2 Remarks on the two mathematised quantifiers, there exists and for all beginning of the XXth century). An important result is the coincidence of the two notions for first order logic known as the completeness theorem, established by Gödel in 1930. It says that a formula is true in every model [START_REF] De | La querelle des universaux de Platon à la fin du Moyen Âge[END_REF] if and only if it is provable (2) -the part (2) implies (1), known as soundness is easier to proved by induction on the derivation. Other famous theorems are the compactness and Lwenheim-Skolem theorems. The first one says that if any finite subset of a set F of formulae is contradiction free (admits a model), so is F , and the second ones say that a theory with an infinite model and a countable language there are models of every cardinality larger than countable. [START_REF] Kneale | The development of logic[END_REF] Those results are well known -especially completeness -and there is by now not much proof theoretical study of quantification. But one should be aware that this correspondence only works for first-order classical logic -and not for higher order logic. For instance when second or higher order quantification is used, sub-Boolean algebras have to be considered. When other logics are considered trickier structures are required to maintain this correspondence. Even in the well studied case of intuitionistic logic, much more complicated models have to used, e.g. (pre)sheaves of L-structures or Kripke models. [START_REF] Gabbay | Quantification in Nonclassical Logic[END_REF] Even if we only consider first order quantification, the correspondence between provability and truth is not as transparent as one may hope. Natural language provides good insights to perceive the distinction between the proof theoretical and the model theoretical approach. More formally stated, completeness expresses the coincidence between • provability ⊢ ∀x. P (x) inferred from a proof without a free hypothesis involving a free x (a proof with a generic x (the precise rule is given thereafter)

• and truth in every model, that is & x∈I P (x) in every domain I

An important remark is that the proof theoretical viewpoint is finite, while the second one involves two infinite sets: models are usually infinite3 , and the family of all models is usually an infinite set as well. The proof theoretic approach makes use of a generic element. To prove something about any number, the proof starts with Let n be any number. . . which means that n as no other property than being a number -this methods goes back at least to Pythagora, (-580 -490), long before any logical formalisation. It should be observed that natural language makes a distinction between the two notion of quantification above: each and all rather concern the complete enumeration of the elements in a collection while every, any or bare plurals (e.g. Ducks lay eggs) rather concern the generic elements, law and universal rules. In natural language quantification is commonly formulated with a restriction to a given class: All the stars go away, and this is also the case in usual mathematics:

∀x ∈ N ∃u 1 ∈ N ∃u 2 ∈ N ∃u 3 ∈ N ∃u 4 ∈ N x = (u 1 ) 2 (u 1 ) 2 (u 2 ) 2 (u 3 ) 2 (u 4 ) 2
When the restriction is a restriction to a well identified class like (inanimate) things or human beings, there are quantifiers without restriction to specific classes like everyone or everything are possible too: they apply to a single property.

The restriction to a given class in quantification disappeared from mathematical logic (but not from type theory) because of the following observation of Frege. Indeed, for philosophical reasons, he insisted in having a single onesorted universe, and using implicitly a correspondence between a set M the corresponding predicate (M (x)), one is able to represent quantification with restriction to a given class:

∀x ∈ M P (x) ≡ ∀x (M (x) ⇒ P (x)) ∃x ∈ M P (x) ≡ ∃x (M (x)&P (x))
To present examples from the most studied quantifiers, we follow Arsitotle square of oppositions:

• All As are Bs • Some As are Bs • No As are Bs • Not alls A are Bs
In the original formulation, the expression A and B denote terms, which are much vaguer than properties or predicates -in the Middle-Age, the theory of suppositiones already contributed to make the notion of term neater.

Existential quantification (Some As are Bs) is formulated with some, there is, a it can also be formulated without restriction to a class of individuals by someone, or something. The last two statements exhibit that natural language is finer grained, and that it makes a difference because of the focus between statement that usual logic consider as equivalent.

(10) There's a tramp sittin' on my doorstep (11) Some girls give me money (12) Something happened to me yesterday (13) Some politicians are crooks [START_REF] Szabolcsi | Quantification. Research Surveys in Linguistics[END_REF] ? Some crooks are politicians (us) Observe that the existential negative (the fourth corner of Aristotle square of oppositions) is NOT lexicalised (in English and other languages). Psycholinguists know that they is harder to grasp, rather ambiguous, and in ordinary conversation an existential negative statement is often understood wrongly as universal negative statements (e.g. example 15 is rather often understood as 16). Also observe in our unambiguous rephrasing 19 of 18, the focus has changed from the ones that can be funded to the ones that cannot, making the rephrased statement tougher. (18) Everyone is entitled to an opinion, but not every opinion is entitled to student government funding.

(19) Everyone is entitled to an opinion, but some opinions are not entitled to student government funding. (us) We already provided some examples of universal statements, here are some more, ranging on a potentially infinite domain:

(20) Each star in the sky is an enormous glowing ball of gas.

(21) All groups of stars are held together by gravitational forces.

(22) Terence Tao, a Fields medalist, has published a paper that proves that every odd number greater than 1 is the sum of at most five primes.

The universal negative statements are expressed either by no, and without restriction to a class by no one, nothing, Here are some examples:

(23) Because no planet's orbit is perfectly circular, the distance of each varies over the course of its year.

(24) Nothing's gonna change my world.

(25) Porterfield went where no colleague had gone previously this season, realising three figures.

From a proof theoretical viewpoint how do ∃ and ∀ work? They both have introduction and elimination rules:

• Universal quantifier -The ∀ introduction rule says as above that when a property has been established for an x which does not enjoy any particular property (i.e. is not free in any hypothesis), one can conclude that the property holds for all individuals:

no free occurrence of x in any

H i H 1 , . . . , H n ⊢ P (x) ∀ i H 1 , . . . , H n ⊢ ∀x. P (x)
-The ∀ elimination rule says that when a property has been established for all individuals it can be inferred from any particular individual: An alternative way to deal with quantification is to use individual concepts that are properties holding of exactly one individual. This is the reason why in Discourse Representation Theory some people write John(x) while others write j: the former notation describes an individual concept John( ) which has the property of being true of exactly one individual, and this can be stated in second and first order logic: X is an individual concept whenever C(X) = (∀x∀y(X(x)∧X(y) ⇒ x = y))∧∃x. X(x) -there are variants in which the existence is not demanded. Universal quantification can be phrased with individual concepts via second order quantification. Indeed, ∀x. P (x) can be expressed as ∀X(C(X) ⇒ P # (X)) with P # (X) = ∃X. (X(x)&P (x)), and, conversely, given a property Q of individual concepts, the quantification ∀X.

H 1 , . . . ,
(C(X) ⇒ Q(X)) corresponds to ∀x. Q b (x) with Q b (x) = ∃X. (C(X) ∧ X(x) ∧ Q(X)
). The equivalence are established by formal proof in second order logic, with second order quantification, and by duality the same result holds for existential quantification. There is a variant according to which the non emptiness is not required, since it is possible to name individuals that do not exist in this case one from of quantification is stronger than the other. One may wonder why using individual concepts and therefore use second order logic. A reason is that it is closer to the notion of term of Ancient and Medieval logic: both Socrates and human beings are terms. A more concrete reason is that, in common possible worlds semantics with rigid designators, it is impossible to interpret I do not believe that Tully is Cicero. [START_REF] Lacroix | Aspects logiques et linguistiques de la quantification[END_REF] Proof theoretic approaches naturally lead to rules of refutation. How does one refute a universal statement ∀xP (x)? Of course it amounts to try to prove the negation, that is an existential statement ∃x¬P (x), but there are different ways to do so. Consider the following example:

(26) [The AKC notes] that any dog may bite.

(27) No, Rex would never bite. (us) (28) Basset hounds do not bite. (us) The difference is that the first answer picks up an element in the relevant model, while the second answer remains with generic elements. This is related to the Avicenian idea that a property of a term (individual or not) is always asserted for the term as part of a class: it is more related to type theory than to the Fregean view of a single universe. [START_REF] Gabbay | Quantification in Nonclassical Logic[END_REF] Hilbert's operators: ι, ǫ, τ, . . .

After the quantifier the one and unique individual such that P . . . introduced by Russell for definite description, Hilbert (with Ackerman and Bernays) intensively used generic elements for quantification, the study of which culminated in the second volume of Grundlagen der Mathematik [START_REF] Hilbert | Grundlagen der Mathematik[END_REF]. It should be stressed that these operators are introduced and describe with natural language examples, which is not so common in Hilbert's writings. We shall first present the ǫ operator which recently lead to important work in linguistics in particular with von Heusinger work. [START_REF] Egli | The epsilon operator and E-type pronouns[END_REF][START_REF] Klaus Von Heusinger | Definite descriptions and choice functions[END_REF][START_REF] Klaus Von Heusinger | Choice functions and the anaphoric semantics of definite nps[END_REF] The first step due to Russell was to denote by ι x . F the unique individual enjoying the property F in a definite description like the first sentence and to remain undetermined when existence and uniqueness do not hold. [START_REF] Russell | On denoting[END_REF] (29) The present president of France was born in Rouen. (us) (existence and uniqueness hold)

(30) The present king of France was born in Pau. (us) (existence fails) (31) The present minister was born in Barcelona. (us) (uniqueness fails)

From this idea, Hilbert introduced an individual existential term defined from a formula: given a formula F (x) with a free variable x one defines the term ǫ x . F in which the occurrences of x in F are bound (this is the original notation, nowadays this term is often written as ǫ x . F ). Whenever an element, say a, enjoys F , then the epsilon term ǫ x . F enjoys F .

Dually, Hilbert introduced a universal generic element τ x . F , which corresponds to the generic elements used in mathematical proofs: if τ x . F enjoys the property F then every individual does.

The evident deduction rules for τ and ǫ are as follows:

• From A(x) with x generic in the proof (no free occurrence of x in any hypothesis), infer A(τ x . A(x))

• From B(c) infer B(ǫ x . B(x)).

The additional rules can be found by duality:

• From A(x) with x generic in the proof (no free occurrence of x in any hypothesis), infer A(ǫ x . ¬A(x))

• From B(c) infer B(τ x . ¬B(x)).

Hence we have F (τ x . F (x)) ≡ ∀x.F (x) and F (ǫ x . F (x)) ≡ ∃x. F (x) and because of negation, one only of these operator is needed, usually the ǫ operator and the logic is known as the epsilon calculus. .

Hilbert turned these symbols into a mathematically quite nice object, since it allows to fully describe quantification and with simple rules. The first and second epsilon theorem basically say that this is an alternative formulation of first order logic.

First epsilon theorem When inferring a formula C without ǫ symbol nor quantifier from formulae Γ not involving the ǫ symbol nor quantifiers the derivation can be done within quantifier free predicate calculus.

Second epsilon theorem When inferring a formula C without ǫ symbol from formulae Γ not involving the ǫ symbol the derivation can be done within predicate calculus.

This way, it provided the first correct proof of Herbrand theorem (much before mistakes where found and solved by Goldfarb) and a proof of the consistence of Peano arithmetic (at the same time as Gentzen did). The extension of the cut elimination patterns to these operators does not seem too complicated and people already worked on them, by [START_REF] Mints | Cut elimination for a simple formulation of epsilon calculus[END_REF] In Hilbert's book these operators are explained with natural language examples, but a very important linguistic property is not stated: the ǫ x F as a type (both in the intuitive and in the formal sense) of a noun phrase, and is meant to be the argument of a predicate (for instance the subject of a verb), thus being a suppositio in the medieval sense. [START_REF] De | La querelle des universaux de Platon à la fin du Moyen Âge[END_REF][START_REF] Kneale | The development of logic[END_REF] Nowadays there has been a renewed interest in these epsilon formulation of quantification, in particular by von Heusinger. He uses a variant of the epsilon for definite descriptions, leaving out the uniqueness of the iota operator of Russell, one reason being that the context often determines a unique object, the most salient one. As say it is a variant because it is not clear whether one still has the equivalence with ordinary existential quantification: he constructs an epsilon term whenever there is an expression like a man or the man but it is not clear how does one asserts that man(ǫ x . man(x)). The distinction between ǫ and η is that the former selects the most salient, while the later selects a new one.

Generalised quantifiers

The abundant literature on generalised quantifiers takes place in a rather conventional setting, along the lines drawn by in particular by Frege. It is assumed that generalised quantifiers like thirty per cent or many or most are functions of two predicates. Indeed, the aforementioned Fregean trick to handle restricted quantification in a one-sorted logic (∀x ∈ M P (x) ≡ ∀x (M (x) ⇒ P (x))) does not apply: as an easy exercise shows, the two sentences below are not equivalent:

(32) Most students go out on Thursday nights.

(33) For most individuals, if they are students then they go out on Thursday nights.

They are classified according to their behaviour with respect to the two predicates: covariant, contravariant, and properties wrt. existential quantification (weakness). Some rules are even provided, but in fine they amount to count how many elements are in the class corresponding to the restriction, in the main predicate itself and in their intersection. The proof rules that are given, at some point, always refers to the intended model, and at this point one can see that they are not proof rules in the ordinary sense. This sometimes leads to inaccurate results. For instance, most is defined as the majority of although their actual usage is quite different: one can assert the first sentence but not the second one in: Indeed, what is clear is that a measure is need but counting is not the only way to measure a set. Otherwise the first sentence would be false, while it appears in an advanced book on number theory, and while anyone knowing some basic maths agrees with such a sentence.

Another problematic point is that the usual vision of (generalised) quantifiers is to consider them as functions of several predicates. The mathematical quantifier are functions of a single predicate: given a predicate P (x) one can form ∀x. P (x). General quantifiers depends on several predicates, usuallly the restriction to a given class and the main predicate. The quantifier Q (some, all, most,...) in a sentence like Q children sleep is supposed, in the common view, to be a function that applies to the predicates children (restriction class) and sleep.

Hence Q children is meaningless in this traditional view. This goes against the syntactic and cognitive structure of language. If a speaker starts a sentence with Q children before he came to the verb, the hearer already has in mind an image of what is Q children with respect to children. This drawback of the common approach is avoided when using Hilbert operators or choice functions. Our argument can be considered as a formal developement of Geach ideas on terms and predicates [START_REF] Thomas | Reference and generality: an examination of some medieval and modern theories[END_REF] 5 Towards rules for some generalised quantifiers With this idea in mind, we started to study quantification from two converging viewpoints. One viewpoint is the interface between syntax and semantics, i.e. how do we map the syntactic structure of a sentence to a logical formula that represents the semantics of the analysed sentence. The other viewpoint is how one handles such formulae: how do we prove and refute them, how do we interpret them?

Regarding the first viewpoint, we advocate for a typed version of Hilbert's generic elements. Consider the following sentences:

(38) Most dogs bite.

(39) Most of the students that passed algebra passed logic.

In those sentences the first restriction class, namely dogs can be viewed as a type, while in the second example the restriction class students that passed algebra is a formula with a unique free variable. The operator we use is a constant in a typed lambda calculus, and actually we have two distinct versions of the operator introducing a most generic element. A first one maps a type to an element in this type (hence the type of the operator is false, but there is no problem to have a constant with this type) and the second ones takes as its argument a predicate over the type student and return a student and adds a presupposition that this student has passed algebra. We propose to do so for all generalise quantifiers, that is to have generic elements corresponding to them, computed from typed Hilbert's style operators. This is a way to compute their semantic representations, but it does not say how they are interpreted (we only provided some hints), not how one argues with such quantifiers. [START_REF] Retoré | Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by "most[END_REF] On this later point, regarding the the majority of quantifier, we thought about what could be rules and refutations for such a quantifier. There are at least two ways to refute that the majority of (meaning at least 50%) the A have the property P :

• Only the minority of the A has the property P • There is another property Q which holds for the majority of the A, with no A satisfying both P and Q.

To add a generalised quantifier to a proof system one should actually introduce a pair of dual quantifiers, a variant ∀ * of ∀ and a variant ∃ * of ∃ Then one has to decide one of the following two possibilities, the first one being unlikely:

• ∀ * x. A(x) implies ∀x. A(x) and so ∃x. A(x) implies ∃ * x. A(x)

• ∃ * x. A(x) implies ∃x. A(x) and so ∀x. A(x) implies ∀ * x. A(x)

In both the cases, one of the two new quantifiers is obtained by extending an existing rule, and the other one oby restricting an existing rule. Although there cannot be complete set of rules, it is likely to find family of rules and refutation techniques that would model a large part of those quantifier's behaviour.

Conclusion

After some critics of the common set theoretic approach, we gave some hints for a proof theoretical approach to quantification. One idea is to use typed versions of Hilbert operator for computing the semantic representations. The other idea is to use principles on proofs and cu-elimination to design the rules of generalised quantifiers.

( 15 )( 17 )

 1517 Not Every Picture Tells a Story[START_REF] Klaus Von Heusinger | Definite descriptions and choice functions[END_REF] No picture tells a story (us) Some Students Do Not Participate In Group Experiments Or Projects.

( 34 )

 34 The majority of French electors voted Hollande in 2012 (35) Most French electors voted Hollande in 2012Indeed, most is a vague quantifier, and as many starts beyond a flexible and context dependent percentage. The fact that the cardinality approach, the usual one, is wrong is proved by the following examples:(36) Most numbers are not prime.(37) Most people have children. (no one can tell whether there is a finite number of them)

  H n ⊢ ∀x. P (x) ∀ e H 1 , . . . , H n ⊢ P (a) • Existential quantifier -The ∃ introduction rule says that whenever a property P holds of an individual a one can infer that there exists an individual enjoying P H 1 , . . . , H n ⊢ P (a) ∃ i H 1 , . . . , H n ⊢ ∃x. P (x) -The ∃ elimination rule is trickier. It says that if assuming P (x) and

nothing more about x we derived C which does not depend on x, and if we have a proof of ∃x. P (x) we can conclude, without the hypothesis P (x) that C: H ′ 1 , . . . , H ′ p ⊢ ∃x. P (x) no free occurrence of x in any H i nor in C P (x), H 1 , . . . , H n ⊢ C ∃ e H ′ 1 , . . . , H ′ p , H 1 , . . . , H n ⊢ C

Unless otherwise stated our examples are from the web. When they are ours, e.g. for phrasing differently an example, we use the mark(us) .

Another problem might be that the quantity a quantifier refers to can be continuous, as in We drank all the wine.

The two quantifiers that are used in mathematics, namely ∀ and ∃ on individuals received a proper logical description, both in syntactical terms with rules (since Aristotle) and in semantical terms with interpretations in models (since the

In first order logic, one can say that the model has less than n elements, but there is not way to say that the model is finite since it requires second order logic