R Vargas

J Neggers

R B Canto

J A Rodrigues

F Hild
email: hild@lmt.ens-cachan.fr

Analysis of Wedge Splitting Test on Refractory Castable via Integrated DIC

Keywords: Castables, Crack growth resistance, Photomechanics, R-curve

One of the key mechanical properties of refractories is their toughness. The latter can be evaluated via wedge splitting tests. One such test is analyzed herein with an integrated approach to digital image correlation. The position of the crack tip, stress intensity factors and T-stress are estimated on two faces of the tested sample made of a refractory castable during the whole cyclic test. It is shown that the change of energy release rate with the crack length can be determined at each time step of the experiment.

Introduction

Refractory castables are known for their capability to maintain enough mechanical and chemical properties in extreme environments [START_REF] Lee | Castable refractory concretes[END_REF]. They are used as insulators in industries that produce base materials such as metals, ceramics and petrochemicals, where high temperatures and/or corrosive processes are involved (e.g., melting metals or cracking petrol). The proper material selection for each application not only improves the security but also increases the lifetime [START_REF] Wachtman | Materials and Equipment -Whitewares -Refractory Ceramics -Basic Science: Ceramic Engineering and Science Proceedings[END_REF]. The brittle fracture of these materials leads to the need for a good understanding of the mechanical behavior (e.g., to prevent accidents). Minimizing thermal shock damage by tailoring the microstructure with respect to crack propagation may increase their lifetime (and reduce its uncertainty), thereby reducing costs and improving the safety of the applications. Investigating tests with stable crack propagation is useful to better understand the mechanisms of fracture and quantify the relevant mechanical parameters.

Stable crack propagation is achievable using, for instance, the Wedge Splitting Test (or WST [START_REF] Tschegg | Equipment and appropriate specimen shapes for tests to measure fracture values[END_REF][START_REF] Brühwiler | The wedge splitting test, a new method of performing stable fracture mechanics tests[END_REF][START_REF] Karihaloo | Coecients of the crack tip asymptotic eld for wedge splitting specimens[END_REF]) in which the elastic energy stored in the machine is minimized. This test, which is very suitable for brittle materials, is very challenging because the displacement (and strain) levels remain very small. The purpose of this work is to assess whether a single WST is suited for the evaluation of R-curve behavior of such materials. Among the classical methods used for R-curve measurements, one possibility is using long cracks (i.e., longer than 1 mm) with stable propagation in standard testing geometries of fracture mechanics [START_REF] Steinbrech | R-curve behavior of ceramics[END_REF]. The crack length is estimated as a function of the compliance obtained on the load-displacement curve after comparing with theoretical values [START_REF] Mazzei | Alumina-mullite-zirconia composites obtained by reaction sintering Part II. R-Curve behavior[END_REF]. If a cyclic experiment is chosen, there are discus-sions on how to calculate the compliance as the reference is not obvious in the case of hysteresis in the loading/unloading cycles [START_REF] Steinbrech | R-curve behavior of ceramics[END_REF]. The crack length can also be estimated by direct observation [START_REF] Sun | R-curve response of silicon carbide whisker-reinforced alumina: microstructural inuence[END_REF] but it may be dierent for each operator.

An approach that was successfully used to monitor cracks is Digital Image Correlation (DIC) [START_REF] Mcneill | Estimation of stress intensity factor by digital image correlation[END_REF][START_REF] Abanto-Bueno | Investigation of crack growth in functionally graded materials using digital image correlation[END_REF][START_REF] Forquin | A method to determine the toughness scatter of brittle materials[END_REF]. Full displacement elds are measured instead of few point data (e.g., extensometry, load). This technique does not directly depend on the operator and it can follow crack propagation, namely, dierent crack positions can be determined in the same test as it propagates [START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF]. To determine Stress Intensity Factors (SIF) and crack tip positions, the measured displacement elds are subsequently post-processed via projections onto known solutions of fractured elastic media. In the case of brittle material fracture it is assumed that, apart from the vicinity of the crack tip, the material behaves elastically. In this specic case, Williams' series [START_REF] Williams | On the stress distribution at the base of a stationary crack[END_REF] describe the stress and displacement elds as functions of mechanical parameters for dierent fracture modes. A least-squares t using Williams' series enables the SIF to be evaluated [START_REF] Mcneill | Estimation of stress intensity factor by digital image correlation[END_REF][START_REF] Abanto-Bueno | Investigation of crack growth in functionally graded materials using digital image correlation[END_REF][START_REF] Forquin | A method to determine the toughness scatter of brittle materials[END_REF] provided the crack tip position is known [START_REF] Roux | Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches[END_REF]. Dehnavi et al. [START_REF] Dehnavi | Utilizing digital image correlation to determine stress intensity factors[END_REF] showed that this method may provide more accurate results compared to photoelasticity when evaluating SIFs.

Another method for estimating SIFs and energy release rates using measured displacements elds consists of performing numerical simulations via, say, Finite Element (FE) analyses. Once the crack tip position is known, it is possible to evaluate the SIFs and T-stresses via standard FE extracting techniques [START_REF] Hattali | Numerical and experimental approaches for the determination of two-parameter fracture mechanics in wedge splitting loading[END_REF]. This analysis has been applied to WST on PMMA. DIC has also been utilized to characterize micro-and macrocracking in magnesia and magnesia spinel materials [START_REF] Belrhiti | Investigation of the impact of micro-cracks on fracture behavior of magnesia products using wedge splitting test and digital image correlation[END_REF][START_REF] Belrhiti | Renement of digital image correlation technique to investigate the fracture behaviour of refractory materials[END_REF]. The aim of the present study is to determine the whole history of fracture mechanics parameters of a refractory castable.

In this paper, an Integrated Digital Image Correlation (I-DIC [START_REF] Roux | Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches[END_REF]) approach is followed for evaluating the amplitudes of the elds in Williams' series to analyze the reported WST. Instead of rst measuring the displacements and then projecting them onto William' series, the two steps are integrated into a single one where the sought amplitudes are a direct result of the registration method. This approach bypasses the need for post-processing the displacement data, thereby reducing errors in the re-projection process [START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF]. This is of particular importance in the present case since the displacements are very small. The paper is organized as follows. First the experimental conguration and the studied material are introduced. The integrated DIC framework is then summarized in order to follow crack propagation, and estimate stress intensity factors and T-stress histories. The procedure is then applied to the pictures of two faces of the sample acquired during the test. It is shown that the R-curve behavior of the studied material can be obtained from the analysis of a single test.

Wedge Splitting Test

The geometry of the WST specimen used in this work is shown in • C, there is no phase transformation from α-quartz to β-quartz, which would lead to expansion.

However, the anisotropic phases could induce dierent thermal strains, which can initiate and propagate cracks in the specimen [START_REF] Pereira | A study about the contibution of the α-β phase transition of quartz to thermal cycle damage of a refractory used in uidized cracking units[END_REF]. These microcracks along with some weakly bonded grains to the matrix may debond and cause an R-curve behavior. For the mechanical properties of the studied material, the Young's modulus is equal to 17 GPa and the Poisson's ratio to 0.2.

Further characterization of the material analyzed herein can be found in

Refs. [START_REF] Miyaji | The coke eect on the fracture energy of a refractory castable for the petrochemical industry[END_REF][START_REF] Cabrelon | Efeito do tempo de exposição a uma atmosfera coqueificante na microestrutura e nas propriedades de um concreto refratário usado na indústria petroquímica[END_REF].

The images of the two lateral surfaces were taken using two cameras (Canon T5 model) with 28-135 mm lenses and the illumination was provided by LED lamps. For each face, 313 pictures were acquired with a rate of one frame every 8 s. The cameras were triggered by the testing machine controller. The denition of the pictures is 2100 × 1653 pixels and their dynamic range is of the order of 58,000 gray levels. The physical size of one pixel was 62 µm. To illustrate the challenges faced with such an experiment, Figure 2 shows the measured displacement eld in both directions via T3-DIC (see Section 3.1) for the maximum load when the rigid body translations have been removed. The maximum amplitude is very small (i.e., 0.5 pixel or 31 µm at the most). This type of test and material is therefore very challenging for DIC analyses since the signal to noise ratio is extremely small [START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF]. Digital Image Correlation (DIC) consists of using images to measure the motion of material points due to, say, mechanical loadings [START_REF] Sutton | Computer vision-based, noncontacting deformation measurements in mechanics: A generational transformation[END_REF]. These images can be 2D or 3D pictures and the scale of the displacements mainly depends on the imaging device that leads to physical sizes of pixels (or voxels) ranging from nanometers to kilometers [START_REF] Hild | Digital image correlation[END_REF]. Its increasing popularity is partly explained by the constant improvements of DIC schemes and new imaging devices (e.g., digital cameras with always increasing denitions) along with the possibilities of getting full-eld measurements instead of local point data.

Let us consider a simple 2D case where f is the image of the reference conguration and g a picture of the deformed sample. In the absence of noise, gray level conservation reads f (x) = g(x + u(x)).

(

) 1
As there is always some noise during acquisition, the sum of squared dierences is minimized over the region of interest (ROI)

φ = ROI (f (x) -g(x + u(x))) 2 , (2)
with respect to a chosen parameterization of the displacement eld. This approach is optimal for white, homogeneous and Gaussian noise [START_REF] Hild | Digital image correlation[END_REF]. The displacement eld is parameterized with a nite number of elds Ψ i with

unknown amplitudes υ i u(x) = i υ i Ψ i (x), (3)
so that u depends on the vector {υ υ υ} gathering all amplitudes υ i . Without prior knowledge on the kinematics the best approach would be choosing a robust Ψ i that works in the majority of cases, such as a nite elements discretization [START_REF] Besnard | Finite-element displacement elds analysis from digital images: Application to Portevin-Le Chatelier bands[END_REF]. In the following, T3-DIC will be used. It is based on a nite element discretization made of 3-noded linear elements [START_REF] Leclerc | Integrated digital image correlation for the identication of mechanical properties[END_REF][START_REF] Roux | Mechanical assistance to dic[END_REF]. The degrees of freedom in such a discretization have a local support, which is slightly bigger than an element due to the connectivity of the mesh. However, this local support makes the solution susceptible to acquisition noise [START_REF] Roux | Mechanical assistance to dic[END_REF][START_REF] Hild | Comparison of Local and Global Approaches to Digital Image Correlation[END_REF]. This is of particular importance for the case at hand for which the displacements have variations in displacement of the order of tens of micrometers at the most.

A direct improvement for an FE-based discretization is to disconnect nodes along the crack on the mesh using the crack path, which is obtained from the DIC residuals for instance [START_REF] Roux | Mechanical assistance to dic[END_REF][START_REF] Fagerholt | Measuring discontinuous displacement elds in cracked specimens using digital image correlation with mesh adaptation and crack-path optimization[END_REF] or by resorting to enriched (i.e., X-FEM) of kinematics [START_REF] Réthoré | Extended digital image correlation with crack shape optimization[END_REF]. However, a more integrated path is to reduce the allowable kinematics to exactly those described by closed-form solutions of the experiment [START_REF] Roux | Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches[END_REF] in which υ i are directly the sought mechanical parameters instead of nodal displacements. In cracked elastic media, Williams' series provide closed-form expressions for the elds Ψ i under plane stress and plain strain states [START_REF] Williams | On the stress distribution at the base of a stationary crack[END_REF][START_REF] Henninger | Enriched kinematic elds of cracked structures[END_REF]. If the latter ones are directly used in an integrated DIC code [START_REF] Roux | Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches[END_REF][START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF], then no post-processing is needed to evaluate the fracture mechanics parameters (e.g., crack tip position, SIF, T-stress).

In the integrated DIC code, the elds Ψ i introduced in Equation ( 3) correspond to those found in Williams' series [START_REF] Williams | On the stress distribution at the base of a stationary crack[END_REF]. Considering the origin at the crack tip with the crack face on the negative x-axis, the displacements elds are written as [START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF] u(z)

= II j=I p f n=p i ω j n ψ ψ ψ j n (z), (4)
where the vector elds are dened in the complex plane

z = x + yi = r exp (iθ), (5)
and j = I is related to mode I (opening) regime, and j = II to mode II (shearing). The corresponding elds are described by

ψ ψ ψ I n = A(n) 2µ √ 2π r n/2 κ exp inθ 2 - n 2 exp i(4 -n)θ 2 + (-1) n + n 2 exp - inθ 2 (6)
and

ψ ψ ψ II n = iA(n) 2µ √ 2π r n/2 κ exp inθ 2 + n 2 exp i(4 -n)θ 2 + (-1) n - n 2 exp - inθ 2 , ( 7
)
where κ is equal to (3 -ν)/(1 + ν) for plane stress states or 3 -4ν for plane strain states, ν the Poisson's ratio, r the distance from the crack tip, θ the angular position, and A(n) are dened by

A(n) = cos nπ 2 2 + sin nπ 2 . (8)
Equations ( 6) and ( 7) provide the sensitivity elds that after being multiplied by the amplitudes ω j n provide the total displacement elds. Equation (8) inputs consistent vector directions (for mode I and mode II) at the crack vicinity for the elds related to odd values of n and is valued as 1 or -1

for integer values of n. Amplitudes ω I 1 and ω II 1 give access to SIFs for mode I (K I ) and mode II (K II ), respectively. The amplitude ω I 2 provides the so- called T-stress, ω II 2 the rigid body rotation; the use of two additional terms in the series, ω I 0 and ω II 0 , allow for rigid body translation corrections. Although not usual, negative values of p i can be used to account for nonlinear eects in the vicinity of the crack tip [START_REF] Roux | Digital image correlation and fracture: An advanced technique for estimating stress intensity factors of 2d and 3d cracks[END_REF][START_REF] Henninger | Enriched kinematic elds of cracked structures[END_REF][START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF]. These negative n elds are referred to as the super-singular elds.

Considering a straight crack propagation along the x-axis, the displacement related to a mispositioned crack by a small distance d reads [START_REF] Roux | Digital image correlation and fracture: An advanced technique for estimating stress intensity factors of 2d and 3d cracks[END_REF] u(z

+ d) = u(z) + d ∂u(z) ∂z , (9)
and it is noted that

- ∂ψ ψ ψ j n ∂z = n 2 ψ ψ ψ j n-2 . (10)
Equation ( 4) can be substituted in Equation ( 9), in addition to the property shown in Equation ( 10) to obtain

wj n = w j n -d (n + 2)w j n+2 2 , ( 11
)
where wj n is the amplitude of the series after the shift and w j n before it.

Because of the singular character for n = -1 when r = 0, wI

-1 cancels out d = 2w I -1 w I 1 , (12)
which provides an estimation of crack tip shift to nd the correct position.

Methodology

The proposed methodology consists of dierent steps:

1. The crack path is assumed to be straight (since there is a groove on two opposite faces to guide crack propagation, see Figure 1(a));

2. The initial guess of the crack tip position is based, at rst, upon the transverse strain eld along the groove [START_REF] Saracura | Surface crack network detection on MgO-based refractory castable by digital image correlation[END_REF], which is determined from the displacement measured with T3-DIC (e.g., see Figure 2);

3. The Williams Series parameters are chosen e.g., radial normalization (see section 3.2.1), and a truncation proposal to evaluate the innite series, which is discussed in Section 3.2.2;

4. Integrated-DIC is performed to nd the amplitudes for the Williams series elds using a xed crack-tip position;

5. The crack-tip position is updated using the estimated crack shift d as described in Equation ( 12); 6. Steps 4 and 5 are repeated until convergence.

Normalization

The farther from the crack tip the displacements are assessed, the more terms of Williams' series are needed [START_REF] Veselý | Multiparameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens[END_REF][START_REF] Malíková | The inuence of higher order terms of Williams series on a more accurate description of stress elds around the crack tip[END_REF]. The higher order terms combined with large distances lead to oating point rounding errors due to the wide range of values present in the ψ ψ ψ j n elds. For that reason, a normalization on the radius is introduced

r * = r r 0 , (13)
where r 0 is the chosen normalization parameter. The chosen normalization improves oating point accuracy for high order terms without any impact on the solution space by reducing the range of r * , and thus removing conditioning issues related to rounding errors. In the present work r 0 and the evaluation radius are chosen such that r * ∈ [0, 1].

The displacement eld is rewritten as

u(z) = II j=I p f n=p i b j n ψ ψ ψ j n (z), with ψ ψ ψ j n (z) = ψ ψ ψ j n (z) r n/2 0 , (14)
so that the corresponding amplitudes become

b j n = ω j n r n/2 0 . (15)

Number of Terms of the Series

As seen in Equation ( 4) it is necessary to choose p i and p f to truncate the series so it can be numerically solved. Even though super-singular elds are not mandatory, the proposed approach needs p i = -1 for the estimation of the crack tip position (Equation ( 12)). As proposed in earlier studies, the value p i = -3 is considered to account for non-linear kinematics surrounding the crack tip [START_REF] Henninger | Enriched kinematic elds of cracked structures[END_REF][START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF]. Besides the -3 term, the domain applied for Integrated-DIC is shaped to exclude the direct vicinity of the crack, thereby reducing the impact of nonlinear eects on the results (Figure 5). Henninger et al. [START_REF] Henninger | Enriched kinematic elds of cracked structures[END_REF] have shown that p f = 7 was sucient to describe the analysis of a CT test for an elastoplastic material in small scale yielding regime. In the case of the WST, the studied material is brittle (or quasi-brittle) and a bigger radius of evaluation was applied to use more information from the images. Because of these dierences, analyses will be run to validate the choice of p f and the normalization procedure.

Results and Discussions

This section shows the results on the WST (Figure 1(a)) using the methodology described in Section 3. The integrated DIC routine is part of the Correli 3.0 framework, which is developed at LMT-Cachan [START_REF] Leclerc | Correli 3.0[END_REF].

Front Face

The analysis of all 312 image pairs is performed with dierent numbers of terms of Williams' series. In Figure 3 the results are shown for three dierent truncations (i.e., p f = [START_REF] Tschegg | Equipment and appropriate specimen shapes for tests to measure fracture values[END_REF][START_REF] Sun | R-curve response of silicon carbide whisker-reinforced alumina: microstructural inuence[END_REF][START_REF] Williams | On the stress distribution at the base of a stationary crack[END_REF]).

Figure 3 about here

The following observations are drawn:

• The I-DIC method to nd a proper crack tip converges from the third cycle on for p f = 3. The other truncations (i.e., p f = 8 and p f = 13)

nd the crack tip position from the start even though extremely small displacements occur at the beginning of the test (i.e., very low signal to noise ratio);

• p f = 3 underestimates K I and overestimates the crack length after the third cycle peak when compared to the other truncations even though it follows the same trend. It is worth noting that the crack length vanishes at the root of the pre-notch;

• The truncations p f = 8 and p f = 13 provide identical results meaning that p f = 8 gives an equivalent description of the kinematics when compared with series with a higher number of terms (for the three studied truncations);

• All three analyzed truncations show that the studied WST is close to pure mode I as the levels of K II are approximately equal to zero;

• The T-stress value increases upon loading and decreases in the unloading phase as expected. The T-stress related to p f = 3 deviates with the cycles from the levels observed when p f = 8 and p f = 13. In the last cases, a convergence to same values is noted and a maximum level around 4 MPa 2 is reached from the third to the fth cycle.

The gray level residual allows the user to evaluate which truncation variant describes the kinematics of the tests better. For comparison purposes 2 It is worth noting that with the chosen eld ψ ψ ψ I 2 , a positive T-stress is compressive.

T3-DIC is also run and considered as a reference since more degrees of freedom (i.e., nodal displacements) are measured in comparison with I-DIC.

Consequently T3-DIC can better describe the overall kinematics and would have lower residuals but may become more sensitive to acquisition noise. For this comparison, the residuals for any DIC analysis read

R(x) = f (x) -g(x + u meas (x)), (16)
which are the gray level dierences between the reference image f and the deformed image g corrected by the measured displacement eld u meas . For a given loading step, the root mean square (RMS) gray level is considered to globally evaluate the quality of registration ρ(x) = RMS (R(x)) .

(

) 17
When two DIC techniques are compared, the dierence ∆ρ over the same

Region Of Interest (ROI) is considered ∆ρ = ρ I-DIC(p f ) -ρ T3-DIC . (18)
The RMS residuals ρ and ∆ρ normalized by the dynamic range (i.e., number of gray level values) are shown in Figure 4 for the three dierent truncations. Figure 4(a) shows ρ over the whole ROI over which T3-DIC or I-DIC was performed. The global residuals are very close, thereby indicating that both image registrations have converged. It is worth noting however that the ROIs are not identical for the four analyses since the ROI for T3-DIC is rectangular and nearly covers the whole speckled surface (Figure 2), whereas I-DIC is based on circular ROI (Figure 5). This dierence explains the fact that the residual of T3-DIC is slightly higher than those of the I-DIC because the T3 result contains the crack path, which inates the residual (marginally in the present case).

The same trend, which is seen on every curve (apart from p f = 3 at the beginning), shows that the chosen kinematics (i.e., Williams' series) is consistent with the analyzed case. High values of ρ for the rst two cycles for p f = 3 are observable (i.e., the orange line is out of the range of Figure 4(a)).

This result is due to the inaccurate crack tip position for the same truncation, corroborating the fact that a higher p f (i.e., p f = 8) is more suitable for this analysis.

Figure 4 about here

All the reported gray level residuals show uctuations from one analyzed picture to the next. These uctuations are due to illumination variations during the test. It is believed that part of the variations observed in Figure 3 are a direct consequence of the unstable illumination and are not actually present in the experiment. The fact that the same uctuations are observed on T3-DIC and I-DIC results substantiates that statement.

In Figure 4 In all the analyses performed herein, 2D-DIC procedures were carried out. One limitation is associated with out-of-plane motions [START_REF] Fayolle | Contrôler une machine d'essai avec une caméra[END_REF][START_REF] Sutton | The Eect of Out of Plane Motion on 2D and 3D Digital Image Correlation Measurements[END_REF]. In the present case they are extremely small. Had they been more signicant, the I-DIC residuals would not have remained so low and very close to T3-DIC levels since the reduced kinematic basis does not account for such eects.

The oscillations on the measured SIFs, crack length and T-stress are believed to be related to the very small amplitudes of measured displacements. In the present case p f = 8 is the best compromise overall, since adding more terms (e.g., p f = 13) does not change the results nor signicantly decreases registration residuals. It is important to note that in the literature it is found that higher order terms could be important when describing the elds far from the crack tip, especially for bigger cracks [START_REF] Veselý | Multiparameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens[END_REF][START_REF] Malíková | The inuence of higher order terms of Williams series on a more accurate description of stress elds around the crack tip[END_REF]. The residuals indicate that a moderate number of terms is sucient provided the SIFs, Tstress and crack tip locations have converged.

Back Face

For the studied experiment, images of both faces were taken during loading. The same analysis is conducted on the back face and the results are shown in Figure 6. Not only are the overall trends identical, but all the observations made for the front face are also valid. The only notable exception is that results with the rst truncation (i.e., p f = 3) are closer to the other ones.

Coupled Analysis

For comparison purposes, the results for p f = 8 obtained for both faces are shown in Figure 8. Interestingly, crack propagation is not strictly identical on both sides. In the case of a WST on brittle materials, it is unlikely to maintain a perfect alignment of the wedge as the crack propagates. K I increases as the crack propagates, which is an indication of the R-curve behavior. One kink in the reported K I SIF is visible at the third cycle. It is directly related to the dierence in crack length from the two sides. At that moment, the crack propagates faster on the back, thereby weakening the stresses causing the measured K I on this side to be lower. On both sides, K II remains close to zero. The uctuations on K II are believed to be related to noise.

Consequently, it can be concluded that the test is in quasi pure mode I condition. At the very end, it appears that K II starts to increase slightly, but a maximum absolute value of 0.1 MPa √ m is negligible compared to the maximum K I level of 2 MPa √ m.

Figure 8 about here

The T-stress corresponds to the stress parallel to the crack propagation direction [START_REF] Gupta | A review of T-stress and[END_REF]. The absolute increase of T-stress with loading is consistent with rising SIFs. Conversely, it decreases in amplitude when K I decreases.

The uctuations of the T-stress are at the most equal to ±0.5 MPa, which correspond to strain uctuations of the order of ±3 × 10 -5 . These strain uctuations are extremely small. They are related to measurement uncertainties. Further, as the studied material is less brittle than most refractories, thus easier to achieve stable crack propagation, the test was performed with faster loading rate than usual. It is worth noting that there is a 20% dierence between the crack tip positions, stress intensity factors and T-stress levels between the two faces.

Had only one camera been used, it would have led to a ±10%-dierence with respect to their averages. This point underlines the fact that two cameras are highly advised to be used for WST experiments.

Let us consider the dimensionless crack length

α = a H ef f (19)
Plotting the average energy release rate G measured from the analyses of both faces as a function of the average values of α enables the R-curve behavior to be investigated (Figure 9). In the present case, only the loading part of each cycle is reported. The rising trend of the curve means that more energy is needed for each increment of crack propagation. It is interesting to note that a steeper slope is observed when α > 0.7. This result is compatible with the equations used for R-curve calculations [START_REF] Mazzei | Alumina-mullite-zirconia composites obtained by reaction sintering Part II. R-Curve behavior[END_REF], although none of these equations were assumed herein. The mean energy release rate when 0.3 < α < 0.7 is approximately equal to 35 J/m 2 . For the the whole propagation curve, the average value is 60 J/m 2 . Williams' series expansion to be validated. This rst step is crucial to make sure that the reported results are trustworthy even though the experimental conguration is very challenging for non-integrated DIC purposes.

One key aspect related to cracked media is the location of the crack tip.

In the present case, because a speckle pattern was applied to the surfaces and the presence of the grooves, visual estimates were not possible. The use of the rst super-singular eld proved to be reliable. Consequently, it was shown that it is possible to measure crack lengths, K I , K II and T -stresses even though the displacement amplitude remains very small. The measurements on both faces of the specimen are important as crack propagation may not be aligned with the out-of-plane direction. Measurements on a single side on the WST could lead to biased results, even though it is possible that both faces follow the same trend as seen in the test reported herein.

With the knowledge of K I , K II and crack length, the R-curve behavior is accessible. For the studied material the R-curve behavior is clearly revealed by using a single experiment. This result proves the feasibility of the integrated DIC framework for the quantication of cracking in refractories via global parameters such as stress intensity factors, and T-stresses. To further validate the present framework the next step may be to compare such results with standard procedures (e.g., via work of fracture estimates [39]). A study to check if lower order terms of Williams' series are related to the Fracture Process Zone [START_REF] Roux | Digital image correlation and fracture: An advanced technique for estimating stress intensity factors of 2d and 3d cracks[END_REF][START_REF] Henninger | Enriched kinematic elds of cracked structures[END_REF][START_REF] Mathieu | Identication of a crack propagation law by digital image correlation[END_REF] or other fracture mechanisms could be evaluated with a known microstructure and material behavior by focusing more about the crack tip. Last the estimation of R-curve behavior with the proposed method on other materials and compositions may also be undertaken.

  Figure 1(a). A right cuboid 100 mm in height, 72.5 mm in thickness, and 100 mm in width is chosen. The loading was applied by the wedge to the cylinders to open the specimen in pure mode I presumably. The test was driven with a controlled velocity of the machine actuator set to 1.3 µm/s. The sample contains two vertical grooves (i.e., a local thickness reduction of 7 mm) in the middle of front and back faces to guide crack propagation along a straight line, and the specimen was only supported at the bottom on a line passing through both grooves. The test consisted of ve cycles (see Figure 1(b)) with the last unloading starting at 70% of the maximum applied load to ensure that the main crack has not entirely propagated through the sample. The pre-load was set to 30 N, which was the value used to dene the unloaded state between cycles.

Figure 1

 1 Figure 1 about here

Figure 2

 2 Figure 2 about here

  (b) the residual dierence is now computed for the same ROIs in I-DIC and T3-DIC. A generally positive dierence is obtained, which indicates that I-DIC residuals are slightly higher than those of T3-DIC analyses. This is to be expected because the number of degrees of freedom are signicantly reduced in I-DIC in comparison with T3-DIC leading to a much more restricted solution space. The fact that the dierences are insignicant is an additional validation that Williams' series form a suitable reduced kinematic basis. It is also interesting to see how much p f = 3 deviates from the other two truncations as the crack grows (see Figure4(b) after image 70). This trend reinforces the fact that higher p f are required, especially for longer cracks.

Figure 2

 2 Figure 2 already illustrated the challenges faced in the present case. Fig-

Figure 5

 5 Figure 5 about here

Figure 6

 6 Figure 6 about here

Figure 7

 7 Figure 7 about here

Figure 1 (

 1 b) shows the loading curve of the cyclic test with the ve cycles. Small oscillations are observed, which in turn explain part of the uctuations on the reported SIFs and T-stress histories.

Figure 9 about here 5 .

 5 Figure 9 about here

4 ( 36 5 37 6 9 RFigure 1 :

 4363791 Figure 1: (a) Picture showing the geometry of WST. The surface has been prepared for DIC purposes. The wedge and cylinders used for the loading are highlighted. H ef f corresponds to the loaded height, a is the crack length considering the loading point as a = 0, and ∆a is the measured propagation increment. (b) Loading curves with blue dots showing machine acquisition and red circles interpolated points for each image taken during the test

Figure 2 :

 2 Figure 2: Displacement elds for the maximum applied load (i.e., image 96) without considering rigid body translations. (a) Displacements in x direction. (b) Displacements in y direction. Note that the maximum amplitude is less than 0.5 pixel (or 31 µm)

Figure 3 :Figure 4 :[ 3 Figure 5 :

 3435 Figure 3: Results for three dierent numbers of terms in Williams' series (p f = [3, 8, 13]). The rst plot shows the actuator displacement and the second one the loading history. The vertical solid lines are related to the start of each loading and unloading parts. The vertical dashed lines mark the maximum load level for each cycle. The third plot shows the measured crack length with the present methodology. Stress Intensity Factors (SIFs) for mode I in solid lines and mode II in dotted lines are shown in the third graph. The T-stress is nally plotted

Figure 6 :Figure 7 :Figure 8 : 2 ]Figure 9 :

 67829 Figure 6: Results for three dierent numbers of terms in Williams' series (p f = [3, 8, 13]).Same ve plots reported in Figure3, showing the actuator displacement, the loading history, the measured crack length, the Stress Intensity Factors (SIFs) for mode I in solid lines and mode II in dotted lines and the T-stress, respectively. The vertical solid lines are related to the start of each loading and unloading parts. The vertical dashed lines mark the maximum load level for each cycle

Acknowledgements

This work was partially supported by BPI France (DICCIT project). JAR thanks CNPQ for the productivity scholarship, grant #307127/2013-3. RV's stay at LMT was supported through an RIA scholarship, grant #2015/11104-7, São Paulo Research Foundation (FAPESP).


Jackei K Wong

Wilfred K Lin
email: wilfred.lin@gmail.com

Jackei H K Wong

Wilfred W K Lin

An Overview of Semantically-Based TCM Telemedicine Systems

Keywords: Semantic Network, Ontology, Telemedicine, Traditional Chinese Medicine

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The knowledge of Traditional Chinese Medicine (TCM) has existed for more than 3000 years till now, while TCM practices are in various forms according to different geographical and environmental constraints. The exchange of medical knowledge and clinical experience was limited due to transportation difficulties, language barriers etc. As times go by, the stored medical information has been gradually refine to constitute more than 5000 pieces of works in extant. Useful herbal ingredients including plant parts, minerals and animal matter have been added and incorporated into the conceptual TCM pharmacopeia.

Traditional Chinese Medicine (TCM) has been widely used for many centuries in China, it is gaining more and more adoption all over the world. The trends in the use of TCM will be aided by standard and uniform vocabulary and an agreed consensus by the domain expert, it is crucial to capture the underlying clinical TCM body of knowledge and practices in a computer-based representation. This has a semantic basis in which the focus is on the meaning of the knowledge but not the syntactic format of its representation. Ontology will be utilized as well to make the knowledge more readily searchable and queried.

TCM & Telemedicine

One of the earliest definitions of the notion of Telemedicine can be found in the publication [START_REF] Lacroix | G-7 Global Healthcare Applications Sub-project 4[END_REF]. It refers to make use of the Internet to deliver medical care to every corner all over the world. Thus, those web-based medical system has at least some telemedicine elements, independent of its scale. Telemedicine systems can be broadly divided into different types, according to their goals and functions as follows: a)

Curative Systems -medical practitioners use the system to achieve the diagnosis and treatment goals. b)

Consultative Systems -through the system interface the user can obtain needed information, such as information about named patent drugs, and addresses/expertise of medical practitioners in the region/vicinity. c) Medical Information Management Systems in terms of data storage and retrieval (e.g. medical images). d)

Decision Support Systems -this happens in various forms, for example, the physician, who is using a telemedicine system (e.g. the PuraPharm's D/P (diagnosis/prescription) system in a mobile clinic [START_REF] Jackei | TCM (Traditional Chinese Medicine) Telemedicine with Enterprise Ontology Support -a Form of Consensus-Certified Collective Human Intelligence[END_REF] may import biometric reports to aid the diagnostic decision/precision as shown by Fig. 2.1.

Fig. 2.1 Imported information to aid diagnosis

The aim of doing this is to let people including non-medical domain expert and registered medical personnel consult and verify knowledge if necessary from the knowledge base. Yet, a knowledge base can be for a general purpose and similar to a dictionary in this sense. It also help experts to clarify doubts due to multi-representations owing to disparate national or regional conceptions of a medical phenomenon. A typical example in the Western/allopathic medicine area is the UMLS (Unified Medical Language System [UMLS]), which was developed by the US National Library of Medicine to resolve the differences in Western/allopathic clinical terminology due to regional and/or national disparities. The UMLS is ontology-based. Another ontologybased system is the disease and treatment ontology for Western Allopathic Medicine [Hadzic05 and Hadzic10]. By its nature the UMLS is not for frontline clinical application to allow computer-aided diagnosis and treatment in contrast to the PuraPharm's TCM (Traditional Chinese Medicine) telemedicine mobile clinic (MC) system. The UMLS is consultative in nature. That is, it is not a clinical system but a consultation setup that people can interact with to sort out terminology problems. Therefore, its aim is to provide an interactive learning, reference, and bridging mechanism for knowledge gaps in a global sense. For example, in conventional/Western/allopathic medicine different countries may have different definitions for an observed phenomenon. In order to resolve the similarity and differences of various definitions, as well as language peculiarities on a global scale, meta-thesauri can serve as an effective means as shown by the UMLS.

Explicit & Implicit Semantics

If a single statement composed of a string pattern which can induce various interpretations for different people with different perspectives, the semantics of this string is then considered implicit. This is similar to deciphering the embedded logic in a given program without its original detailed specification. The logical representation can vary from one interpreter to another. For example, the hierarchy represented in the UML (Unified Modeling Language) style in Fig. 3.1 can result in ambiguous interpretations (i.e. semantics) from different people for the "logical points" a and b, which can be logically AND or OR; vice versa; or EXLUSIVE OR, leading to unexpected results. For curative medicine, this kind of logical freedom is disadvantageous to the patients. For this reason the semantics in the ontology must be explicitly defined by the principle of "single meaning for every semantic path". The 3-dimensional subsumption hierarchy in Fig. 3.2 contains many operations or semantic paths (e.g. {3,5,8} and {3,6,9}). Yet, from a 2-dimensional viewpoint Fig. 3.1 is simply a network representation of many possible operational paths (i.e. traversal paths) between any two points. To create an operational ontology-based system (with a mini-ontology) out of this tree, it is necessary to elaborate this 2-dimensional view into a 3-dimensional one. Then, the focus is represented by the chosen "lead", which in reality is the first point where the parsing mechanism begins to process. For example, if node 1 is the chosen lead for parsing in Fig. 3.2, then the possible 14 semantic paths for the 3-dimensional subsumption hierarchy are the following: {1,2}; {1,3}; {1,3,5}; {1,3,5,8}; {1,3,6}; {1,3,6,9}; {1,3,6,10}; {1,4}; {1,4,7}; {1,4,7,6}; (1,4,7,6,9}; and {1,4,7,6,10}. If every semantic path is supported by only a single dedicated software module/object, then the meanings of the set of semantic paths (represented by the equal number of software modules or objects) form the lexicon for this particular system. As a result, the system always gives a clear, consistent and unambiguous (i.e. explicit) answer to every query, which is another form of a semantic path in the lexicon. Although the semantic paths in the lexicon are explicit, every query is constructed "implicitly" or with user-transparency according to the input sequence of the atomic elements. In fact, the semantic paths can be further classified into more specific semantic groups for various goals, similar in fashion to the conceptual UMLS framework.

Ontology-based TCM Telemedicine System -Major Aspects

The focus of this paper is to give an overview of the semantic TCM telemedicine system. The following aspects should be addressed:

a) Ontology Modelling b) Ontology Implementation Tool c) Internet Capability d)
Cross-layer Logical Transitivity e)

Automatic System Generation f) Pervasive Support g) Ontology Evolution

Ontology Modelling

The design of the system begins with the ontology model blueprint layout followed by the consensus certification. The ontology includes the whole or part of the formalisms and knowledge in the relevant domain. In this sense, an ontology-based system is data/knowledge oriented. This model should be understandable by both TCM domain experts and system developers so as to facilitate evaluation and critiquing of the ontology by the domain experts for correctness and completeness.

Ontology Implementation Tool

The tool is usually a high level language, which can correlate all the concepts in the ontology into a logical subsumption hierarchy. The ontology modelling blueprint is mainly for human understanding, and the embedded subsumption hierarchy should be translated meticulously into the corresponding semantic network for machine understanding/processing/execution. Therefore, it is necessary to choose a tool that has the support of "ontology model blueprint-to-semantic-net translation". It is better for the conversion process to be automatic [START_REF] Jackei | An Ontology Supported Meta-Interface for the Development and Installation of Customized Web-based Telemedicine Systems[END_REF]. In this light, the languages (or metadata models/systems) proposed by W3C (World Wide Web Consortium) [START_REF] W3c | Ontology Definition MetaModel[END_REF][START_REF]W3C, Web Service Architecture[END_REF], namely, XML (Extensible Mark-up Language), RDF (Resource Description Framework), and OWL (Web Ontology Language) are good to choose from, as they have widespread automatic translation support.

Internet Capability

Telemedicine relies on the Internet to achieve different goals on the web. For example, the telemedicine system may send out analysts or data-miners to search the web for necessary information to support the system's ontology evolution -the concept of a living ontology [START_REF] Jackei | Text Mining for Real-time Ontology Evolution[END_REF][START_REF] Lin | Artificial Neural Network Based Chinese Medicine Diagnosis in Decision Support Manner and Herbal Ingredient Discoveries, Data Analytics for Traditional Chinese Medicine Research[END_REF][START_REF] Allan | Semantically Based Clinical TCM Telemedicine Systems[END_REF]. This is well exemplified by the 2 nd generation of the PuraPharm D/P (diagnosis/prescription) telemedicine system that supports the YOT (a charitable organization in Hong Kong) mobile clinics in Hong Kong. These mobile clinics have been treating thousands of patients weekly in recent years.

Cross-layer Logical Transitivity

A practical telemedicine system should have a 3-layer architecture. These three layers are as follows:



Bottom Layer -the knowledge/database that embeds the subsumption hierarchy that represents the logical relationships among the physical data items/entities included in the consensus-certified ontology.  Middle Layer -this subsumption hierarchy is also realized in the middle layer as the semantic network for machine understanding and execution.  Top Layer -the query system that implements the ontology for user understanding and manipulation.

The three layers are logically clones of one another, and therefore they should have cross-layer semantic transitivity. With this transitivity any entity in any layer should have corresponding representations in the other two layers.

It is useful to compare the TCM Curative and Decision Support System with the 3 Layer Architecture of the UMLS consultation system. The UMLS is ontology-based and has three distinctive layers: i) the modularized query system (the modules are semantic groups) at the top level, ii) the middle logical semantic-net layer, which was constructed from the semantics embedded in the information of the bottom ontological layer, and iii) the bottom ontology is integrated by nature and normally has a subsumption hierarchy of various sub-ontologies of different origins [START_REF] Gruber | A Translation Approach to Portable Ontology Specification[END_REF][START_REF] Gruber | Toward Principles for the Design of Ontologies Used for Knowledge Sharing[END_REF][START_REF] Guarino | Ontologies and Knowledge Bases: Towards a Terminological Clarification, Towards Very Large Knowledge Bases: Knowledge Building and Knowledge Sharing[END_REF].

Fig. 4.4.1 The 3-layer UMLS hierarchy [UMLS]

There is, therefore, some similarity between the overall structures of the two systems even though one is used for Curative and Decision Support Purposes whilst this is used as a consultation system.

Automatic System Generation

Cross-layer semantic transitivity can be achieved correctly by automatic system generation or customization (ASG/C). This approach is a new software engineering paradigm, which requires the user to provide the ontology blueprint layout. With support of the master ontology, where the ontology specification is either a part or the whole of it, the ASG/C mechanism generates/customizes the final ontology-based system in one shot.

Pervasive Support

A telemedicine system requires the support of a wireless-based pervasive computing infrastructure (PCI), which maintains the smart space for the collaborating systems. In the PuraPharm mobile clinic environment, the collaborating systems are the mobile clinics. The essence of the PCI support is better explained by using the successful Pu-raPharm's mobile clinic (MC) based telemedicine D/P (diagnosis/prescription) system depicted in Fig. 4.6.1. The PCI maintains the smart space, which is each occupied by a mobile clinic. The mobile clinic then communicates with the central system, as well as its peers, via the wireless means provided by the PCI. The MC operation is semi-autonomous because the physician can treat the patient at the spot, but the case history of the patient may have to be downloaded from the central computer that runs the fast network. The MC has to inform the central system of its updated local drug inventory. The central system also collects the necessary MC statistics on-line for proactive planning and action. If the MC physician needs help in the diagnostic process, the central system would solicit the relevant information from other friendly sites via the Internet.

Ontology Evolution Approach

It is important that the TCM ontology keeps itself updated from time to time by taking into account the new knowledge and insights that are being generated as time passes. It should be able to absorb information from every fresh case into the "master" ontology as new knowledge. In this light, this master ontology is a living and evolving system. Hence, it is clear that there is a need for a framework of ontology evolution for the TCM ontology so that it reflects the new knowledge and insights. To achieve ontology evolution, we need to:



Ascertain the new knowledge  Represent this potential new knowledge temporarily in a form compatible with the ontology  Carryout consensus certification of this new potential new knowledge  Enhancing the master ontology only with the consensus certified portions of the new knowledge

In order to ascertain the new knowledge, a text mining approach will be utilized. The data and text mining approach suggests potential changes to the TCM ontology. A temporary representation of these potential changes is stored in a part of the master aliasing table. The proposed potential changes to the ontology are then subject to consensus certification by a panel of TCM domain experts, and only those changes that are approved by this consensus certification are then included into the master TCM ontology through the master aliasing table.

Conclusion

This paper discussed an overview of semantically-based TCM telemedicine systems. The underlying principles of such a TCM telemedicine system were briefly explored. The proposed future work is to apply the technique of deep learning and predictive analysis for diagnosis/prescription differentiation recommendations.

  Fig. 3.1 Implicit logical representation -implicit semantics (bilingual)

Fig. 4

 4 Fig. 4.6.1 A PuraPharm's pervasive MC-based telemedicine D/P system


Liang Zhao
email: zhaoliang0415@gmail.com

Jia Jia
email: jjia@tsinghua.edu.cn

Ling Feng
email: fengling@tsinghua.edu.cn

Teenagers' Stress Detection based on Time-Sensitive Micro-blog Comment/Response Actions

Accurately detecting psychological stress in time is a significant issue in the modern stressful society, especially for adolescents who are not mature enough to cope with pressure well. Micro-blog offers a new channel for teens' stress detection, since more and more teenagers nowadays prefer to express themselves on the lively virtual social networks. Previous work mainly rely on tweeting contentsto detect tweeters' phycological stress. However, a tweet is limited to 140 characters, which are too short to provide enough information to accurately figure out its tweeter's stress. To overcome the limitation, this paper proposes to leverage details of social interactions between tweeters and their following friends (i.e., time-sensitive comment/response actions under a tweet) to aid stress detection. Experimental results through a real user study show that time sensitivity of comment/response acts plays a significant role in stress detection, and involving such interaction acts can improve the detection performance by 23.5% in F-measure over that without such interactions.

Introduction

The increasingly faster life pace in the competitive society often makes people stressful, especially for teenagers who are too immature to deal with psychological pressures. Currently, 20% teenagers have psychological illness around the world [START_REF]Sohu news[END_REF]. An online survey of 1018 U.S. teens (aged [START_REF] Park | Perception differences between the depressed and non-depressed users in twitter[END_REF][START_REF] Tan | User-level sentiment analysis incorporating social networks[END_REF][START_REF] Wang | A depression detection model based on sentiment analysis in micro-blog social network[END_REF][START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF][START_REF] Yang | How do your friends on social media disclose your emotions[END_REF] made by the American Psychological Association in August, 2013 found that teens suffered stress in all areas of their lives, from school to friends, work and family, which negatively affected every aspect of their lives, and about 27% of the teens experienced extreme stress and 55% experienced moderate stress in the past school year [4]. If such pressures cannot get properly relieved in time, the teenagers will suffer severe physical and mental problems under accumulated pressures, such as clinical depressions, insomnia, and even committing suicide. According to China Center for Disease Control and Prevention [START_REF]The week news[END_REF], suicide has become the top cause of death among Chinese youth, and excessive stress is considered to be a major factor of suicide. Also in Korea, suicide has become teenagers' No.1 killer in the past two years [START_REF]Sohu news[END_REF]. Annual increase of adolescent suicide rate has become a world-wide common problem.

As adolescence is a critical period for one's growth and development, it has significant value to pay attention to teenagers' psychological status and discover their suffering pressures in time. With the popularity of social networks, micro-blog offers another low-cost sensing channel to analyze teenagers' psychological pressures through their tweets, since more and more teenagers turn to micro-blog for information acquisition, personal interaction, self-expression, and emotion release. Some research work has already made efforts to detect user's stress and depression through micro-blog by analyzing their tweeting behaviors [START_REF] Park | Perception differences between the depressed and non-depressed users in twitter[END_REF][START_REF] Choudhury | Prediction depression via social media[END_REF][START_REF] Choudhury | Social media as a measurement tool of depression in populations[END_REF][START_REF] Shen | Exploiting temporal information in a two-stage classification framework for content-based depression detection[END_REF][START_REF] Wang | A depression detection model based on sentiment analysis in micro-blog social network[END_REF]. Leveraging tweeting contents such as linguistic and visual features to analyze user's stress has been proven feasible [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF][START_REF] Lin | Psychological stress detection from cross-media microblog data using deep sparse neural nework[END_REF]. However, a tweet faces the limitation of only 140 characters, which is too short to provide enough content information to figure out stress and sometimes users may not express their stress so directly. To address the limitation, we propose to further involve comment/response acts under the tweet (comments, responses, likes and forwards) to better supplement stress detection. Such interactions are attached with unique timestamps. Considering time sensitivity, we select the interactions within a certain time gap right after the tweet is posted and construct a timesensitive feature space for stress detection together with content of the tweet. Based on [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF], we combine the content of both the tweet and time-sensitive comment/response acts under the tweet to extract content features for the four stress categories (academic, affection, interpersonal, self-cognition), respectively. From the observations that stressful tweets often receive more comments from friends, especially comments with care, comfort and encourage, and the psychological study [START_REF]Social media and the cost of caring[END_REF] that users get inactive when suffering stress, we extract several novel interacting behavior features such as effective comment rate, reply rate, effective reply rate, and average interaction depth to help improve the stress detection. Our user study of 36 high school teenagers shows that time sensitivity of comment/response acts plays a significant role in stress detection and such acts in 30 minutes after the tweet posted are proved to be the most effective. Involving such interaction acts improves the detection performance by 23.5%.

To the best of our knowledge, this is the first work combining tweet contents and time-sensitive comment/response acts under the tweet for stress detection. There are also no previous stress detection work, specifying features for different stress categories.

The remainder of the paper is organized as follows. We review the related work in Section 2. Section 3 analyzes and extracts features from time-sensitive comment/response acts for teens' stress detection. Experimental performance through a real user study is evaluated in Section 4. Finally, we conclude the paper in Section 5.

Related Work

Computer-aided sentiment analysis and applications in social network has drawn much attention in recent years [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF][START_REF] Li | Helping teenagers relieve psychological pressures: a micro-blog based system[END_REF][START_REF] Lin | Psychological stress detection from cross-media microblog data using deep sparse neural nework[END_REF][START_REF] Zhang | Moodcast: emotion prediction via dynamic continuous factor graph model[END_REF]. Many studies focus on the single tweet, leveraging content features such as text-based linguistic attributes and visual factors such as emoticons and images. [START_REF] Zhao | Moodlens: an emoticon-based sentiment analysis system for chinese tweets[END_REF] proposed a system called Moodlens to do sentiment analysis for Chinese Weibo via emoticons in tweets. The emoticons are divided into four different sentiment categories (i,e, angry, disgusting, joyful and sad), and a fast Naive Bayes classifiers works for the sentiment analysis of tweets.

Beside the content features, simple social interaction attributes are also involved. [START_REF] Lin | User-level psychological stress detection from social media using deep neural network[END_REF] proposed to detect user's psychological stress from social media via a deep convolution network on sequential time series in a certain time period. Simple social features like the number of -mentions, -replies, comments and likes are considered. User-level social connections such as (mutually) follow relationships and (mutually) -mentioned relationships were also investigated in [START_REF] Tan | User-level sentiment analysis incorporating social networks[END_REF] to improve sentiment analysis in Twitter. [START_REF] Yang | How do your friends on social media disclose your emotions[END_REF] explored comments to help predict emotions expressed by images posted on Flickr. However, time sensitivity of such social interaction attributes is not considered in these work.

The most closest related work is [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF][START_REF] Lin | Psychological stress detection from cross-media microblog data using deep sparse neural nework[END_REF]. Focusing on the four main kinds of stress (academic, affection, interpersonal and self-cognition) that troubles teenagers, [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF] extracted different features from teenagers' tweets, such as negative emotion words, negative emoticons, unusual post time and post frequency, etc., and several classifiers were leveraged to learn the potential stress category and corresponding stress level (0-5) behind the tweet. However, [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF] only considered the content and unusual posting behavior of the tweet, ignoring social interactions such as comments and replies under the tweet. Besides, the detection process only returns one stress category and one level for a single tweet, but actually a single tweet may express several kinds of stress with different levels. [START_REF] Lin | Psychological stress detection from cross-media microblog data using deep sparse neural nework[END_REF] designed a deep sparse neural network to detect stress for arbitrary micro-blog users, using content features of the tweet including linguistic attributes as [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF], visual attribute like color theme, brightness, etc, and simple social attributes like number of comments, retweets and favorites. they do consider the social factors, but ignore the details such as content of comments and the interaction of friends' comments and author's reply under the tweet . They only detected whether the user suffers stress, but did not quantitatively measure the stress level. Similarly, [START_REF] Lin | Psychological stress detection from cross-media microblog data using deep sparse neural nework[END_REF] also returned one stress category for one single tweet. In addition, for both the two work, content features are not category-specified and features are all static, no time-sensitive factor considered.

Stress Detection with Time-sensitive Comment/Response Acts

Before introducing the details of stress detection, we first illustrate some notations used in the following of the paper by Table 1. And without loss of generality, we use interaction acts and comment/response acts interchangeably in the rest of the paper. Given a tweet p = T w (u, t 0 , cont, SI ∆t ), four kinds of interaction acts under p constitute SI ∆t , comments, likes, and forwards from friends, as well as user's responses. When ∆t is big enough, then SI ∆t contains all the comments, replies, likes and forwards under p.

As in [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF], let C ategory ={academic, affection,interpersonal,self-cognition} be the set of teenagers' stress categories involved in the study, and L evel ={null, light, moderate,strong} be the set of stress levels, where null means no-stress. For a single tweet p, we leverage time-sensitive interaction acts SI ∆t together with content of p to form a feature space. Exploiting classification methods, the stress detection result of p is represented as Stress(p) = ((C i , Lv 1 ), . . . , (C 4 , Lv 4 )), where C i ∈ C ategory and Lv i ∈ L evel . If ∀Lv i = null (i = 1, . . . , 4), then Stress(p) is a zero vector and p is a non-stressful tweet. Without loss of generality, we call those tweets with non-zero stress vector stressful posts.

F F = {f | f is a friend of u} Friend set of user u c c = comm(f, tc, cont, p), f ∈ F A comment

Modified Content Features

A tweet is only 140 characters limited which is too short to provide enough content information to figure out stress and sometimes users are not likely to express their stress so directly via a brief tweet. Through daily observations, content of the communication between the user and his/her friends under the tweet provides powerful cues to help analyze stress. We consider the content of user interactions with friends (i.e., comments from friends and the user's replies) as part of the tweet to supplement more content information. Assume the combined content of p is denoted as

CCont(p, ∆t) = ∪ f ∈F {c.cont, r.cont|c ∈ C omm (f, p, ∆t), r ∈ R ep (u, f, p, ∆t)} ∪ p.cont
Particularly, interactive comments and responses between user u and friend f are closely related in content and constitute a dialog. We take the content of dialog as a whole, and regard it as an item piece of CCont(p, ∆t). For each item piece in CCont(p, ∆t), we leverage a graph-based Chinese parser [START_REF] Che | Multilingual dependency-based syntactic and semantic parsing[END_REF][START_REF] Che | LTP: a chinese language technology platform[END_REF] to analyze linguistic associations, including the correspondence between stress categories and negative emotion words, and the grammatical relation between adverbs of degree and the modified negative emotion words, etc. A single tweet may convey several kinds of stress at the same time. Thus, for each stress category in C ategory , we specify content features from CCont(p, ∆t) as in [START_REF] Xue | Detecting adolescent psychological pressures from micro-blog[END_REF]. i.e., number of negative emotion words, number of positive and negative emoticons, number of exclamation and question marks, emotional degree, etc.

Time-sensitive Comment/Response Features

Comment/Response acts under a tweet is time-sensitive especially when the user is suffering from stress. For example, when a user posts a tweet expressing depression, his/her friends will always make in-time comments within a short time gap after the tweet is released. We select the interaction acts under the tweet p within [t 0 , t 0 + ∆t] to extract the comment/response features.

Commenting features from crowd Comments, likes and forwards are basic commenting features and always show the social attention to a tweet.

Number of comments from friends.

The set of all the comments under the tweet p within [t 0 , t 0 + ∆t] is

C omments (F, p, ∆t) = ∪ f ∈F C omm (f, p, ∆t)

Number of likes.

People always put a like seal on a tweet to show their positive emotion or attitude to the tweet. Compared with those positive tweets, stressful tweets (negative tweets) obtain much less likes, even no like. We take the number of likes under a tweet as an indicator of potential stress, denoted as |L ikes (F, p, ∆t)|.

Number of forwards.

Users tend to forward public information such as news, advertisements and jokes, and seldom retweet personalized stressful tweets of another user. So stressful tweets enjoy less possibility to be forwarded by friends. The number of forwards here is denoted as |F wrds (F, u, p, ∆t)|.

Number of effective comments. Among all the comments from friends, we further check the details of the comments and distinguish those containing care, comfort, or encourage (e.g., "What's up?", "Don't worry", "Everything will be OK", or hug emoticon, etc.). Such comments are considered as effective comments. The set of effective comments under tweet p is denoted as EC omments (F, p, ∆t). A lexicon with 132 such Chinese phrases, sentences and emoticons is constructed to identify effective comments. A tweet with more effective comments is more likely to be stressful.

Effective comment rate (short for ECR, denoted as ECR(F, p, ∆t)) is calculated as

ECR(F, p, ∆t) =

|EC omments (F, p, ∆t)| |C omments (F, p, ∆t)| + 1 where |(•)| stands for the number of items in set (•) and we smooth the equation by adding 1 upon denominator. Obviously, a higher ECR denotes a bigger probability that the tweet is stressful.

Particularly, with any two of the three features (number of comments/effective comments and effective comment rate) we can deduce the other one. Thus, for commenting features we can choose any two.

Replying features of the user

Besides the social behaviors of the crowd (friends), behaviors of the user himself also make sense in stress detection. Psychological study [START_REF]Social media and the cost of caring[END_REF] shows that a user in stress may perform low activeness in social networks. Such inactiveness can be revealed from user's reactions to the comments from friends. Three features corresponding to the user's replying behaviors are identified.

Reply rate. If a user is absorbed in big stress, s/he tends to be inactive, which can be revealed from his/her activeness of reply to the comments. The reply rate (short for RR, denoted as RR(u, p, ∆t)) is calculated by the rate of replies over total number of comments. Assume R eplies (u,

F, p, ∆t) = ∪ f ∈F R ep (u, f, p, ∆t)
is the set of user replies to all the friends under p, then

RR(u, p, ∆t) = |R eplies (u, F, p, ∆t)| |C omments (F, p, ∆t)| + 1
A lower reply rate suggests that the user is not so active and it is highly possible that s/he is suffering stress. Similarly, among the three features (number of comments/replies, and reply rate), we can deduce the other one with any two.

Effective reply rate. Effective replies are those responses to the effective comments. The set of effective replies under p within [t 0 , t 0 + ∆t] is

ER eplies (u, F, p, ∆t) = {r|r.c ∈ EC omments (F, p, ∆t), r.t r ∈ [t 0 , t 0 + ∆t]}
We measure the effective reply rate (short for ERR, denoted as ERR(p, ∆t)) by the proportion of effective reply over the total number of effective comments.

ERR(p, ∆t)

= |ER eplies (u, F, p, ∆t)| |EC omments (F, p, ∆t)| + 1
Average interaction depth with friends. A friend may comment multiple times under the same tweet, and the user may also make corresponding replies. Then, such interaction between them constitutes a dialog. In the dialog, once a new comment-reply pair comes, the interaction depth between the friend and the user accordingly increases by 1. Assume a friend f and the user u make a comment-reply dialog under tweet p, then the interaction depth between f and u in tweet p within [t 0 , t 0 + ∆t] is calculated as

iDep(f, u, p, ∆t) = min(|C omm (f, p, ∆t)|, |R ep (u, f, p, ∆t)|)
For all the friends who comment the tweet, the average interaction depth is computed by

avg iDep(F, u, p, ∆t) = 1 |F | ∑ f ∈F iDep(f, u, p, ∆t)
The average interaction depth reveals the user's activeness as well. The smaller the average interaction depth is, the less active the user performs, so that s/he has a higher risk of stress suffered.

Experimental Study

Setup

Psychological stress detection is a highly personalized issue and there are no available benchmark specially for the problem. In this work, we collect data ourselves and conduct a user study on a real micro-blog data set. 36 high school students (15 males and 21 females, aged between 15 and 17) in Shaanxi Province, China, participated in the user study. 21,648 tweets from 2013/1/1 to 2015/5/1 were collected from their accounts in Tencent Weibo1 , averagely 636 tweets per teenager. Recalling the real situations, they were asked to scan their own tweets one by one and annotated the psychological stress on the four stress categories in C ategory and corresponding stress levels in L evel expressed in each single tweet. We take the annotation as the ground truth. For each teenager, chronologically, we use the early 66% of his/her tweets as the training data, and the rest 34% as the testing data.

General Performance of Comment/Response acts

Four different classifiers, including Naive Bayes, Logistic, SVM and Gaussian Process are used to perform the single-tweet based stress detection over the feature space of each stress category, respectively. Precision and recall are leveraged to evaluate the performance. With the comment/response acts selected within ∆t after the tweet posted, assume for each stress category C i ∈ C ategory , T P (C i , Lv i , ∆t), T N (C i , Lv i , ∆t), F P (C i , Lv i , ∆t), F N (C i , Lv i , ∆t) represents the number of true positive, true negative, false positive and false negative samples detected of stress level Lv i , respectively. Thus,

P recision(C i , ∆t) = 1 |L evel | ∑ Lvj ∈L evel precision(C i , Lv j , ∆t) Recall(C i , ∆t) = 1 |L evel | ∑ Lvj ∈L evel recall(C i , Lv j , ∆t)
where precision(C i , Lv j , ∆t) = T P (Ci,Lvj ,∆t) T P (Ci,Lvj ,∆t)+F P (Ci,Lvi,∆t) , and recall(C i , Lv j , ∆t) = T P (Ci,Lvj ,∆t) T P (Ci,Lvj ,∆t)+F N (Ci,Lvj ,∆t) . Table 2 compares the performance with ∆t = 30 minutes. Averagely speaking, Logistic and SVM work the best in the four classifiers for all the stress categories, with the average F-measure over 70%, which is 10.7% better than NB, and 50% better than Gaussian.

Investigation of Time Sensitivity

We investigate the time sensitivity of comment/response acts with different ∆t value. Logistic is selected as the classifier in this experiment since it performs the best of the three. Different time gap ∆t (= 10, 20, 30, 40, and +∞ minutes) are selected to extract comment/response features, where all the interaction acts under a tweet are involved when ∆t = +∞. Fig. 1 shows the performance of different time sensitivity (∆t). Obviously, for each stress category, the detection results are time-sensitive. With the increase of ∆t, the performance first improves and then falls again as ∆t getting bigger. Particularly, when ∆t = 30min, the detection performance reaches a peak, with the average F-measure over 70%. The result coincides with our daily observation. When a user posts a stressful tweet, his/her friends often comments in time to express care, comfort and encourage. With ∆t increases within [0, 30] (counted in minute), such effective information accumulates and makes the detection more accurate.

Impact of Comment/Response Acts

Table 3 compares the detection performance with/without comment/response acts under Logistic classifier. We set ∆t = 30 minutes for time-sensitive interaction acts. Due to user's indirect expression, without interaction acts cannot provide enough information and performs worse. When involving the comment-/response acts, the average F-measure for all the stress categories reaches over 70%, outperforms the other case 23.5%, which proves the significance of timesensitive comment/response acts in stress detection.

Conclusion

In this paper, together with content of tweets, we involve time-sensitive comment/response acts under a tweet to help better detect stress revealed from a

Fig. 1 .

 1 Fig. 1. Performance with different time sensitivity (∆t)

Table 1 .

 1 Notations covered in tweets

	Notation	Representation	Description
	p	p = Tw(u, t0, cont, SI

∆t ) A tweet posted by user u at time t0 with the content of cont, and set of time-sensitive interactions acts SI ∆t during [t0, t0 + ∆t]

  Set of replies to f within ∆t L ikes (F, p, ∆t) = {lk|∀f ∈ F, lk.t l ∈ [t0, t0 + ∆t]} Set of likes within ∆t F wrds (F, p, ∆t) = {f w|∀f ∈ F, f w.t f ∈ [t0, t0 + ∆t]} Set of forwards of p within ∆t

from f at time tc under tweet p, and cont is the content of the comment r r = rep(u, tr, c, cont, p) u's reply to comment c at time tr under tweet p, and cont is the content of the reply lk lk = like(f, t l , p), f ∈ F Friend f puts a like seal on p at t l fw f w = f wrd(f, t f , p), f ∈ F Friend f forwards p at time t f Comm(f, p, ∆t) = {c|c.tc ∈ [t0, t0 + ∆t]} Set of comments from f within ∆t Rep(u, f, p, ∆t) = {r|r.tr ∈ [t0, t0 + ∆t]}

Table 2 .

 2 General Performance (∆t = 30 minutes)

	Stress	Naive Bayes Prec. Rec. F-ms. Prec. Rec. F-ms. Prec. Rec. F-ms. Prec. Rec. F-ms. Logistic SVM Gaussian
	Aca 0.69 0.69 0.69 0.71 0.67 0.69 0.73 0.67 0.70 0.77 0.70 0.73
	Aff 0.53 0.72 0.61 0.81 0.72 0.76 0.87 0.81 0.83 0.44 0.38 0.41
	Inter 0.67 0.70 0.68 0.81 0.72 0.76 0.73 0.63 0.67 0.56 0.36 0.44
	Self 0.60 0.66 0.53 0.69 0.67 0.68 0.66 0.64 0.65 0.32 0.33 0.33
	Avg. 0.

62 0.69 0.65 0.76 0.70 0.72 0.75 0.69 0.71 0.52 0.44 0.48

Table 3 .

 3 Comparison with/without comment/response acts

	Stress	Without C/R acts Prec. Rec. F-meas. Prec. Rec. F-meas. With C/R acts
	academic	0.596 0.553 0.574 0.713 0.669 0.690
	affection	0.558 0.579 0.568 0.808 0.722 0.763
	interpersonal 0.744 0.613 0.669 0.808 0.722 0.763
	self-cognition 0.553 0.5	0.568 0.693 0.667 0.679
	avg.	0.

613 0.561 0.586 0.756 0.695 0.724 teenager

  's tweet. Focusing on the four main categories of adolescent stress (academic, affection, interpersonal, and self-cognition), we specify content features for each stress category, and involve several novel features extracted from timesensitive comment/response acts. 33 high school students aged 17 participated in our user study to evaluate the framework. Experimental results show that stress detection performance varies with different time sensitivity, and involving comment/response acts can better improve the F-measure of multi-category stress detection by 23.5%.

One of the biggest Chinese micro-blog platform, http://t.qq.com/

Acknowledgement

The work is supported by National Natural Science Foundation of China (61373022, 61370023, 61073004), and Chinese Major State Basic Research Development 973 Program (2011CB302203-2).


Trung Van Nguyen

Jason J Jung
email: j2jung@gmail.com

Hanh Huu Hoang

A Novel Approach for Resolving Knowledge Inconsistency on Ontology Syntactic level

Keywords: ontology integration, consensus theory, syntactic level, conjunction, inconsistency

Solving the inconsistency of knowledge is a challenging task in the ontology integration. There are two levels for processing knowledge inconsistence which are based on logics: syntactic level and semantic level. In this paper, we propose a consensus-based method to resolve inconsistent knowledge on the syntactic level, where a knowledge state can be represented by a conjunction of literals.

Introduction

The inconsistency consists of two levels in knowledge processing based on logics [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]: the syntactic level and the semantic level. In the syntactic level, knowledge states can be represented by logic expressions, and they are in conflict if expressions' syntaxes are different. Meanwhile, in the semantic level, the knowlege inconsistency and consistency are considered further at their interpretations [START_REF] Van Nguyen | A Consensus-Based Method for Solving Concept-Level Conflict in Ontology Integration[END_REF].

In this paper, we propose a consensus-based method to resolve the knowledge inconsistency on its syntactic level. One of the most important things in consensus-based methods is the distance function of two elements in the universe set. There have been several and similar approaches to evaluate distance between two logic expressions: Zhisheng Huang, Frank van Harmelen [START_REF] Huang | Using semantic distances for reasoning with inconsistent ontologies[END_REF] measure a so-called relevance between two formulas by considering the number of their common and different symbols. Ferilli [START_REF] Ferilli | Plugging Taxonomic Similarity in First-Order Logic Horn Clauses Comparison[END_REF][START_REF] Ferilli | Similarity-Guided Clause Generalization[END_REF] further considered occurrences of objects, predicates in the formulas based on taxonomic background knowledge such as WordNet ontology. We assume that, a knowledge state can be expressed as a conjunction of literals as [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]. However, by using other distance function of two sets of symbols than [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF], we analyse and prove some interesting properties of postulates for consensus functions. Based on these properties, we propose a new algorithm for determining the consensus for a conflict profile of conjunctions.

Our paper will be detailed and structured as follows: Section 2 formalises the problem of determining the consensus for a conflict profile of conjunctions. Meanwhile, Section 3 presents postulates for the consensus function and analyse their properties. Based on this, we propose a new algorithm for determining the consensus in Section 4. The paper is then concluded with discussions and future work in Section 5.

Problems of determining consensus for a conflict profile of conjunctions

In this section, we recall essential notions directly used in formalising the problem of determining the consensus for a conflict profile of conjunctions in Nguyen's work [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]. Assume that, for expressing opinion about a subject in the real world, an expert agent uses a conjunction of literals t 1 ∧t 2 ∧. . . t k , where t i ∈ L or t i = ¬t i and t i ∈ L. L is a definite set of symbols, which expresses a positive logic value, reference to an event in the real world.

A conjunction x can be expressed as (x + , x -), where x + contains t ∈ L, and x -contains t and ¬t ∈ L. For example, x = a ∧ ¬b ∧ c, which a, b, c ∈ L can be written as (x + , x -), where x + = {a, c} and x -= {b}.

By Conj(L) we denote the set of all conjunctions with symbols from set L.

Definition 1 (Nonconflicting conjunction) A conjunction (x + , x -) where

x + , x -⊆ L is nonconflicting if x + ∩ x -= ∅ .
Definition 2 (Inconsistent conjunctions, sharply inconsistent conjunctions) Let x = (x + , x -), x = (x + , x -) ∈ Conj(L) are nonconflicting conjunctions. We say:

(a) x is inconsistent with x if

x + ∩ x -= ∅ or x + ∩ x -= ∅ , (b)
x is sharply inconsistent with x if they are inconsistent and

x + ∩ x + = ∅ and x -∩ x -= ∅ .
Definition 3 A set of nonconflicting conjunctions

X = x i = (x + , x -) ∈ Conj(L) : i = 1, 2, . . . , n is inconsistent if x∈X x + ∩ x∈X x -= ∅, otherwise it is consistent.
Then we propose an our own distance function d ∧ for conjunctions. This function is based on the distance between sets of symbols.

Definition 4 (Distance between two finite sets) By the distance between two finite sets X 1 , X 2 we understand the following number

η(X 1 , X 2 ) = card(X 1 X 2 ) card(L) (1)
where, card(L) is the number of elements in L, and X 1 X 2 is symmetric difference of the two sets X 1 and X 2 .

Definition 5 (Distance between two conjunctions [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]) By the distance between two conjunctions x 1 , x 2 ∈ Conj(L) we understand the following number

d ∧ (x 1 , x 2 ) = w 1 .η(x + 1 , x + 2 ) + w 2 .η(x - 1 , x - 2 ) ,
where

• η(x + 1 , x + 2 )
is the distance between sets of nonnegated symbols in conjunctions

x 1 and x 2 . • η(x - 1 , x - 2 )
is the distance between sets of negated symbols in conjunctions x 1 and x 2 .

• w 1 , w 2 are the weights of distances η(x

+ 1 , x + 2 ) and η(x - 1 , x - 2 ) in distance d ∧ (x 1 , x 2 )
, respectively, which satisfy the conditions:

w 1 + w 2 = 1 and 0 < w 1 , w 2 < 1 .
In this paper, we use

w 1 = w 2 = 1 2 .
By U we denote a finite set of objects representing possible values for a knowledge state. We also denote:

• k (U) is the set of all k-element subsets (with repetitions) of set U (k ∈ IN, set of natural numbers). • (U) = k∈IN k (U)
is the set of all nonempty subsets with repetitions of set U. An element in (U) is called as a conflict profile.

The problem of determining consensus for a conflict profile of conjunctions is formulated as follows [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]:

For a given conflict profile of conjunctions

X := {x i = (x + i , x - i ) ∈ Conj(L) : i = 1, 2, . . . , n}.
It is necessary to determine a conjunction x * ∈ Conj(L), called as a consensus of X.

Consensus functions and Postulates for consensus

We also start with recalling definitions in [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF]:

Definition 6 (Consensus function for profiles) By a consensus function for profiles of conjunctions we understand a function

C : (Conj(L)) → 2 Conj(L) ,
which satisfies one or more of the following postulates.

P1. For each conjunction (x * + , x * -) ∈ C(X) there should be

x∈X x + ⊆ x * + and x∈X x -⊆ x * -. P2. For each conjunction (x * + , x * -) ∈ C(X) there should be x * + ⊆ x∈X x + and x * -⊆ x∈X x -. P3. If X is consistent then conjunction ( x∈X x + , x∈X x -) should be a consensus of X. P4. For each conjunction (x * + , x * -) ∈ C(X), there should be x * + ∩ x * -= ∅. P5. A consensus x * ∈ C(X) should minimize the sum of distances: x∈X d ∧ (x * , x) = min x∈X d ∧ (x , x) | x ∈ Conj(L)
P6. For each symbol z ∈ L and a consensus x * ∈ C(X), the form of appearance of z in x * depends only on its forms of appearance in conjunctions belonging to X.

In a consensus (x * + , x * -) ∈ C(X), set x * + (resp., set x * -) is called as the positive component (resp., the negative component).

By C co we denote the set of all consensus functions for profile of conjunctions. Then, we analyse properties of the postulates for consensus functions. We denote:

• A consensus function C satisfies a postulate P for a profile X written as C(X) P . • A consensus function C satisfies a postulate P for all profiles , written as C P . • A postulate P is satisfied for all consensus functions C ∈ C co , written as

C co P .
The first proposed theorem presented below shows that postulates P1 and P2 are the consequences of postulate P5. Let X ∈ (Conj(L)) is a profile of conjunctions, C ∈ C co is a consensus function which satisfies postulate P 5. Let (x * + , x * -) ∈ C(X) is a consensus of X. To prove P 1 is also satisfied by C, we have to prove

x∈X x + ⊆ x * + (2)
and

x∈X x -⊆ x * - (3)
For the first dependence, let's assume that x∈X x + x * + ; this means, there exists a symbol t ∈ x∈X x + such that t / ∈ x * + . In this case we create set x * = (x * + , x * -) where x * + = x * + ∪ {t}. For each x ∈ X, we have

η(x * + , x + ) = card(x * + x + ) card(L) = card((x * + ∪ {t}) x + ) card(L) .
Because of t / ∈ x * + and t ∈ x∈X x + , we have ∀x ∈ X:

card((x * + ∪ {t}) x + ) = card(x * + x + ) -1
So, we have ∀x ∈ X:

η(x * + , x + ) = card((x * + ∪ {t}) ÷ x + ) card(L) = card(x * + x + ) -1 card(L) < card(x * + x + ) card(L) = η(x * + , x + ) .
Finally, we have:

x∈X η(x * + , x + ) < x∈X η(x * + , x + ) d ∧ (x * , X) = x∈X 1 2 .η(x * + , x + ) + 1 2 .η(x * -, x -) < x∈X 1 2 .η(x * + , x + ) + 1 2 .η(x * -, x -) = d ∧ (x * , X)
This is contradictory to the assumption that (x * + , x * -) ∈ C(X) ∧ C(X) P 5 . So, we have (2) is satisfied. The (3) can be proved similarly.

(b) P 5 P 2 can be easily and similarly proved as the proof of P 5 P 1. We omit the proof due to the limit of pages.

Another property of the postulate P5 is also stated in [START_REF] Nguyen | Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing[END_REF], wherein definition of distance between sets, and therefor conjunctions are defined slightly different to ours in this paper, as: Theorem 2 The positive and negative components of a consensus satisfying postulate P5 can be determined in an independent way; that is, conjunction

(x * + , x * -) is a consensus of X if and only if conjunction (x * + , ∅) is a con- sensus of profile X = {(x i + , ∅) : i = 1, 2, . . . , n}, and conjunction (∅, x * -) is a consensus of profile X = {(∅, x i -) : i = 1, 2, . . . , n} [4].
Theorem 2 is still valid in our paper's context. However, this theorem does not show how to construct a consensus of a conflict profile. Actually, the consensus can be determined based on the following theorem.

Theorem 3 Let X = {x i , i = 1, 2, . . . , n} is a profile of conjunctions, X ∈ (Conj(L)). We denote

• Z + = x∈X x + . • Z -= x∈X x -. • f + (z) = card{x i ∈ X | x i + z}. • f -(z) = card{x i ∈ X | x i - z}.
Assume that C(X) satisfies postulate P5. In this case, x * = (x * + , x * -) is a consensus of X if and only if (a)

x * + = z ∈ Z + | f + (z) >= n 2 and (b) x -+ = z ∈ Z -| f -(z) >= n 2 .
Proof. As Theorem 2, we can formulate a consensus x * = (x * + , x * -) satisfying postulate P5 by independently formulating x * + and x * -for X + = {x i + , i = 1, 2, . . . , n} and X -= {x i -, i = 1, 2, . . . , n}. We have to prove that (a)

x * + = z ∈ Z + | f + (z) >= n 2
. The proof for (b) is similar.

First, as Theorem 1, x * + contains only literals belonging to Z + . We will prove that, for any conjunction x ∈ Conj(L), we have:

(i) If z ∈ Z + such that f + (z) ≥ n 2 and z / ∈ x + then d ∧ ((x + , x -), X + ) ≤ d ∧ ((x + ∪ {z}, x -), X + ), and (ii) If z ∈ Z + such that f + (z) < n 2 and z / ∈ x + then d ∧ ((x + , x -), X + ) > d ∧ ((x + ∪ {z}, x -), X + ).
We have:

d ∧ ((x + ∪ {z}, x -), X) = y∈X 1 2 . card((x + ∪ {z}) y + ) card(L) + 1 2 . card(x -y -) card(L)
and

card((x + ∪ {z}) y + ) card(L) =        card(x + y + ) -1 card(L) if y + z, card(x + y + ) + 1 card(L) if y + z. Let X z := {x ∈ X | x + z} and X z := {x ∈ X | x + z}. We have, card(X z ) = f + (z) and card(X z ) = n -f + (z). So: y∈X card((x + ∪ {z}) y + ) card(L) = y∈Xz card((x + ∪ {z}) y + ) card(L) + y∈Xz card((x + ∪ {z}) y + ) card(L) = y∈Xz card(x + y + ) -1 card(L) + y∈Xz card(x + y + ) + 1 card(L) = y∈X card(x + y + ) card(L) + -f + (z) + n -f + (z) card(L) = y∈X card(x + y + ) card(L) + n -2.f + (z) card(L) .
Finally, we have

d ∧ ((x + ∪ {z}, x -), X) = y∈X 1 2 . card((x + ∪ {z}) y + ) card(L) + 1 2 . card(x -y -) card(L) = y∈X 1 2 .( card(x + y + ) card(L) + n -2.f + (z) card(L) ) + 1 2 . card(x -y -) card(L) = d ∧ (x, X) + 1 2 . n -2.f + (z) card(L) Therefore, when n -2.f + (z) ≤ 0, or f + (z) ≤ n 2
, adding z to x + will not make increase sum of distances of x to X. Otherwise, when f + (z) < n 2 , adding z to x + will make increase sum of distances of x to X. Finally, (i) and (ii) are satisfied.

Back to proving (a), we can see that, start at the set z

∈ Z + | f + (z) >= n 2 ,
we can not remove any element(s) from this set, and can not add any other element(s) from Z + in process of determining the positive component of the consensus. Hence, this is the optimal positive component of consensus! ((a) is satisfied).

4 Proposed algorithm for determining consensus

Algorithm

Based on our proposed theorems in the previous section, we introduce an algorithm for determining the consensus x * = (x * + , x * -) for profile X ∈ (Conj(L)) as Algorithm 1.

Input: Profile X ∈ (Conj(L)), X = (xi + , xi -), i = 1, 2, . . . , n , xi + ∩ xi -= ∅ ∀i = 1,
foreach z ∈ Z + do f + (z) := card{x ∈ X | x + z}; foreach z ∈ Z -do f -(z) := card{x ∈ X | x -z};
(a)

x * + := {z ∈ Z + | f + (z) ≥ n 2 }; x * -:= {z ∈ Z -| f -(z) ≥ n 2 }; if (x * + ∪ x * -= ∅) then (b) foreach z ∈ x * + ∩ x * -do if d∧ (x * + \ {z}, x * -), X < d∧ (x * + , x * -\ {z}), X then x * + := x * + \ {z}; else x * -:= x * -\ {z}; else if (Z + ∩ Z -= ∅) then (c)
x * := (Z + , Z -); else (i) If both positive and negative of the P5-consensus are empty, the algorithm will find the consensus satisfying postulate P3 (step (c)) if X is consistent.

In case of X is inconsistent, as step (d), the algorithm will choose from X an element which has minimum sum of distances to others elements in X.

The consensus in this case satisfies postulate P4 (because

x i + ∩ x i -= ∅, ∀i = 1, 2, . . . , n).
(ii) If in step (a), the positive or negative component is not empty, we refine them for satisfying postulate P4, and also ensure that the sum of distances to elements in X is minimal.

Beside that, in all cases of the two above branches (i) and (ii), we construct x * + (respectively x * -) from Z + (respectively Z -). Therefore, the consensus always satisfies postulate P2. The consensus also satisfies postulate P1 because it construct from consensus which satisfies postulate P5, after that, elements which are removed because of their occurrences are smaller than n 2 .

The computational complexity of Algorithm 1 is O(n.m 2 ), where n is the number of elements in X, m = max card(

x∈X x + ), card( x∈X x -) .

Example

Let's assume that, to specify the property hasSpouse in an ontology, an agent can use a conjunction in Conj(L) where L = {t 1 , t 2 , t 3 , t 4 }. These symbols represent the following facts:

• t 1 : hasSpouse is symmetric.

• t 2 : hasSpouse is reflexive.

• t 3 : hasSpouse is functional.

• t 4 : hasSpouse is a subproperty of hasRelationshipW ith.

6 agents a 1 , a 2 , . . . , a 6 express their opinions as Table 1: We will use Algorithm 1 to determine consensus from opinions of the above 6 agents. Firstly, we formalize the profile X: X = ({t 1 , t 3 , t 4 }, {t 2 }), 2 * ({t 1 }, {t 3 , t 4 }), ({t 1 }, {t 3 }), ({t 3 }, {t 1 }), ({t3}, ∅) .

After step (a) of the algorithm, we have x * + = {t 1 , t 3 } and x * -= {t 3 , t 4 }. Because x * + ∪ x * -= ∅, we have to find a way to remove common literal(s) of the two components (as step (b)): With x * + ∩ x * -= {t 3 }, we compare two sums of distances d ∧ (({t 1 }, {t 3 , t 4 }), X) and d ∧ (({t 1 , t 3 }, {t 4 }), X). We easily have • d ∧ (({t 1 }, {t 3 , t 4 }), X) = 15 8 ,

• d ∧ (({t 1 , t 3 }, {t 4 }), X) = 13 8 .

Hence, consensus of X is ({t 1 , t 3 }, {t 4 }), or t 1 ∧ t 3 ∧ ¬t 4 .

Conclusion

In this paper, we formalised a method to determine the consensus of knowledge states presented as conjunctions of literals. We defined a distance between two conjunctions, proved relevant theorems for dependencies of postulates. Based on these theorems, we proposed a novel algorithm for determining the consensus for a profile of conjunctions.

As future work, we would like to analyse opportunities of using the more complex structure for presenting knowledge state than the conjunction or disjunction of literals. We also would like to apply the Algorithm 1 to determining consensus axioms in process of the ontological engineering in a wiki-based environment [START_REF] Tudorache | Supporting Collaborative Ontology Development in Protege[END_REF][START_REF] Tudorache | WebProtege: A collaborative ontology editor and knowledge acquisition tool for the web[END_REF] such as collaborative ontology development or ontological annotation.

Theorem 1 A

 1 consensus function C ∈ C co which satisfies postulate P5 should also satisfies postulates P1 and P2; that is (C P 5) ⇒ (C P 1 ∧ C P 2).

  Proof. We prove (a) (C P 5) ⇒ (C P 1) and (b) (C P 5) ⇒ (C P 2) as follow:(a) C P 5 ⇒ C P 1

2 ,

 2 . . . , n. Output: Consensus x * ∈ Conj(L) satisfies one or more postulates in {P4, P1, P2, P3, P5}. begin Z + := x∈X x + ; Z -:= x∈X x -;

x 1 :

 1 * := x1; for i := 2 to n do if d∧(x * , X) > d∧(x, X) then x * := xiAlgorithm Determine consensus for profile of conjunctionsAs shown in Algorithm 1, we start by finding the consensus satisfying postulate P5 (step (a)). After that:

Table 1 .

 1 Knowledge states for example

	Agent Knowledge state
	a1 t1 ∧ ¬t2 ∧ t3 ∧ t4
	a2	t1 ∧ ¬t3 ∧ ¬t4
	a3	t1 ∧ ¬t3
	a4	t1 ∧ ¬t3 ∧ ¬t4
	a5	¬t1 ∧ t3 ∧ ¬t4
	a6	t3

Acknowledgement This work was partly supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A05007154).