Alexandra P Schneider

Benoit Paoletti

Xavier Ottavy

Christoph Brandstetter

INFLUENCE OF A TURBULENCE CONTROL SCREEN ON THE AERODYNAMIC AND AEROELASTIC BEHAVIOR OF A UHBR FAN

A composite fan stage representative of a modern Ultra High Bypass Ratio (UHBR) architecture has been investigated experimentally on a novel test facility at Ecole Centrale de Lyon.

For these experiments, a turbulence control screen (TCS), a hemisphere, consisting of honeycomb and wiremesh panels, was installed in front of the rig in order to ensure homogeneous, disturbance-free inflow conditions. This kind of screen was developed in the early 1970 years to investigate flight-noise on static test beds. Today, they are commonly used in aero-engine and fan tests, because they improve the accuracy of acoustic measurements and provide more reproducible performance tests.

However, the influence of such screens has been investigated only from an acoustic point of view in the past. This study presents a back-to-back comparison of measurements with and without the TCS, which allows a characterization of the effects on aerodynamic and aeroelastic behavior of the fan stage. The investigation was carried out for multiple stable operating points on two different speed lines to obtain a global image of the influence at part and design speed. The utilization of steady and unsteady instrumentation in different axial and circumferential duct positions allows a detailed analysis of similarities and differences of the configuration without and with the TCS and provides insight into underlying physical mechanisms.

INTRODUCTION

In the early 1970 years it was recognized that the radiated noise of aircraft engine fans shows much higher tonal noise levels (i.e. the amplitudes of the blade passing frequency (BPF) and its higher harmonics in the acoustic spectra are higher) in static tests compared to in-flight tests [START_REF] Cumpsty | The Cause of Tone Generation by Aero-Engine Fans at High Subsonic Tip Speeds and the Effect of Forward Speed[END_REF][START_REF] Feiler | Effects of forward velocity and acoustic treatment on inlet fan noise[END_REF][START_REF] Roundhill | Model and full scale test results relating to fan noise in-flight effects[END_REF]. This leads to the fact that flight noise levels were typically overpredicted when static * Corresponding author: christoph.brandstetter@ec-lyon.fr test beds were used for acoustic characterization of new aircraft engines or fans.

Analytical and experimental studies proved that these higher BPF levels were caused by an interaction of rotor blades with inflow distortions or atmospheric turbulence [START_REF] Filleul | An investigation of axial flow fan noise[END_REF][START_REF] Mani | Noise due to interaction of inlet turbulence with isolated stators and rotors[END_REF][START_REF] Hanson | Spectrum of rotor noise caused by atmospheric turbulence[END_REF][START_REF] Cumpsty | The Cause of Tone Generation by Aero-Engine Fans at High Subsonic Tip Speeds and the Effect of Forward Speed[END_REF][START_REF] Feiler | Effects of forward velocity and acoustic treatment on inlet fan noise[END_REF]. (Unsteady) velocity disturbances cause varying angles of attack when the blades are passing through them. This results in unsteady lift forces, which work as a dipole source and hence radiate random noise [START_REF] Hanson | Spectrum of rotor noise caused by atmospheric turbulence[END_REF]. Under static test conditions velocity disturbances caused by atmospheric turbulence are stretched in the streamwise direction as they are sucked into the engine intake. At the same time they are contracted in the directions perpendicular to the main flow direction forming elongated vortical structures with a length that can exceed multiple rotor diameters. These structures are chopped several times by the rotor blades and are hence quasistationary disturbances in the non-rotating frame of reference i.e. periodic disturbances in the rotating frame of reference. This results in narrow band frequency peaks around the BPF and its higher harmonics [START_REF] Hanson | Spectrum of rotor noise caused by atmospheric turbulence[END_REF][START_REF] Cumpsty | The Cause of Tone Generation by Aero-Engine Fans at High Subsonic Tip Speeds and the Effect of Forward Speed[END_REF][START_REF] Roundhill | Model and full scale test results relating to fan noise in-flight effects[END_REF]. The comparison of in-flight, windtunnel and static tests showed that these disturbances are reduced with forward speed producing BPF peaks with lowered amplitudes under flight conditions [START_REF] Hodder | The effects of forward speed on fan inlet turbulence and its relation to tone noise generation[END_REF][START_REF] Shaw | Inlet turbulence and fan noise measured in an anechoic wind tunnel and statically with an inlet flow control device[END_REF].

In order to reduce the discrepancy between static and inflight acoustic tests several research institutes started to develop so-called turbulence control screens (TCS, or inflow control device, ICD) [START_REF] Cocking | The effect of an inlet flow conditioner on fan distortion tones[END_REF][START_REF] Lowrie | The design and calibration of a distortion reducing screen for fan noise testing[END_REF][START_REF] Shaw | Inlet turbulence and fan noise measured in an anechoic wind tunnel and statically with an inlet flow control device[END_REF][START_REF] Gedge | A design procedure for fan inflow control structures[END_REF][START_REF] Atvars | The development of inflow control devices for improved simulation offlight noise levels during static testing of a HBPR turbofan engine[END_REF]. These structures, typically consisting of honeycomb panels and/or wire-mesh screens, were placed upstream of the fan rotor in form of planar screens [START_REF] Roundhill | Model and full scale test results relating to fan noise in-flight effects[END_REF] or with a hemispherical [START_REF] Lowrie | The design and calibration of a distortion reducing screen for fan noise testing[END_REF][START_REF] Shaw | Inlet turbulence and fan noise measured in an anechoic wind tunnel and statically with an inlet flow control device[END_REF] or geodesic shape [START_REF] Atvars | The development of inflow control devices for improved simulation offlight noise levels during static testing of a HBPR turbofan engine[END_REF] in order to ensure homogeneous inflow conditions. Acoustic and aerodynamic investigations of these structures showed a significant reduction of inflow turbulence intensities and therefore lowered BPF amplitudes and peak widths (especially at subsonic operating conditions) while broadband noise levels stayed nearly unchanged [START_REF] Cumpsty | The Cause of Tone Generation by Aero-Engine Fans at High Subsonic Tip Speeds and the Effect of Forward Speed[END_REF] Accepted manuscript, ?? [START_REF] Roundhill | Model and full scale test results relating to fan noise in-flight effects[END_REF][START_REF] Cocking | The effect of an inlet flow conditioner on fan distortion tones[END_REF][START_REF] Lowrie | The design and calibration of a distortion reducing screen for fan noise testing[END_REF][START_REF] Shaw | Inlet turbulence and fan noise measured in an anechoic wind tunnel and statically with an inlet flow control device[END_REF][START_REF] Gedge | A design procedure for fan inflow control structures[END_REF][START_REF] Atvars | The development of inflow control devices for improved simulation offlight noise levels during static testing of a HBPR turbofan engine[END_REF][START_REF] Woodward | Effect of inflow control on inlet noise of a cut-on fan[END_REF][START_REF] Peracchio | Assessment of inflow control structure effectiveness and design system development[END_REF][START_REF] Preisser | Flight effects on fan noise with static and wind-tunnel comparisons[END_REF][START_REF] Homyak | A compact inflow control device for simulating flight fan noise[END_REF]. This allows to simulate in-flight noise radiation on static test beds which is much less cost intensive than acoustic characterization in fly-over tests. Since these early studies the use of TCS to simulate in-flight noise radiation under static test conditions was accepted and many test facilities for acoustic investigations of fans or aircraft engines are equipped with such structures ( [START_REF] Rademaker | Mode detection with an optimised array in a model turbofan engine intake at varying shaft speeds[END_REF][START_REF] Mueller | Europe's largest aero acoustic test facility for aero engine fans-the development and operation of the anecom aerotest anechoic chamber[END_REF][START_REF] Khaletskiy | Acoustic test facility for aero engine fans[END_REF][START_REF] Schulz | UFFA -Universal Fan Facility for Acoustics, An Enhancement of Europe's Largest Aero Acoustic Test Facility for Aero Engine Fans[END_REF][START_REF] Sturm | Large scale inflow distortions as a source mechanism for discrete frequency sound from 12 Accepted manuscript, ?? isolated axial fans[END_REF][START_REF] Funke | Microphone-array measurements of a Rolls-Royce BR700 series aeroengine in an indoor test-bed and comparison with free-field data[END_REF][START_REF] Behn | Separation of tonal and broadband noise components by cyclostationary analysis of the modal sound field in a low-speed fan test rig[END_REF][START_REF] Caldas | Development and assessment of an inflow control device and a bell-mouth for a low-speed aeroacoustic fan rig[END_REF]). However, in most of the mentioned studies the influence of the TCS is analyzed only from an acoustic point of view. The results of the back-to-back comparisons of the facility with and without TCS presented in literature confirm the findings mentioned above. At subsonic blade tip speeds BPF amplitudes were significantly reduced if the facility is operated with TCS while at supersonic tip Mach numbers the influence of the TCS on the acoustic spectra is small. Broadband noise levels are hardly affected by TCS for all operating conditions [START_REF] Schulz | UFFA -Universal Fan Facility for Acoustics, An Enhancement of Europe's Largest Aero Acoustic Test Facility for Aero Engine Fans[END_REF][START_REF] Köhler | The Influence of the TCS on the Circumferential Mode Distribution in the Inlet of a Fanrig (UFFA)[END_REF][START_REF] Sturm | Large scale inflow distortions as a source mechanism for discrete frequency sound from 12 Accepted manuscript, ?? isolated axial fans[END_REF][START_REF] Caldas | Development and assessment of an inflow control device and a bell-mouth for a low-speed aeroacoustic fan rig[END_REF][START_REF] Grizewski | Cyclostationary Analysis of Fan Noise Influenced by an Inflow Control Device[END_REF]. In addition, novel mode decomposition methods yield that no additional propagating modes were introduced due to the use of TCS and that cut-on modes can be stabilized (i.e. they are more prominent in the spectra) through TCS [START_REF] Caldas | Development and assessment of an inflow control device and a bell-mouth for a low-speed aeroacoustic fan rig[END_REF][START_REF] Grizewski | Cyclostationary Analysis of Fan Noise Influenced by an Inflow Control Device[END_REF]. Besides a detailed acoustic characterization Caldas et al. [START_REF] Caldas | Development and assessment of an inflow control device and a bell-mouth for a low-speed aeroacoustic fan rig[END_REF] investigated the flowfield upstream of the rotor via hot-wire anemometry. They found a reduction of the averaged turbulence intensity from 1.8% to 0.3% as well as lower fluctuation of the axial velocity over the channel height if the TCS is used in the experiments. A decomposition of turbulence intensity levels into different frequencies is not presented. There is lack in literature about the influence of a TCS on the flowfield in the rotor plane and on the mechanical behavior of the rotor. In the case of slender, lightweight composite rotor blades this information is crucial due to the high sensitivity of the blades to changes in aerodynamics. Especially near the stability limit the susceptibility to blade vibrations rises and small inflow disturbances can trigger safety-critical vibration amplitudes or the onset of rotating stall if they interact with the rotor blades.

At the test facility ECL-B3 at Ecole Centrale de Lyon (ECL), used for investigations of UHBR fan stages, a hemispherical TCS is usually installed in front of the intake for acoustic and performance measurements. According to established procedures at ECL, operability measurements are usually conducted without TCS. In order to make results of both configurations comparable to each other and provide information for design of experiments (DoE) procedures for future measurement campaigns, it is necessary to study the influence of the TCS in detail. Salze et al. [START_REF] Salze | New modular fan rig for advanced aeroacoustic tests-Acoustic characterization of the facility[END_REF] already analyzed acoustic spectra from measurements with and without TCS. These measurements have been carried out within the project ENOVAL at the test facility ECL-B3 (see also [START_REF] Rodrigues | Aerodynamic investigation of a composite lowspeed fan for UHBR application[END_REF]) and allowed the validation of TCS for acoustic experiments.

Based on that, this study presents a more detailed back-toback comparison of both configurations to allow a characterization of the influence of the TCS on the aerodynamic and aeroe-lastic behavior of the fan stage. It is analyzed if higher inflow disturbances, which appear without TCS, result in a higher instationarity of the flow field and hence higher fluctuations of aerodynamic flow features like the shock at transonic operating conditions. Besides that, the study focuses on the effect of the TCS on the stable operating range i.e. the influence on stall onset and potentially safety-critical synchronous and non-synchronous blade vibrations.

In order to overcome the lack of information in literature concerning the effect of a TCS on characteristic flow features such as broadband turbulence, inflow distortion and mechanical behavior of the rotor, this study aims to provide more insight in the aerodynamic and aeroelastic influence of a TCS. Therefore this paper is structured as follows:

• The experimental setup is introduced including the different probe positions used within this study. The overall fan performance is shown for two investigated speedlines.

• The inflow conditions of the rotor stage are characterized for both measurement configurations.

• At design speed the influence of the TCS on rotor steady and unsteady aerodynamics is discussed for different operating conditions. Furthermore the effect on structure mechanics and the aeroelastic coupling between rotor flow and blade vibrations is analyzed in detail.

• The results of the design speed line are completed by the analysis of blade tip flow and related blade vibrations at part speed in order to obtain global trends for the whole operating range.

TEST FACILITY ECL-B3

The test facility ECL-B3 was designed and built in cooperation between ECL and Safran Aircraft Engines through the ANR-EQUIPEX program. It is used for investigations of fan architectures representative of modern UHBR stages at scales around 1:4. The stage investigated within this study consists of a composite, low speed transonic fan and Outlet Guide Vanes (OGV), designed by Safran AE. The latter have been designed specifically for this rig in order to provide the rotor with representative exit conditions without separation of core and bypass stream.

Setup

The ECL-B3 test rig presented in Fig. 1 was built to enable highly accurate aerodynamic and acoustic characterization of the vehicle, such as the modern UHBR fan rotor used for the studies in this paper. The test vehicle is placed in an anechoic chamber, acoustically isolated from the machine room, which hosts a 3MW electric motor allowing a rotational speed of up to 16000rpm. A torquemeter is mounted between the fan shaft and the gearbox shaft enabling an accurate measurement of the applied power. The rig is operated in an open cycle, thus air is sucked in through traversing rows of silencers on the roof before it enters the core section. Subsequently the air flows into an axisymmetric coned shaped throttle controlling the massflow before exiting through an exhaust system and a final row of silencers to atmosphere. The Venturi nozzle within the 25 m long circular pipe of the exhaust system allows precise massflow measurements.

FIGURE 1: SCHEMATIC VIEW OF ECL-B3 TEST FACILITY

To ensure homogeneous, disturbance-free inflow conditions a Turbulence Control Screen (TCS) is installed in front of the core section for acoustic and performance measurements. This sphere with a diameter of about 2 m consist of wiremesh and honeycomb panels in order to reduce the incoming turbulence and inflow distortions (Fig. 2).

TCS FIGURE 2: ECL-B3 TEST FACILITY WITH TURBULENCE CONTROL

SCREEN

The main parameters of the investigated fan stage are summarized in Table 1.

Test procedure

The ENOVAL aerodynamic test campaign consisted in two maneuvers: the fan mapping measurements, with full traversals of the stage exit plane at stable operating conditions, and the operability measurements during which the machine was throttled towards the stability limit. The latter will be investigated in detail within this study.

To characterize the influence of the TCS, measurements with the sphere in front of the facility (screen configuration) will be compared to measurements without it (open configuration). Several stable operating points at two different speedlines are used for this back-to-back comparison.

Instrumentation + WPT

FIGURE 3: SCHEMATIC VIEW OF THE MACHINE CORE AND PROBE

POSITIONS

The machine core schematized in Fig. 3 was designed in a modular fashion granting a time-efficient and flexible change of test configuration. It also facilitates the application of instrumentation, as multiple accesses are available for traversable instrumentation around the circumference. The acquisition system allows more than 800 signals to be recorded simultaneously. The machine core is instrumented with pressure and temperature sensors as well as microphones distributed from the bellmouth shaped intake to the throttle mechanism at various meridian positions, on the hub and casing.

Besides flush-mounted static pressure probes, miniature high frequency response wall pressure transducers (WPT) are placed in various axial and circumferential positions in order to observe unsteady aerodynamics in the machine. The measurement of structural vibrations was implemented through blademounted strain gauges on the rotor, transferred via telemetry (see [START_REF] Brandstetter | Project PHARE-2-A High-Speed UHBR Fan Test Facility for a New Open-Test Case[END_REF] for details). The fan performance map shown in Fig. 4 is obtained by reducing the massflow through different settings of the outlet throttle for two different speed lines. As mentioned above, this procedure leads to slightly differing operating conditions (shifted massflows) between both configurations. In order to enable a better classification of the investigated operating points of the operability measurements, those of the fan mapping measurements (for the configuration with the TCS) are shown in Fig. 4 as well (unfilled black dots).

In Fig. 4 it is visible, that the characteristics for both configurations show a similar total pressure ratio over a wide range of massflow. In addition, the stall margin is nearly identical for both configurations for the shown part and design speed line.

As indicated by the marked operating points in Fig. 4, four approximately equally spaced operating points of the operability measurements will be used for a detailed comparison of the screen and the open configuration at design speed in section DE-SIGN SPEED. For the analysis of the part speed behavior three operating points OP PS1 to OP PS3 will be discussed in section PART SPEED. Before this detailed investigation of different operating points, the inflow conditions will be characterized for both configurations in the following section. For this characterization the operating point OP DS1 and an operating point with a rotational speed near design speed will be used.

INFLOW CONDITIONS

Based on the literature cited in the introduction above, it is assumed that inflow inhomogeneity and unsteadiness are reduced, if the TCS is installed in front of the facility. In order to analyze the influence of the TCS on the inflow conditions of the fan stage, static pressure probes and WPTs upstream of the rotor plane (see Fig. 3) are used in this section to characterize the flow field in this region.

The unsteadiness of the flow field upstream of the rotor can be analyzed by regarding the static pressure time fluctuations (pressure at a given sensor position p s,i minus time average indicated by (•) over the whole measurement time), normalized with the dynamic inlet pressure

∆p rel,i = ∆p s,i p dyn,i = p s,i -p s,i p t,in -p s,i (1)
of static pressure probes in varying circumferential positions i in the stage intake (see Fig. 5). For the comparison of both conopen screen These structures can therefore be assumed to be quasistationary in the non-rotating frame of reference and can be considered as a slow and homogeneous variation of the fan operating conditions. For the screen configuration static pressure fluctuations are within about 0.1 %p dyn significantly lower as for the open configuration. This indicates a strong reduction of the global unsteadiness of the flow field due to the TCS.

To investigate the inhomogeneity (circumferential asymmetry) of the flow field upstream of the rotor, Fig. 6 presents the circumferential profile of the static pressure for both configurations (0 • corresponds to the 12h position). This graph shows the local temporal average of the wall pressure p (θ ), recorded at stable operating conditions using sensors traversed around the circumference and normalized with the dynamic pressure ( (•) here indicates an average over all circumferential positions):

p θ = p (θ ) -p (θ ) p t,in -p (θ ) (2)
circ. position

[%] From Fig. 6 it is evident that the static pressure varies about ±2.5 %p dyn around the circumference for the open configuration. If the TCS is installed, this variation is reduced to about ±1 %p dyn , which leads to a more homogeneous inflow. Besides that, it is remarkable that the static pressure distribution for the screen configuration resembles a sinusoidal signal, whereas it is more complex in the case of the open configuration. While the sinusoidal pattern corresponds to a circumferential mode order of one, the strong pressure gradient in the pattern of the open configuration is realized through a superposition of different, higher mode orders. This relation becomes even more obvious by regarding Fig. 7, which shows the spatial Fourier Transformation (FT) of the circumferential pressure profiles p θ presented in Fig. 6. It is clearly visible that the circumferential pressure distribution of the screen configuration contains mainly a single mode order. In contrast, the FT of the open configuration depicts a composition of the pressure profile of mode order 1 and 2 with nearly equal amplitudes as well as higher mode orders with lower amplitudes.

This proves that the TCS reduces not only the unsteadiness of the inflow, but also the circumferential inhomogeneity. The remaining circumferential asymmetry with mode order 1, which is present even if the TCS is installed, can be explained by the geometry of the facility chamber. As stated in the SETUP section, air is sucked in from the roof what results in a quasi-stationary, non-uniform flow field upstream of the stage intake. This nonuniformity is smoothed through the TCS but can not be completely homogenized. In addition to the global unsteadiness of the flow field, analyzed in Fig. 5, the local unsteadiness (i.e. local, temporal fluctuations of the unsteady pressure, which is calculated by subtracting an ensemble average of 10 rotor revolutions, see eq. ( 1) in [START_REF] Brandstetter | Project PHARE-2-A High-Speed UHBR Fan Test Facility for a New Open-Test Case[END_REF]) can be characterized by the standard deviation

σ θ = σ p unsteady (t) (θ ) p t,in -p (θ ) (3)
of the unsteady pressure p unsteady (t). Fig. 8 shows this parameter, normalized with the dynamic pressure, depending on the circumferential position for both configurations. It becomes visible that the local unsteadiness for the open configuration fluctuates between 4 % and 6.2 % around the circumference. In contrast to that, it varies only marginally between 2.8 % and 3.3 % for the screen configuration. This results in higher spatial gradients and an increased average unsteadiness over the whole circumference in the open case. Thus, the local flow unsteadiness strongly varies without application of the TCS. The figures presented in this section highlight the differences in inflow conditions between the configurations with and without TCS. Confirming results from literature, the TCS reduces global and local, temporal and spatial pressure fluctuations and gradients and therefore ensures a more homogeneous flow field upstream of the rotor.

DESIGN SPEED

In this section the effect of the different inflow conditions, which have been identified in the previous section, on aerodynamic and aeroelastic properties will be investigated in detail at four stationary operating points (as presented in Fig. 4) at the design speedline.

Ensemble averaged flow structure

The flow field in the rotor tip region can be visualized by using the axial WPT array above the rotor blades (Fig. 9a)), which is located at a circumferential positon of 336 • (indicated in Fig. 6). This means that Fig. 9a) represent the flow field, which is observed by a sensor at a distinct circumferential position during the time of one rotor revolution and not the circumferential pattern at a given point in time. The presented flow fields are obtained by ensemble averaging the signal of each sensor over 100 rotor revolutions and are shown for the screen configuration. Shocks are clearly visible for all operating points in Fig. 9a) due to a sharp pressure rise upstream of the LE. This shock results from transonic flow over the blade's suction side in the rotor tip region and indicates transonic operating conditions at design speed. The reduction in massflow from OP DS1 to OP DS4 leads to lower axial velocities and in consequence to a reduced relative suction side velocity. Hence, shock strength is decreased from OP DS1 to OP DS4 . In addition, the shock is shifted upstream i.e. away from the LE, when the back pressure rises due to closing of the outlet throttle. The flow pattern becomes highly asymmetric around the circumference (in the rotating frame of reference) at throttled operating points. While the flow field is nearly identical urations at the blade tip is enabled by Fig. 10, which shows the signal of the WPT directly upstream of the LE for OP DS2 , OP DS3 and OP DS4 . OP DS1 is similar to OP DS2 and omitted for brevity.

According to the results presented in Fig. 9a), the signal has been ensemble averaged over 100 rotor revolutions in order to remove temporal fluctuations. Thus, Fig. 10 visualizes the ensemble averaged shock position and strength of the 16 channels.

DS2 DS3 DS4

FIGURE 10: EVOLUTION OF THE ENSEMBLE AVERAGED FLOW ASYMMETRY WITH ROTOR THROTTLING AT DESIGN SPEED (WPT IN AXIAL ARRAY UPSTREAM OF LE USED)

Fig. 10 confirms that the shock is shifted upstream and the shock strength is reduced if the rotor is throttled. These trends can be observed for both configurations and the shock position in the passage is nearly identical in both cases at all presented operating points. At the unthrottled operating point OP DS2 the shock position and strength is highly symmetric around the circumference. The detailed comparison of both configurations reveals slightly lower shock strengths for the open configuration compared to the screen configuration at this operating point. If the massflow is reduced from OP DS2 to OP DS3 , a distinct asymmetry pattern evolves, which results in strongly varying shock strength around the circumference. Comparing the signals of the open configuration to these of the screen configuration, a strong difference in channel 15 can be noticed. For the open configuration the shock strength of this channel is only marginally reduced due to rotor throttling, whereas it significantly decreases in the screen case. In addition, the overall asymmetry is slightly weaker for the open configuration at OP DS3 , i.e. the difference between strong and weak shocks is smaller than for the screen configuration (the standard deviation is reduced by about 3%). A further reduction in massflow to OP DS4 leads to a change in absolute shock strength, but has no influence on the asymmetry pattern. This means that the channels with a reduced shock strength are identical for OP DS3 and OP DS4 and that the discrepancy of shock strength in channel 15 between both configurations remains high. Besides that, only minor differences between open and screen asymmetry pattern are visible at OP DS4 , which are negligible compared to differences in shock strength around the circumference. Thus, it is concluded that the TCS has, apart from channel 15, no influence on the observed asymmetry pattern and that this pattern is a rotor characteristic and stationary in the rotating frame of reference. Wilson et al. [START_REF] Wilson | The effect of stagger variability in gas turbine fan assemblies[END_REF] and Lu et al. [START_REF] Lu | Effect of geometry variability on transonic fan blade untwist[END_REF] describe blade untwist as responsible for inhomogeneous shock patterns at unloaded conditions, but near the stability limit, the presented resolution of the flow field has not been reported in literature and seems to be specific for low-speed composite fans. In a previous study at the same test facility but with a different rotor, Brandstetter et al. [START_REF] Brandstetter | Compressible modal instability onset in an aerodynamically mistuned transonic fan[END_REF] have shown that the fan assembly developed an asymmetric shock pattern in a similar way, which correlated with the geometry variability of the blades, but assumed, that started flow conditions are prevalent in individual blades. The results presented here show that all shocks remain detached from the leading edge. It is intended to use Tip Timing data in future studies to correlate shock position and fluctuation with actual stagger angles of individual blades.

Acoustic facility resonance

In the study mentioned above, it was also found that the asymmetry in the circumferential shock pattern interacts with a planar acoustic mode, which evolves in the exhaust system of the facility for all transonic operating conditions near the stability limit (see sketch in Fig. 11a)). For the fan analyzed in [START_REF] Brandstetter | Compressible modal instability onset in an aerodynamically mistuned transonic fan[END_REF] modal oscillations started to rise some hundred revolutions before rotating stall occurred. An amplification between asymmetric shock pattern and acoustic mode resulted in the initiation of a single stall cell and thus limited the stable operating range. The frequency of this mode is around 14 Hz for all operating To analyze the occurrence of the 14 Hz acoustic mode, a WPT in the stage intake has been used. Fig. 11b) shows the amplitude of the 14 Hz pressure fluctuation over the massflow range of operability measurements for both configurations. The graph has been obtained by performing a FFT with a Hanning-Window with a window size of 120 rotor revolutions (frequency resolution ≈ 1 Hz) and averaging the 14 Hz amplitude over all windows for each operating point individually.

In contrast to the study by Brandstetter et al. [START_REF] Brandstetter | Compressible modal instability onset in an aerodynamically mistuned transonic fan[END_REF], who investigated a fan with a higher tip speed, it can be seen in Fig. 11b) that the acoustic mode develops for both configurations only for intermediate massflows slightly lower than design massflow. At higher and at lower massflow rates amplitudes diminish rapidly and thus the acoustic mode does not influence the stability limit for the rotor investigated here.

The comparison of open and screen configuration reveals a shift of maximum 14 Hz amplitude to lower massflows, if the TCS is not installed in front of the facility. It is remarkable that the maximum reached amplitude is nearly identical for both configurations. Hence, the TCS affects the onset of the acoustic ductmode, shifting it towards higher massflow but the maximum amplitude remains constant.

Unsteady aerodynamics

The unsteady aerodynamics of the blade tip flow i.e. the frequency content of the flow field in this region, can be investigated by regarding spectra of the WPT above the LE in Fig. 12. The presented mean spectra are obtained by normalizing the raw pressure signal with the total pressure at the stage intake, calculating a FFT with a Hanning-window with a window size of 40 rotor revolutions and averaging all windows for each operating point respectively. In order to isolate non-synchronous pressure fluctuations an ensemble average of 20 revolutions is subtracted from the signal before the FFT is calculated. The spectra for OP DS1 are not shown here, because they are nearly identical for both configurations and no remarkable peaks are visible. Corresponding to Fig. 11, a peak at 14 Hz (< EO 0.1) is visible for the screen configuration in the spectrum of OP DS2 and for the open configuration at OP DS3 respectively. Due to a modulation of this frequency at the rotor blades, strong peaks around the BPF are visible for the configuration, for which the 14 Hz peak is observed. In addition, scattering of the acoustic mode causes sidebands around the BPF with distances of multiple integer EO (see [START_REF] Brandstetter | Interpretation of stall precursor signatures[END_REF] for details). Besides these differences at OP DS2 and OP DS3 related to the acoustic mode, it is noticed that noise levels are identical for both configurations. This similarity can be observed at the highly throttled operating point OP DS4 as well. The reduction in massflow from OP DS2 to OP DS4 results in rising noise levels and in the formation of a broadband hump around EO 8. This broadband hump denotes the presence of convective disturbances as described by Rodrigues et al. [START_REF] Rodrigues | Aerodynamic investigation of a composite lowspeed fan for UHBR application[END_REF] and Brandstetter et al. [START_REF] Brandstetter | Interpretation of stall precursor signatures[END_REF].

Aeroelastic behavior

The mechanical behavior of the rotor blades at different operating points can be analyzed by regarding the spectra of a representative blade mounted strain gauge shown in Fig. 13. The spectra have been calculated using the same parameters as the WPT spectra presented in Fig. 12 and are normalized with the maximum amplitude of the screen configuration at OP DS4 . In contrast to the spectra shown above, the ensemble average was not subtracted here. This allows a comparison of synchronous vibration amplitudes in addition to the analysis of non-synchronous vibrational frequencies. In Fig. 13 the broadband vibration levels as well as the eigenmode vibration amplitudes differ only slightly between both configurations at the shown operating points. In contrast to that the strain gauge spectra show significantly higher vibration amplitudes at integer engine orders below EO 7 for the open configuration. These strong blade vibrations with low integer EO frequencies can be explained by the observed differences in inflow conditions in Fig. 6 and7. As described in the previous section, the static pressure profile upstream of the rotor is strongly asymmetric around the circumference and con-DS2 DS3 DS4 sists of several mode orders for the open configuration. These mode orders are fixed in the non-rotating frame of reference and represent therefore a periodic disturbance in the rotating frame of reference. Thus, they force the rotor blades to vibrate with frequencies, which are integer multiples of the rotor speed Ω S r . At the last stable operating point OP DS4 the amplitudes of these synchronous vibrations, especially those with a frequency of EO 1, are of the same order of magnitude as the amplitudes of the first eigenmode. This indicates that the synchronous vibrations are not at all negligible. In the screen configuration the circumferential asymmetry i.e. the inflow inhomogeneity of the static pressure profile is strongly reduced, resulting in a strong reduction of synchronous vibration amplitudes of nearly all EO frequencies below EO 7. Besides these differences the comparison of the strain gauge spectra for both configurations at OP DS3 depicts a peak at 14 Hz for the open configuration. This vibration is attributed to the occurrence of the planar acoustic mode for the measurement without TCS at this operating point. As observed above, this mode is not present at the representative operating point for the screen configuration. In contrast to that, at OP DS2 a 14 Hz peak should be present in the strain gauge spectrum for the screen configuration, as the acoustic duct mode is clearly visible in the corresponding WPT spectrum. But due to the lower amplitude of the 14 Hz pressure fluctuation compared to the open configuration at OP DS3 , the corresponding vibration amplitude is lower as well and is hidden between broadband vibration below EO 0.5.

The rising amplitudes of the third eigenmode can be explained by comparing the strain gauge spectra in Fig. 13 to the WPT spectra in Fig. 12. Within the mentioned broadband hump around EO 8, which is visible at OP DS4 in the WPT spectra of both configurations, distinct frequency peaks at EO 7.2 and EO 8.8 establish. These peaks indicate the presence of convective disturbances with nearly constant propagation speed in the stationary frame of reference, which is determined by the aerodynamics of the mean flow [START_REF] Brandstetter | Interpretation of stall precursor signatures[END_REF]. Rodrigues et al. [START_REF] Rodrigues | Aerodynamic investigation of a composite lowspeed fan for UHBR application[END_REF] have shown that it lies within 55 and 60 % of the rotational speed for the fan investigated here, what corresponds to a propagation velocity of

Ω R a Ω S r = Ω S a Ω S r -1 = -0.4 to -0.45 (4)
Accepted manuscript, ??

in the rotating frame of reference. When the rotor is throttled towards the stability limit, a lock-in of these convective disturbances with the structural eigenmode with the eigenfrequency ω v,lock = 4.8 in the rotating frame of reference occurs. Due to the lock-in the global propagation speed Ω R a is slightly adjusted, so that the resonance condition

ω v,lock = ω a,lock = N a Ω R a,lock (5)
is fulfilled with an integer aerodynamic wave number of N a = -12. The necessity of matching inter-blade phase angles of the aerodynamic wave ϕ a and the vibration pattern

ϕ v ϕ v = ϕ a -→ N v ≡ N a (mod N b ) (6)
results in an aliased structural nodal diameter equal to N v = 4, because N a is greater than 0.5 • N b , where N b is the number of rotor blades [START_REF] Stapelfeldt | Non-synchronous vibration in axial compressors: Lock-in mechanism and semianalytical model[END_REF].

From Fig. 13 it is evident that vibrations in the third eigenmode can already be observed at O DS2 and OP DS3 for both configurations, but with lower amplitude as at OP DS4 . To compare the evolution of NSV for both configurations quantitatively, Fig. 14 shows the amplitudes of the structural vibration and the corresponding pressure fluctuation amplitudes depending on the massflow for all operating points of the operability measurements. In Fig. 14 the amplitudes of the pressure fluctuations with EO 8.8 (and EO 7.2 respectively) start to rise at higher massflows than the amplitudes of the third eigenmode vibration for both configurations. This confirms the findings in Brandstetter et al. [START_REF] Brandstetter | Measurements of Radial Vortices, Spill Forward, and Vortex Breakdown in a Transonic Compressor[END_REF], where small vortical disturbances are detected long before the stability limit is reached. They travel around the circumference until a lock-in with a blade eigenfrequency occurs and vibration amplitudes start to rise. The comparison of both configurations shows slightly higher pressure fluctuation amplitudes at all operating points for the screen configuration and as well slightly higher vibration amplitudes at the two operating points with the lowest massflow. This indicates a reduced NSV amplitude for the open configuration, however, the graphs presented in Fig. 14 show that the evolution over massflow is comparable. Further studies will be necessary to clarify, if steady inflow inhomogeneity reduces the tendency towards NSV. In addition, this similarity of NSV behavior between both configurations proves that synchronous and non-synchronous vibrations are linearly superimposed and do not influence each other in the presented measurement setup. This is yet challenging for experiment conduction, as real-time mode decomposition is necessary for surveillance measurements to distinguish between eigenmode vibration and synchronous vibration. The investigations described above revealed differences as well as similarities between both configurations at design speed. The similarities concerning asymmetric shock pattern around the circumference, unsteady aerodynamics at the blade tip and NSV confirm a negligible influence of the TCS on these phenomena. In contrast to that, strong inhomogeneity in inflow conditions forces the rotor blade to vibrate with low integer EO frequencies in the open configuration, which can not be neglected as they occur at the same amplitude level as critical non-synchronous vibrations.

PART SPEED

In this section a selection of the investigations presented above are conducted for the part speed line, in order to characterize the influence of the TCS is this regime and provide a more global picture.

As described above, Fig. 9b) visualizes the ensemble averaged part speed flow field above the blades for the screen configuration, where the rotor works subsonic. In accordance to design speed line findings, reducing the massflow leads to a reduction of the axial velocity, which can be seen in a smaller low pressure region near the LE at OP PS3 compared to OP PS2 and OP PS1 . In contrast to the design speed operating points, the circumferential asymmetry at throttled operating points is much weaker at part speed. Thus, differences between screen and open configuration are even smaller at this rotational speed and it is concluded that the TCS has no influence on the ensemble averaged blade tip flow field at the respective circumferential sensor position ( 336 • ).

In order to analyze unsteady aerodynamics, Fig. 15 presents the spectrum of the WPT above the LE for the configurations with and without TCS at OP PS2 , which is representative for the whole part speed line. The mean spectra are calculated in the same way as those for design speed and the ensemble average has been subtracted. In Fig. 15 marginal differences in broadband noise level for both configurations are observed. Significant differences are only visible in the low frequency range and around the BPF (the BPF peak itself is not visible due to subtraction of the ensemble average). The peak in the low frequency range below EO 0.1, which is only visible for the open configuration, has a higher peak width as the 14 Hz peak at design speed. This indicates that this peak is related to a broadband, low frequency disturbance. The frequency peak around the BPF has the same amplitude as the low frequency peak for the open configuration and is caused by a modulation of the low frequency disturbance at the rotor blades. To further investigate this phenomenon, enhanced flow field measurements in the upstream region, combined with Particle Image Velocimetry (PIV) measurements in the rotor section are envisaged for future investigations. As already mentioned above, the spectra of OP PS2 are representative for the part speed line, i.e. the phenomena observed here, are present at OP PS1 and OP PS3 as well.

To compare the mechanical behavior of the rotor blades at part speed, Fig. 16 shows the mean spectra of one representative blade mounted strain gauge (the same which has been used for design speed) at OP PS2 , calculated with the same parameters as for design speed. As above, and in contrast to the WPT spectra, the ensemble average has not been subtracted here. The spectra in Fig. 16 show identical broadband vibration amplitudes over the whole frequency range as well as nearly identical peak amplitudes for the eigenmodes. In contrast to this similarity, Fig. 16 reveals significantly higher integer EO vibration amplitudes for the open configuration below EO 7, which again can be explained with the different inflow conditions in both cases. Thus, these observations fit perfectly to those in the design speed section and confirm a global characterization of the influence of the TCS over the whole operating range.

CONCLUSION

In the presented study, the influence of a TCS on the aerodynamic and aeroelastic behavior of a modern composite low-speed UHBR fan stage has been investigated experimentally. In order to characterize the underlying physical phenomena a back-toback comparison of measurements with and without TCS at different operating points at two different speed lines is presented. The comparison of inflow conditions for both configurations revealed significant differences concerning circumferential inhomogeneity and unsteadiness of the flow field upstream of the rotor. For the open configuration the static pressure profile around the circumference in the stage intake is composed of different circumferential mode orders while it has a pure sinusoidal shape with mode order 1 in the case of the screen configuration. The interaction of this asymmetric pressure profile with the rotor results in strong synchronous vibrations at all investigated operating points at design and part speed. In the screen case inflow conditions are more homogeneous and synchronous vibration amplitudes are significantly reduced.

Besides this remarkable difference, the investigation showed a negligible influence of the TCS on steady and unsteady aerodynamics in the blade tip region including aerodynamic flow features like shock strength and distribution. The aeroelastic behavior of the rotor blades at non-synchronous vibrational frequencies was found to be in good agreement for both configurations, too. It is remarkable that NSV, which is the stability limiting phenomenon, develops for both configurations in the same way and is linearly superimposed to synchronous vibrations in the presented setup. This results in a comparable stable operating range of both configurations.

The detailed aerodynamic and aeroelastic characterization of the influence of the TCS presented in this study provides insight into physical mechanisms and complements the acoustic investigations, which had been carried out in the past. Therefore it closes the gap of knowledge in literature concerning aerodynamic and aeroelastic effects of a TCS and serves as a basis for the design of experiments for future measurement campaigns.

ACKNOWLEDGMENT

The presented research was supported through the European Union's Seventh Framework Programme for research, technological development and demonstration, ENOVAL, grant agreement N604999

FIGURE 4 :

 4 FIGURE 4: FAN PERFORMANCE MAP AND INVESTIGATED OPER-ATING POINTS

FIGURE 5 :

 5 FIGURE 5: TEMPORAL STATIC PRESSURE FLUCTUATION IN STAGE INTAKE AT OP DS1 (DESIGN SPEED) FOR 12 CIRCUMFERENTIALLY DISTRIBUTED SENSORS, FLUCTUATION REPRESENTATIVE FOR ALL STUDIES OPERATING POINTS figurations the signals for operating point OP DS1 during a measurement time of one minute (sampling frequency = 5 Hz) are used. These curves are qualitativly representative for all operating points at design and part speed. Fig. 5 shows static pressure fluctuations of up to 0.6 % of the dynamic inlet pressure for the open configuration. These fluctuations are related to large scale, aerodynamic fluctuations with characteristic timescales, resulting in circumferentially coherent variations of the static pressure.These structures can therefore be assumed to be quasistationary in the non-rotating frame of reference and can be considered as a slow and homogeneous variation of the fan operating conditions. For the screen configuration static pressure fluctuations are within about 0.1 %p dyn significantly lower as for the open configuration. This indicates a strong reduction of the global unsteadiness of the flow field due to the TCS.

FIGURE 6 :

 6 FIGURE 6: FLUCTUATION OF LOCAL TEMPORAL AVERAGE OF WALL PRESSURE FROM TRAVERSED WPTS UPSTREAM OF ROTOR PLANE NEAR DESIGN SPEED

FIGURE 7 :

 7 FIGURE 7: MODE DECOMPOSITION OF STATIC PRESSURE DISTRI-BUTION p θ UPSTREAM OF ROTOR PLANE NEAR DESIGN SPEED

Fig. 6

 6 and 8 indicate that the local turbulence level and the local average flow conditions, at which the fan operates around the circumference are inhomogeneous for the open configuration. This clearly explains increased tonal noise emissions, as it has been observed by Salze et al. [27], due to unsteady loading. The results from Fig. 5 additionally indicate a slowly fluctuating operating condition of the fan in the open case.

FIGURE 8 :

 8 FIGURE 8: LOCAL, TEMPORAL STATIC PRESSURE FLUCTUATIONS σ θ UPSTREAM OF ROTOR PLANE NEAR DESIGN SPEED

2 FIGURE 9 :

 29 FIGURE 9: ENSEMBLE AVERAGED FLOW FIELD AT ROTOR TIP (FROM AXIAL WPT ARRAY AT 336 • ) FOR THE SCREEN CONFIGURA-TION: a) DESIGN SPEED; b) PART SPEED

FIGURE 11 :

 11 FIGURE 11: AMPLITUDE OF PLANAR ACOUSTIC DUCT MODE (14 HZ) OVER MASSFLOW

FIGURE 12 :FIGURE 13 :

 1213 FIGURE 12: SPECTRA OF WPT ABOVE LE AT DIFFERENT OPERATING POINTS AT DESIGN SPEED, ENSEMBLE AVERAGE SUBTRACTED

FIGURE 15 :

 15 FIGURE 15: SPECTRA OF WPT ABOVE LE AT OP PS2 (PART SPEED), ENSEMBLE AVERAGE SUBTRACTED

3 FIGURE 16 :

 316 FIGURE 16: SPECTRA OF REPRESENTATIVE BLADE MOUNTED STRAIN GAUGE OP PS2 (PART SPEED)

TABLE 1 :

 1 MAIN PARAMETERS OF UHBR FAN STAGE

	Outer casing diameter	508 mm (20")
	Rotor number of blades	16
	Stator number of blades	36
	Design Blade Tip Speed	280-340 m/s
	Design Tip gap size	∼ 0.8% tip chord

  the Clean Sky 2 Joint Undertaking (JU) under grant agreement N864719, CATANA. The JU receives support from the European Union's Horizon 2020 research and innovation programme and the Clean Sky 2 JU members other than the Union. The paper reflects only the author's view and the JU is not responsible for any use that may be made of the information it contains. Assessment of the test facility was enabled through financial supports of Agence Nationale de la Recherche (ANR, Project d'EqupEx PHARE) and Conseil pour la Recherche Aeronautique Civile (CORAC -Programme CUMIN). Buildings and infrastructure were supported by ECL, instrumentation supported by Institut Carnot (INGENIERIE@LYON -Project MERIT). We are grateful for the continuous collaboration and financial support of SAFRAN AE since the beginning of this project and specifically for the present measurement campaign. The authors would like to particularly acknowledge the precious contributions of Gilbert Halter, Lionel Pierrard, Pierre Laucher and Sebastien Goguey.

	NOMENCLATURE
	BPF	Blade Passing Frequency
	DS	Design Speed
	ECL	Ecole Centrale de Lyon
	EO	Engine Order
	FFT, FT (Fast) Fourier Transformation
	ICD	Inflow Control Device
	JU	Joint Undertaking
	ṁ	massflow
	N a	aerodynamic wave number (circumferential mode order)
	N v	structural Nodal Diameter
	N b	number of rotor blades
	NSV	Non Synchronous Vibrations
	LE	Leading Edge
	OP	Operating Point
	p	pressure
	PIV	Particle Image Velocimetry
	PS	Part Speed
	SAE	SAFRAN Aircraft Engines
	TCS	Turbulence Control Screen
	TE	Trailing Edge
	WPT	Wall Pressure Transducer
	θ	circumferential position
	Π t	Total Pressure Ratio
	σ	standard deviation
	ϕ	inter-blade phase angle
	Ω S r	angular velocity of the rotor
	Ω S a	propagation velocity of convective disturbance
	ω S a	angular frequency of pressure fluctuation
	ω R v	angular vibration frequency

11

Accepted manuscript, ??

and

Accepted manuscript, ??

The presented research was supported through the European Union's Seventh Framework Programme for Research, technological development and demonstration ENOVAL, grant agreement N604999 and the Clean Sky 2 Joint Undertaking (JU) under grant agreement N864719, CATANA. The JU receives support from the European Union's Horizon 2020 research and innovation programme and the Clean Sky 2 JU members other than the Union. This publication reflects only the author's view and the JU is not responsible for any use that may be made of the information it contains. catana.ec-lyon.fr christoph.brandstetter@ec-lyon.fr


Mathieu D'aquin
email: m.daquin@open.ac.uk

Formally Measuring Agreement and Disagreement in Ontologies *

Keywords: I.2.4 [ARTIFICIAL INTELLIGENCE]: Knowledge Representation Formalisms and Methods Measurement, Experimentation Ontologies, Agreement, Disagreement, Consensus, Controversy

Ontologies are conceptual models of particular domains, and domains can be modeled differently, representing different opinions, beliefs or perspectives. In other terms, ontologies may disagree with some particular pieces of information and among themselves. Assessing such agreements and disagreements is very useful in a variety of scenarios, in particular when integrating external elements of information into existing ones. In this paper, we present a set of measures to evaluate the agreement and disagreement of an ontology with a statement or with other ontologies. While our work goes beyond the naive approach of checking for logical inconsistencies, it relies on a complete formal framework based on the semantics of the considered ontologies. The experiments realized on several concrete scenarios show the validity of our approach and the usefulness of measuring agreement and disagreement in ontologies.

INTRODUCTION

Ontologies are knowledge artifacts representing particular models of some particular domains. They are built within the communities that rely on them, meaning that they represent consensual representations inside these communities. However, several ontologies can cover the same domain, while being built by and for different communities. In these cases, different perspectives, points of view and opinions might be expressed on the same concepts and objects of the domain, i.e. ontologies might disagree. Knowing to which extent an ontology agrees with another one, or with a particular statement, can be very useful in many scenarios. When using several ontologies in a common application, for example, disagreement can create unexpected results for the user. Also, when reusing statements from other ontologies while building a new one, there is a need for some formal measures to indicate whether or not there exists a general agreement concerning a candidate statement, in the current ontology or in other, external ontologies. Realizing that there is a high level of disagreement in available ontologies with a given statement, or that there is no clear cut between agreement and disagreement, can be very useful in pointing out potentially problematic statements or ontologies. One way to detect whether there is a disagreement between two ontologies is to rely on the presence of logical contradictions. The two ontologies can be merged, based on mappings between their entities, and the resulting model be checked for inconsistencies and incoherences (the same approach can be used to check if an ontology disagrees with a statement). While this approach would certainly detect some forms of disagreement, it suffers from a number of limitations. First, it only checks whether the ontologies disagree or not. It does not provide any granular notion of disagreement and, if no contradictions are detected, it does not necessary means that the ontologies agree. Indeed, while two ontologies about two completely different, non overlapping domains would certainly not disagree, they do not agree either. More importantly, logical contradictions are not the only way for two ontologies to disagree. Indeed, there could also be conceptual mismatches, like in the case where one ontology declares that "Lion is a subclass of Species" and the other one indicates that "Lion is an instance of Species". Even at content level, logical contradictions would not detect some form of disagreements. Indeed, the two statements "Human is a subclass of Animal" and "Animal is a subclass of Human" do not generate any incoherence. However, they disagree in the sense that, if put together, they generate results that were not expected from any of the two ontologies. This other type of disagreement could be checked by using the notion of conservative extension [START_REF] Ghilardi | Did I damage my ontology? a case for conservative extensions in description logics[END_REF]. Informally, a conservative extension of an ontology is an ontology where axioms have been added which do not 'affect' the relations that can be inferred about the entities of the original ontology. Therefore, merging two ontologies and checking whether the result is a conservative extension of both the original ontologies would give indications of some forms of disagreement. However, this would also only result in a 'black box test', not providing a granular notion of disagreement or a proper notion of agreement. For these reasons, we developed a set of measures to assess both the level of agreement and the level of disagreement between a statement and an ontology or a set of ontologies, as well as between two ontologies. While these measures provide quantitative evaluations for agreement and disagreement, they rely on the formal properties of the ontologies and on the semantics of the ontology language to compare what is expressed by different statements and ontologies, detecting logical contradictions as well as other forms of contradictions.

ASSUMPTIONS AND REQUIREMENTS

Based on the usage scenarios quickly sketched above and on the analysis of the limitations of the basic approaches relying on logical contradictions and conservative extensions, we devised an number of requirements that our measures should fulfill: R1: Ontologies agree with themselves. This is a fairly obvious starting point, meaning that our measures should provide maximal results for agreement (and no disagreement) when checking an ontology against itself. It also means that we assume the ontologies we assess to be consistent, coherent, and homogeneous in terms of modeling.

R2: Covering different domains is not agreeing. We consider that there is a fundamental difference between agreeing and not talking about the same things. This means that, when applied on ontologies or statements that cover completely different domains (i.e. for which there is no mapping between the entities), our measures should indicate that there is no disagreement and no agreement.

R3: Different levels of agreement/disagreement. As already mentioned, there are different reasons for which an ontology might disagree with another one (at the level of the content, logically or not, at the level of the representation, etc.) These different kinds of disagreements should be considered with different levels of importance, leading to granular measures rather than binary tests. R4: Independent from matching techniques. In order the check the agreement/disagreement of an ontology with respect to another ontology or a statement, corresponding entities should be related through mappings. However, the way these mappings are produced should not affect the computation of the agreement/disagreement measures. Therefore, we will assume the existence of mappings we can exploit, without considering any particular approach to produce such mappings. In our experiments, we will use a simple technique based on the lexical correspondence between the entities' names. R5: It is possible to agree and disagree at the same time. Two ontologies may agree on some statements and disagree on some others, meaning that, depending on the number of statements in each category and on the level of agreement/disagreement for each statement, the two ontologies might agree and disagree at different levels. It should even be possible for an ontology to both agree and disagree with one single statement. Indeed, we consider the case of an ontology that contains the statement "Lion is a subclass of Species" and for which we want to check whether it agrees with the statement "Lion is an instance of Species". As already mentioned, this ontology disagrees at a modeling level with this statement. However, at content level, it agrees to a certain extent that Lion is included in Species.

BASIC FRAMEWORK

In this section, we consider an ontology O to be defined as a set of statements (corresponding to axioms in the description logic terminology). A statement is the expression of a relation between two entities of the ontology in the form of a triple < subject, relation, object >.

In RDF-based ontology languages, relation corresponds to the identifier of a property (its URI), subject corresponds either to the URI of an entity or to an anonymous resource, and object corresponds to the URI of an entity, an anonymous resource or a literal. In the following, we base our definition of agreement and disagreement on whether or not an ontology conflicts with a relation linking two named entities. Hence, we chose to ignore the cases of anonymous entities (i.e., blank nodes in RDF) and literals. This does not mean that our measures could not be applied to ontologies containing such elements, but simply that we will only use statements where the subjects and objects are identifiers of entities.

As already mentioned, the atomic element on which ontologies can express agreement or disagreement is the statement. Indeed, an ontology can contain information that contradict, or on the contrary enforce the one expressed through a particular statement, and so can agree or disagree with it. We define two elementary functions representing respectively the agreement and the disagreement levels of an ontology O with respect to a statement s =< subject, relation, object >:

agreement(O, s) → [0..1] disagreement(O, s) → [0..1]
We chose to use two distinct measures for agreement and disagreement so that an ontology can, at the same time and to certain extents, agree and disagree with a statement (cf. R3, R5). These two measures have to be interpreted together to indicate the particular belief expressed by the ontology O regarding the statement s. For example, if agreement(O, s) = 1 and disagreement(O, s) = 0, it means that O fully agrees with s and conversely if agreement(O, s) = 0 and disagreement(O, s) = 1, it fully disagrees with s. Now, agreement and disagreement can vary between 0 and 1, meaning that O can only partially agree or disagree with s (cf. R3) and sometimes both, when agreement(O, s) > 0 and disagreement(O, s) > 0 (cf. R5). Finally, another case is when agreement(O, s) = 0 and disagreement(O, s) = 0. This basically means that O neither agrees nor disagrees with s, for the reason that it does not express any belief regarding the relation encoded by s (cf. R2).

The actual values returned for both measures, when different from 0 and 1, are not very important. They correspond to different levels of dis/agreement and only an order between pre-defined levels is needed to interpret them. In this work, we consider two different levels of agreement and of disagreement different from 0 and 1, defined as follows: 0 < A1 < A2 < 1 0 < D2 < D1 < 1 Note again that the actual values for these levels are not significant, only the total order between them. However, to facilitate comparisons of measures, desirable properties are that A1 + A2 = 1, D1 + D2 = 1, A1 + D1 = 1 and A2 + D2 = 1.

To be able to compute a (non-null) level of dis/agreement, it is necessary that the ontology O covers the entities related by the statement s. Thus, we need to identify entities in O that correspond to the entities in the tested statement s. For this, we assume the existence of a function match(O, e) that returns the identifier of an entity e in O (cf. R4). To simplify the notation, we will call s and o the matching entities in an ontology O of the subject and object of a statement < s, r, o > respectively.

Note that the match function does not need to be completely defined, meaning that it can happen that no matching entities are found in O for s or o. However, the following definitions will assume the existence of s and o . Hence we consider that agreement(O, t) = 0 and disagreement(O, t) = 0, with t =< s, r, o >, iff match(O, s) or match(O, o) are undefined.

MEASURING AGREEMENT AND DIS-AGREEMENT OF AN ONTOLOGY RE-GARDING A STATEMENT

Based on the basic definitions of the previous section, we can now devise a formal way to compute the agreement and disagreement measures between statements and ontologies. As mentioned before, these measures should essentially assess whether or not the relation between entities expressed in the considered statement s is 'validated' by the ontology. The central element to consider for our measures is therefore the type of the relation r in the considered statement < s, r, o >. This relation can either be a property included in the ontology representation language, i.e., one of {subClassOf, eq-uivalentClass, domain, range, disjointW ith, type, sa-meAs, dif f erentF rom, subP ropertyOf}, or a generic, user-defined property R (e.g., isP artOf , isAuthorOf ). As for the relation in the considered statement, the M RM of an ontology can contain any kind of relation, in particular properties of the language and userdefined relations. In the later case, we need to distinguish the cases of relations that match the one described in the statement (i.e., when match(O, r) = r ).

In order to simplify the notations, we represent the set of statements in a M RM as a set of relations between One of the interesting properties of the set M RM in this notation is that, due to the fact that it is nonredundant, consistent and coherent, and that it does not contain conflicts at modeling level, there exists only a finite set of possible M RM s whatever are the considered ontology and the considered statement. In other terms, there exist only a restricted number of allowed combinations of relations, as MRM sets such as {subClassOf, sub-ClassOf -1 , equivalentClass}, {subClassOf, disjoint-W ith} or {subClassOf, type} do not comply with the definition.

s
Finally, assessing the levels of agreement and disagreement between a statement and an ontology O consists in comparing the relation r expressed in the statement, and the corresponding M RM from O, to check whether they enforce or contradict each other. Considering that there are only a finite set of possible situations, the result of the agreement (respct. disagreement) measure can be completely defined by a matrix establishing the returned values depending on the relation r and on the set M RM . The matrixes we propose for our measures are shown in Table 1, but can be customized for specific needs. The methodology used to build these matrixes and the impact of using different parameters are out of the scope of this paper.

As an example, if we consider the statement st =< P erson, sameAs, Human > and as M RM for the ontology O the set {subClassOf }, we obtain from these matrixes the following values for the measures of agreement and disagreement:

agreement(st, O) = A1 disagreement(st, O) = D1
indicating that st and O both partially agree (because both believe there is an overlap between Human and P erson) and partially disagree (because they do not express the same level of overlap, and they use different modeling, considering classes in one case and instances in the other case).

MEASURING AGREEMENT AND DIS-AGREEMENT BETWEEN TWO ONTOLO-GIES

Considering that ontologies are made of statements, extending the measures above to compute agreement and disagreement between two ontologies should be relatively straightforward, using the average of each measure for each statement of an ontology against the other ontology. However, there are two issues related to this approach. First, the measures would not be symmetric, as declared statements would be considered in one case, and entailed ones in the other case. Second, in cases where the ontologies only have a small overlap, the results would be lowered down by all the statements which would not find matches from one ontology to the other (resulting in null values for both agreement and disagreement).

For these reasons, we define the measures of agreement and disagreement between ontologies in the following way:

agreement(O 1 , O 2 ) = P st∈ST 1 agreement(st,O2 )+ P st∈ST 2 agreement(st,O1 ) |ST1|+|ST2| disagreement(O 1 , O 2 ) = P st∈ST 1 disagreement(st,O2 )+ P st∈ST 2 disagreement(st,O1 ) |ST1|+|ST2|
where

ST 1 = {< s, p, o >∈ O 1 | match(s, O 2 ) = ∅ ∧ match(o, O 2 ) = ∅} and ST 2 = {< s, p, o >∈ O 2 | match(s, O 1 ) = ∅ ∧ match(o, O 1 ) = ∅}.
In this way, only relevant statements are checked for agreement and disagreement (ST 1 and ST 2 ) and the measures are symmetric.

MEASURING CONSENSUS AND CON-TROVERSIES

In some scenarios, it is useful to have measures on how much a statement is dis/agreed in a set of available ontologies, i.e., to which extent there is a consensus over this statement in these ontologies. Conversely, a related information concerns the level of controversy on the statement, i.e. whether there is a clear cut between agreement and disagreement.

To compute such measures, we need to assess of the global dis/agreement in the considered set of ontologies with a statement st. We represent the available ontologies as a set R of ontologies, which in practice can be implemented as an ontology repository. In our experiments we will use the set of ontologies collected by the r sClass equiv. dom. range disj. type same diff. sProp. R

∅ 0 0 0 0 0 0 0 0 0 0 sClass 1 A2 0 0 0 A2 A1 0 A1 0 sClass -1 A1 A2 0 0 0 0 A1 0 0 0 equiv. A2 1 0 0 0 A1 A2 0 A1 0 disj. 0 0 0 0 1 0 0 A2 0 0 dom. 0 0 1 0 0 0 0 0 0 0 dom. -1 0 0 0 0 0 0 0 0 0 0 range 0 0 0 1 0 0 0 0 0 0 range -1 0 0 0 0 0 0 0 0 0 0 dom./range 0 0 1 1 0 0 0 0 0 0 dom. -1 /range -1 0 0 0 0 0 0 0 0 0 0 sProp A2 A1 0 0 0 A1 A1 0 1 0 sProp -1 0 A1 0 0 0 0 A1 0 A1 0 type A2 A1 0 0 0 1 A1 0 A1 0 type -1 0 A1 0 0 0 A1 A1 0 0 0 same A1 A2 0 0 0 A1 1 0 A1 0 match 0 0 0 0 0 0 0 0 0 1 match -1 0 0 0 0 0 0 0 0 0 0 mmatch 0 0 0 0 0 0 0 0 0 0 same/match A1 A2 0 0 0 A1 1 0 A1 1 same/match -1 A1 A2 0 0 0 A1 1 0 A1 0 same/mmatch A1 A2 0 0 0 A1 1 0 A1 0 diff. 0 0 0 0 A2 0 0 1 0 0 diff./match 0 0 0 0 A2 0 0 1 0 1 diff./ match -1 0 0 0 0 A2 0 0 1 0 0 diff.mmatch 0 0 0 0 A2 0 0 1 0 0 r sClass equiv. dom. range disj. type same diff. sProp. R ∅ D1 D1 D2 D2 D1 D1 D1 D1 D1 D2 sClass 0 D2 D1 D1 1 D2 D1 1 D2 D1 sClass -1 D1 D2 D1 D1 1 D1 D2 1 D1 D1 equiv. D2 0 D1 D1 1 D1 D2 1 D1 D1 disj. 1 1 D1 D1 0 1 1 D2 1 D1 dom. D1 D1 0 0 D1 D1 D1 D1 D1 D1 dom. -1 D1 D1 D1 D1 D1 D1 D1 D1 D1 D1 range D1 D1 0 0 D1 D1 D1 D1 D1 D1 range -1 D1 D1 D1 D1 D1 D1 D1 D1 D1 D1 dom./range D1 D1 0 0 D1 D1 D1 D1 D1 D1 dom. -1 /range -1 D1 D1 D1 D1 D1 D1 D1 D1 D1 D1 sProp D2 D1 D1 D1 1 D1 D1 1 0 D1 sProp -1 D1 D1 D1 D1 1 D1 D1 1 D1 D1 type D2 D1 D1 D1 1 0 D1 1 D1 D1 type -1 D1 D1 D1 D1 1 D1 D1 1 D1 D1 same D1 D2 D1 D1 1 D1 0 1 D1 D1 match D1 D1 D1 D1 D1 D1 0 0 D1 0 match -1 D1 D1 D1 D1 D1 D1 0 0 D1 D1 mmatch D1 D1 D1 D1 D1 D1 0 0 D1 D2 same/match D1 D2 D1 D1 1 D1 0 1 D1 0 same/match -1 D1 D2 D1 D1 1 D1 0 1 D1 D1 same/mmatch D1 D2 D1 D1 1 D1 0 1 D1 D2 diff. 1 1 D1 D1 D2 1 1 0 1 D2 diff./match 1 1 D1 D1 D2 1 1 0 1 0 diff./match -1 1 1 D1 D1 D2 1 1 0 1 D1 diff./mmatch 1 1 D1 D1 D2 1 1 0 1 D2
= {O ∈ R | match(s, O) = ∅ ∧ match(o, O) = ∅}.
The level of consensus concerning a statement st corresponds to the level of certainty on whether ontologies in R agree or disagree with st. We say that there is a high level of (positive consensus) if the overall agreement about this statement is high and the overall disagreement is low. Thus, we define the measure of consensus in a set of ontologies R upon a statement st as follows:

consensus(st, R) = agreement(st, R)disagreement(st, R) this measure should be interpreted in the following way:

• if consensus(st, R) > 0 then it represents the level of 'positive' consensus in R about st, meaning that there is a consensus on agreement.

• if consensus(st, R) < 0 then it represents the level of 'negative' consensus in R about st, meaning that there is a consensus on disagreement.

We consider the notion of controversy to be the inverse from the one of consensus: there is a high level of controversy on a given statement when there is no clear cut between agreement and disagreement, i.e. there is a low level of consensus. Therefore, the measure of controversy in a set of ontologies R upon a statement st can simply be computed in the following way:

controversy(st, R) = 1 -|consensus(st, R)|

USAGE SCENARIOS AND EXPERIMENTS

To test the behavior of our measures, we experiment on computing them on three concrete scenarios based on the Watson collection of ontologies. In these experiments, we use a simple lexical matching technique, and define A1 = 0.25, A2 = 0.75, D2 = 0.25 and D1 = 0.75.

Assessing Statements in the Watson Plugin

Watson [START_REF] D'aquin | Watson: Supporting next generation semantic web applications[END_REF] is a gateway to the Semantic Web. It collects, indexes and gives access to online knowledge available in ontologies and semantic documents. It is a Semantic Web search engine, but focusing on supporting applications in exploiting the Semantic Web through a set of high level APIs.

To help ontology engineers benefit from Watson, we developed the Watson Plugin for ontology editors [START_REF] D'aquin | Reusing Knowledge from the Semantic Web with the Watson Plugin[END_REF]. This plugin allows the developer of an ontology to query Watson for entities corresponding to the ones in the built ontology, and to automatically integrate selected statements from these external entities into the ontology.

In this tool, it is essential to be able to assess statements, to identify the ones that can be safely integrated into the built ontology from the ones that require more attention. Here, we consider the case of an ontology engineer who needs to integrate to her ontology the class SeaFood. The Watson Plugin retrieves a set of statements for this class from other ontologies. We then compute the overall agreement and disagreement measures in Watson for each of these statements, as well as the consensus and controversy measures. The results are summarized in Table 2. Note that, in this table, 'lexically similar' statements are grouped together (the table indicates the number of ontologies where each statement appears).

As can be seen from these results, the 4 first statements are fully agreed with by ontologies in Watson, meaning that all the ontologies containing both entities of each statement express exactly the same relation as the one of the statement. The 3 next statements also have a very high level of agreement, and a very low level of disagreement. This is mainly due to a few ontologies containing the right entities, but not necessarily relating them. Hence, there is a high level of consensus on these statements. Finally the 2 last statements are the ones for which there is the highest level of controversy. The last one is by far the most disagreed with (which correlate with the high level of agreement of the other one contradicting it), clearly indicating that it should be considered carefully whether it can be integrated into the ontology being developed.

Another interesting example is the one of the statement < river, subClassOf, sea >, which gives a high level of disagreement (0.766). The disagreement is not 1 in that case, because only very few ontologies express explicitly contradicting relations. However, in this case, the level of agreement is 0: There is no ontology to actually agree with this statement.

Checking Automatically Discovered Relations

A similar scenario to the one presented above concerns automatically discovered relations between ontological entities, in particular in the task of ontology matching [START_REF] Euzenat | Ontology Matching[END_REF]. Indications about the level of dis/agreement concerning the derived relations can help filter out possibly problematic relations and so improve the precision of matching. For this to be achieved, we need to show that there are exploitable correlations between our measures and the 'correctness' of the considered relations.

For this experiment, we exploit the set of ontology map- pings between 2 large thesaurus in the agriculture domain described in [START_REF] Sabou | Exploring the Semantic Web as Background Knowledge for Ontology Matching[END_REF], which has been partially evaluated by 3 persons. We filter out mappings for which the global measures of agreement, disagreement, consensus and controversy cannot be computed (because no ontology contains the corresponding entities). We obtain a set of 456 mappings, out of which 325 have been evaluated to be correct (71.3% precision).

To check the behavior of our measures, we computed the averages of the measures of global agreement, global disagreement, consensus and controversy for both the mappings that have been evaluated correct by evaluators and the ones marked as incorrect (see Table 3). As expected, these values show a significant difference, with agreement and consensus favoring correct mappings, while disagreement and controversy favor incorrect mappings. To confirm these results, we also computed the correlations between each measure and the evaluated correctness of the mappings 2 . The results (see Table 3) show clear positive correlations for agreement and consensus, and negative correlations for disagreement and controversy (though the correlation for controversy is less significant). This confirms that there is a link between our agreement-related measures and the correctness of statements and so that these measures can be used to facilitate the assessment of such relations. Indeed, we calculated that, using the adequate threshold, we could obtain a precision value of up to 80% on the tested mappings by filtering on the measure of consensus alone.

Facilitating the Selection of Ontologies

Watson and other Semantic Web search engines provide the elementary functionalities to search and explore ontologies, but to better support the task of selecting the right ontologies, there is a need for a complete overview of the set of candidate ontologies they return and on 2 Using the Pearson sample correlation measure.

how they relate to each other. Here, we experiment on using the agreement and disagreement measures to provide one element of such an overview. We used the 21 ontologies returned by Watson when querying for semantic documents containing a class with the term SeaFood in its ID or label and computed the agreement and disagreement measures for all pairs of ontologies in this set. The results are shown in Figure 1 where ontologies are numbered according to their rank in Watson 3 .

Analyzing these diagrams, it appears that there is a certain level of 'coherence' in the results. In particular, homogeneous clusters can be built from the agreement and disagreement values. Indeed, the ontologies O1, O2, O3, O4, O5, O6, O7, O11, O12, O13, O16, O17, O18, O19 and O20 all fully agree with each other and, at the same time, partially agree and disagree with O14 and O15. O14 and O15 also form a cluster since they agree with each other, and consistently disagree with the same set of ontologies (the reason being that O14 and O15 are the ontologies considering that SeaFood is a subclass of Meat, but agree on all the other related statements). O21 is also particular, since it disagrees with most of the ontologies of the first cluster, sometimes fully. Indeed, it also considers SeaFood to be a subclass of Meat, and additionally disagrees on several other statements with some of the other ontologies (for example, it considers that tuna is a subclass of fish while several other ontologies consider tuna as an instance of fish). O8, O9 and O10 are particular since there is only a very small overlap between them and the other ontologies. For example, O9 only agrees with O11 that Vegan is a subclass of Vegetarian.

As a result of this experiment, it appears that the agreement and disagreement measures provide interesting elements for analyzing a set of candidate ontologies to identify possible contradictions, exceptions, as well as agreem t disagreem t cons. contro. avg. correct 0.60 0.30 0.30 0.32 avg. incorrect 0.45 0.41 0.05 0.40 correlation 0.166 -0.165 0.165 -0.109

Table 3: Average of each measures on the sets of correct and incorrect mappings, and Pearson correlation between the measures and the correctness of the mappings. sets of ontologies expressing compatible knowledge, hence supporting a more informed choice of ontologies to reuse.

CONCLUSION AND FUTURE WORK

In this paper, we presented a set of formally defined measures relying on the formal semantics of ontologies to assess the agreement and disagreement between a statement and an ontology or a set of ontologies, as well as between two ontologies. We have realized a straightforward implementation of all the measures described above and tested them on a number of examples.

At a short term, we intend to provide these measures as Web services on top of Watson, allowing external applications to check agreement related measures for particular statements. In particular, these services will be used in the Watson Plugin to provide useful indications to help the user in selecting good statements, and to rank them according to their level of dis/agreement.

Another interesting direction concerns the computation of 'explanations' for the measures, showing what statements conflict or enforce the one which is tested and, in addition to providing measures of agreements and disagreements between ontologies, also computing precisely 'on what' the considered ontologies dis/agree.

Finally, we believe that there are many possible usage scenarios for our measures which we have not explored yet. In particular, it would be interesting to investigate how meta information such as trust statements on particular ontologies could be propagated based on the dis/agreement values between these ontologies.

1

  http://watson.kmi.open.ac.uk

Figure 1 :

 1 Figure 1: Agreement (top) and disagreement (bottom) relations among the 21 test ontologies. Plain lines represent full dis/agreement (measures' values = 1). Dashed lines represent partial dis/agreement (measures' values greater than 0).

  Also, M RM (O, < s, r, o >) should not contain any modeling conflict, meaning for example that it should not imply that an entity is at the same time a class and an individual, like in the two statements < s, subClassOf, o > and < s, type, o >.

	The non-redundant R-module of an ontology O with
	respect to a statement < s, r, o > is a subset of the cor-
	responding R-module such that none of the statements
	included can be inferred from other statements in the
	set. Formally, it is defined by M RM (O, < s, r, o >) =
	{st =< s , r , o > or st =< o , r , s > | st ∈ RM (O, < s, r, o >) ∧ RM (O, < s, r, o >) \ {st} |= st}. Note that, since we exclude statements involving the meta-model
	of the language, a non-empty R-module cannot lead to
	an empty non-redundant R-module.

To assess dis/agreement between this statement and the ontology O, we then need to compare the relation encoded in the statement, and the relations that are expressed between corresponding entities in O. In other terms, we need to extract from O statements that express relations between s and o , the entities matching s and o. Note that these statements should not necessarily be declared in O, but can also be entailed from O. This leads to the definition of the R-module of an ontology O with respect to a statement < s, r, o >. The R-module of an ontology O with respect to a statement < s, r, o > is the list of statements of the form < s , ?, o > or < o , ?, s > that are entailed by O. Formally, it is defined by RM (O, < s, r, o >) = {st =< s , r , o > or st =< o , r , s > | match(O, s) = s ∧ match(O, o) = o ∧ O |= st}. Note that RM can be empty, meaning that the ontology does not express any relation between the two given entities.

The R-module represents a complete set of statements that O directly or indirectly expresses about the relations between s and o. In order to make it a minimal, concise summary of these relations, we introduce the notion of non-redundant R-module.

In addition, according to requirement R1, we assume that M RM (O, < s, r, o >) is a consistent and coherent set of axioms, so that it cannot contain for ex-ample both statements < s, subClassOf, o > and < s, disjointW ith, o >.

  and o . In this notation, a statement such as < s , subClassOf, o > is represented by the relation subClassOf and the statement < o , subClassOf, s > by the relation subClassOf -1 . Concerning user-defined properties, a statement < s , r , o > is represented by matchRelation if match(O, r) = r , r being the relation in the considered statement, and by mismatchRelation if not.

Table 1 :

 1 Watson system1 . We then compute the agreement and disagreement measures between a statement st and this repository R as a simple average, but taking only into account ontologies matching the entities of st:

	agreement(st, R) = disagreement(st, R) =	P	O∈rR agreement(st,O) |rR|

Matrix definitions of the agreement (top) and disagreement (bottom) measures, depending on the relation r in the considered statement, and the set of relations in the M RM from the considered ontology O. R represents a user-defined property. Other relations are abbreviated.

P O∈rR disagreement(st,O) |rR| where st =< s, p, o > and rR

Table 2 :

 2 Dis/agreement measures on statements from the Watson Plugin with the class SeaF ood. N b1 is a number of ontologies in which the statement appears and N b2 the number of ontologies containing entities matching the subject and object of the statement. Measures of agreement (a), disagreement (d), consensus (cs) and controversy (ct) are computed on the Watson collection.

	Statement	Nb1 Nb2	a	d	cs	ct
	< SeaF ood, disjointW ith, Dessert >	12	12	1.0	0.0	1.0	0.0
	< F owl, disjointW ith, SeaF ood >	11	11	1.0	0.0	1.0	0.0
	< P asta, disjointW ith, SeaF ood >	12	12	1.0	0.0	1.0	0.0
	< SeaF ood, subClassOf, EdibleT hing > 11	11	1.0	0.0	1.0	0.0
	< ShellF ish, subClassOf, SeaF ood >	14	16 0.937 0.047	0.89 0.109
	< F ish, subClassOf, SeaF ood >	12	14 0.928 0.053 0.875 0.125
	< SeaF ood, disjointW ith, F ruit >	11	14	0.85	0.1	0.75	0.25
	< M eat, disjointW ith, SeaF ood >	8	16	0.75	0.22	0.53	0.46
	< SeaF ood, subClassOf, M eat >	4	16 0.125 0.844 -0.719 0.281

* This work was supported by the European Commission in the IST project NeOn (IST-2006-027595).