M Domínguez

J Pons

J Ricart

J Juillard

E Colinet

INFLUENCE OF THE FEEDBACK FILTER ON THE RESPONSE OF THE PULSED DIGITAL OSCILLATOR

This paper introduces a new feedback topology for the Pulsed Digital Oscillator (PDO) and compares it to the classical topology. The 'classic' or single feedback topology, introduced in previous works, shows a strong behavior dependence on the damping losses in the MEMS resonator. A new double feedback topology is introduced here in order to help solving this problem. Comparative discrete-time simulations and preliminary experimental measurements have been carried out for both topologies, showing how the new double feedback topology may increase PDO performance for some frequency ranges.

INTRODUCTION

The use of resonant MEMS devices working near their resonance is widely extended today to a growing number of applications, which include RF components, chemical and gas sensors, accelerometers, gyroscopes, actuators, etc. MEMS resonators are an attractive option to fix the oscillation frequency in such applications because of their high quality and frequency stability propperties. However, most actuation schemes for MEMS (electrostatic, thermoelectric, etc.) are non-linear and therefore the design of large-signal oscillators is not simple. In this way, several oscillator topologies have been proposed in the past; most of them linearize the response of the MEMS by applying a suitable bias voltage and therefore the displacement of the resonator is in the small signal range. On the other hand, large-signal oscillators proposed in the literature exhibited chaotic behavior [START_REF] Bienstman | Periodic and chaotic behaviour of the autonomous impact resonator[END_REF].

The Pulsed Digital Oscillator (PDO) [START_REF] Domínguez | A Novel Sigma-Delta Pulsed Digital Oscillator (PDO) for MEMS[END_REF][START_REF] Domínguez | Analysis of the Σ-∆ Pulsed Digital Oscillator (PDO) for MEMS[END_REF] is a set of sigma-delta based topologies for MEMS that was originally proposed by the authors to overcome these difficulties so that non-chaotic oscillation waveforms can be obtained even working in the large signal range. This work introduces and evaluates a new feedback loop structure for the PDO, called double feedback. The goals of this new architecture are to obtain better results when damping losses in the MEMS resonator are relevant and to enhance the practical oscillation range. To this effect, the main features of the classical, or single feedback, PDO architecture are reviewed in section 2, whereas section 3 introduces the double feedback structure and compares it to the classical one through simulations. Finally, section 4 extends this comparison with experimental results.

...

z -1 F m F(z) X(z) MEMS resonator z -1 z -1 H(z)

PDO FUNDAMENTALS

Architecture and key features

The classical PDO architecture is depicted in Figure 1. We can see that it has a simple and relatively easy to implement structure which includes the MEMS device plus a feedback actuation loop composed by a sign detector, a variable number of delay blocks and an amplifier. Some key features of the PDO are: a) Very short pulses (i.e. deltas) of force of constant amplitude F are supplied to the resonator. This actuation scheme avoids the above mentioned non-linearities present in MEMS actuation. This actuation scheme has been analyzed, extended to other MEMS-based applications and its performance has been evaluated for an accelerometer system in a recent work [START_REF] Colinet | Actuation of Resonator MEMS using Short Pulsed Forces[END_REF].

M. Domínguez, J. Pons, J. Ricart, J. Juillard, E. Colinet Influence of the Feedback Filter on the Response of the Pulsed Digital Oscillator b) The PDO is a sampled circuit and, assuming a typical two-parallel plate MEMS resonator structure, at each sampling time it is only checked if the moveable plate is above or below its 'zero', or rest, position. Such simple position measurement requirements enormously simplify the design and implementation of the MEMS device and of the circuit needed to manage the feedback signal.

c) The PDO is a digital oscillator and, in oversampling conditions, the oscillation frequency (f OSC ) is directly extracted from the spectrum of the bit stream at the output of the sign detector.

d) The PDO exhibits 'perfect' sinusoidal oscillations at the natural frequency of the resonator (f 0 ) for certain sampling frequency (f S ) sets [START_REF] Domínguez | Analysis of the Σ-∆ Pulsed Digital Oscillator (PDO) for MEMS[END_REF]. It has also been demonstrated that the energy transfer from the electrical domain to the mechanical one is maximized in such 'perfect' sample frequencies. e) When the damping losses in the MEMS resonator are relevant, and due to the presence of the 1-bit quantizer in the feedback loop, the oscillation frequency (f OSC ) as a function of the sampling ratio (f 0 /f S ) exhibits a 'fractalized' shape [START_REF] Domínguez | A Novel Sigma-Delta Pulsed Digital Oscillator (PDO) for MEMS[END_REF][START_REF] Domínguez | Analysis of the Σ-∆ Pulsed Digital Oscillator (PDO) for MEMS[END_REF], which looks rather similar to a distorted version of the well-known devil's staircase fractal [START_REF] Feely | A tutorial introduction to non-linear dynamics and chaos and their application to sigma-delta modulators[END_REF]. This effect has also been recently reported for a very similar circuit topology in [START_REF] Colinet | Actuation of Resonator MEMS using Short Pulsed Forces[END_REF].

f) We have recently demonstrated that the PDO can also work very well with sample frequencies below the Nyquist limit [START_REF] Domínguez | The MEMS Pulsed Digital Oscillator (PDO) below the Nyquist limit[END_REF]. This extends the application scope of this kind of oscillator to wider frequency ranges. However, the effects of the damping losses mentioned above become important when working in deep undersampling conditions.

Basic PDO theory

Let us now focus in the PDO structure shown in Figure 1 (for m=1), hereafter called single feedback. By assuming a typical 1D mass-spring-damping model for the parallel-plate MEMS resonator [START_REF] Senturia | Microsystem Design[END_REF] and applying a linear analysis, it can be easily obtained that the structure produces the following normalized digital oscillation frequency [2,3],

)) 1 2 cos( ( cos 2

1 2 0 / 2 1 0 ρ π π π ρ - = - - S f f D f f e f S (1)
being the digital oscillation frequency f OSC =f D f S , and f S the sampling frequency, ρ the dimensionless damping factor and f 0 the natural frequency of the MEMS resonator. These parameters are related to the well-known ones of the MEMS model according to,

m k f km b = = = 0 0 2 2 π ω ρ (2)
where m is the mass of the moveable plate, k is the spring factor, or stiffness, and b is the damping factor. Figure 2 shows the relationship between f D and the sample ratio f 0 /f S for three different values of the damping factor after equation (1) for a given MEMS device parameter set [START_REF] Pacheco | Design of low actuation voltage RF MEMS switch[END_REF] and three different values of the damping losses. It can be clearly seen that when damping losses are small, the oscillation frequency closely follows the evolution of the natural frequency of the resonator. In presence of heavy losses, though, the actual response of the oscillator becomes poorer and f D can clearly depart from the natural frequency of the resonator.

Extensive discrete-time Matlab simulations that have been carried out for the same reference cases reveal that, in the presence of heavy damping losses, the PDO response becomes fractalized and that f D clearly departs from the natural frequency of the resonator, in particular for sampling frequencies close to the Nyquist limit (see Figure 3). This last effect is not only due to the presence of the fractal, but also because of the tendency marked by equation [START_REF] Bienstman | Periodic and chaotic behaviour of the autonomous impact resonator[END_REF].

M. Domínguez, J. Pons, J. Ricart, J. Juillard, E. Colinet Influence of the Feedback Filter on the Response of the Pulsed Digital Oscillator

DOUBLE FEEDBACK TOPOLOGY

In order to obtain a reduction of the influence of the damping losses on the PDO performance, a review of the linear analysis which led to equation (1) has been carried out. From this point of view it can be concluded that such reduction could be obtained by adding some digital filtering in the feedback loop.

According to this and in order to preserve the overall simplicity of the architecture and its design constraints, a new oscillator topology, called double feedback, is proposed here. It includes two feedback paths of different delays (see Figure 4). This double feedback structure works somehow like a low order FIR filter.

Let us also notice that with this structure the force pulses applied to the MEMS can take up to three different values {+2F, +F, 0}, instead of the two possible values {+F, 0} which are possible with the single feedback architecture. Discrete-time simulation results obtained for the same reference cases as in Figure 3 but for a double feedback PDO are shown in Figure 5. After a comparison of the results of Figures 3 and5, it can be easily concluded that the double feedback approach produces a wider range of oscillation frequencies which are closer to the natural frequency of the resonator than in the single feedback case, even in presence of heavy damping losses. In particular, the sample ratio values around the Nyquist limit (f 0 /f S =1/2) produce results similar to the 'no-losses' (ρ=0) case However, the fractalized behaviour still remains, but becomes more evident for the deep oversampling and deep undersampling ranges.

z -1 F F(z) X(z) F + MEMS resonator H(z)

EXPERIMENTAL RESULTS

The promising perspectives provided by the double feedback architecture about a reduction of the effects of the damping losses on the oscillator performance for some frequency ranges have been checked in a first set of experimental measurements.

Measurements setup

The measurements setup is basically the same one that was used in recent works [START_REF] Domínguez | A Novel Sigma-Delta Pulsed Digital Oscillator (PDO) for MEMS[END_REF][START_REF] Domínguez | The MEMS Pulsed Digital Oscillator (PDO) below the Nyquist limit[END_REF] but with the changes in the digital section needed to implement and select between a single and a double feedback loop.

The MEMS resonator comes from the same batch previously described in [START_REF] Domínguez | A Novel Sigma-Delta Pulsed Digital Oscillator (PDO) for MEMS[END_REF] and it is a cantilever with thermoelectric actuation and piezoresistive position sensing through a Wheatstone bridge. The natural

Results and discussion

Figure 7.a shows an oscilloscope screen capture of the resonator position, obtained after amplification, and the set of voltage pulses applied to the MEMS excitation transistors for a single feedback topology with m=1 (see Figure 1) and a 'perfect' sample ratio f 0 /f S =0,25. Let us note that, accordingly to our previous results, an excellent and stable sinusoidal waveform and a regular series of bits of the form '110011 ...' are obtained for this case.

Figure 7.b shows the results for the same case as in Figure 7.a but for a double feedback topology. We can see there that the MEMS input pulses follow the fixed pattern '12101210 ...' and that the resulting position waveform is the same one as in Figure 7.a but with a slight amplitude increase. Moreover, the bit stream spectrums corres-ponding to the single and double feedback cases look exactly the same (see Figure 8). The peak value is located at f OSC =93,68 KHz.

In good agreement with the conclusions of the previous sections, these results tell us that no significant advantages are obtained when the double feedback is applied to the sample ratio f 0 /f S =0,25, which corresponds to a 'perfect' frequency case when working with the single feedback structure. We can also notice that the energy efficiency in the double feedback case is poorer: it provides more energy to the MEMS than in single feedback to obtain the same output response. Again according to the conclusions of previous section, benefits of using the double feedback scheme should be more appearent for sample ratios closer to the Nyquist limit. To this effect, measurements for a sample frequency f S =2,489f 0 have been carried out. This values generates an almost chaotic behaviour (no regular waveforms, no fixed bit patterns, bad spectrum, ...) when using the single feedback structure.

On the other hand, Figure 9 shows that the double feedback structure exhibits a fair senoidal waveform, plus a stable and regular '111100111100 ...' input pattern for the same f S =2,489f 0 case. The corresponding spectrum, shown in Figure 10, is also very good, with a peak value located at f OSC =93,66 KHz. Figure 10. Bit stream spectrum corresponding to the same experimental conditions as in Figure 9.

CONCLUSIONS

Two different feedback loops for PDO structures have been compared. Simulation results show that the double feedback forces the oscillator to put the oscillation frequency closer to the natural frequency of the MEMS resonator, even in the case of heavy damping factors.

Experimental results confirm that the double feedback architecture reduces the influence of the resonator damping losses and it also allows working in wider frequency ranges than the single feedback one, for the same number of delay blocks.

Figure 1 .

 1 Figure 1. Block diagram of the "classic" m-delay pulsed digital oscillator (PDO).

Figure 2 .

 2 Figure 2. Results of the linear analysis of the single feedback structure for three different values of the damping losses.

0. 5 Figure 3 .

 53 Figure 3. Discrete-time simulation results versus linear analysis results for a single feedback PDO topology and relevant damping losses (ρ=0.05).

Figure 4 .

 4 Figure 4. Topology of the double feedback PDO.

Figure 5 .

 5 Figure 5. Discrete-time simulation results for a double feedback structure PDO topology and relevant damping losses (ρ=0.05).

MFigure 6 .

 6 Figure 6. Upper view of the PDO circuit used in the measurements. Due to the thermoelectric actuation of the resonator, force pulses are short voltage pulses provided by open-drain power transistors, while the sign detector role is played by an instrumentation amplifier plus a comparator. Digital control, sampling frequency selection, single and double feedback selection, number of delays and overall timing have been implemented on an isp CPLD. The positive values of force {+2F, +F} for the double feedback case are obtained by modulating the time length of the voltage pulses (1 or 2 µs), instead of their maximum value. In order to work with non-negligible damping values, all measurements were made in air and at room temperature.

Figure 7 .

 7 Figure 7. Oscilloscope screen captures of resonator position (1), MEMS input pulses (2), delayed comparator output (D2,D1) and sample clock (D0), for f S =4f 0 for single (a) and double (b) feedback structures.

Figure 8 .

 8 Figure 8. Bit stream spectrum corresponding to the same experimental conditions as in Figure 7 for both single and double feedback cases.

Figure 9 .

 9 Figure 9. Oscilloscope screen captures of resonator position (1), MEMS input pulses (2), delayed comparator output (D2,D1) and sample clock (D0), for f S =2,5f 0 and a double feedback structure.


Bruno Yun
email: [bruno.yun@lirmm.fr

Rallou Thomopoulos
email: [rallou.thomopoulos@inra.fr

Pierre Bisquert
email: pierre.bisquert]@inra.fr

Madalina Croitoru
email: madalina.croitoru]@lirmm.fr

Defining argumentation attacks in

published or not. The documents may come

Introduction

Socio-economic systems involve various actors who interact, while motivated by different objectives, interests and priorities. Food supply chains are examples of such complex systems, involving actors from producers to process and packaging industrials, distributors, recycling industry, etc. Conceiving sustainable food systems implies taking into account various kinds of concerns, including environmental issues (limited energy consumption, reduced GHG emissions, etc.), economic issues (limited costs for consumers, viable firms, source of employment, etc.), social issues (creating social link, ensuring good living conditions, etc.), ethical considerations (pursuing fairness and equity principles), sensorial preferences (appreciated taste and flavor), nutritional issues (contributing in healthy diets), sanitary issues (chemical and microbiological norms), and practical issues (shelf life, ease of use, etc.). As a consequence, these different concerns lead to inconsistent expectations. This raises the difficult question of how to best meet such expectations when proposing new solutions for the future.

Various methods of reasoning under such kind of inconsistency have already been proposed to tackle decision making in food supply chains. The main approaches employed by the state of the art are multi-criteria analysis or argumentation. In the rest of the paper we will focus on argumentation based approaches. This is justified by the fact that multi criteria design encounters a limitation which is particularly hard to address corresponding author within mathematical frameworks: striking the right balance between problem simplification and real-world complexity [START_REF] Tremblay | Value-based argumentation for policy decision analysis: methodology and an exploratory case study of a hydroelectric project in Québec[END_REF]. Furthermore, in the context of socio-economic systems decision making [START_REF] Delhomme | Designing an argumentative decision-aiding tool for urban planning[END_REF] the strength of argumentation lies in reasoning traceability, discussion fostering and decision explanation, all leading to a better acceptance of the final decision by all parties [START_REF] Bisquert | Formalizing cognitive acceptance of arguments: Durum wheat selection interdisciplinary study[END_REF][START_REF] Thomopoulos | Decision support for agri-food chains: A reverse engineering argumentation-based approach[END_REF].

An argumentation system consists of a set of arguments and a binary relation on that set, expressing conflicts among arguments. Argumentation has been formalized both in philosophy and in computer science [START_REF] Mackenzie | Begging the question in non-cumulative systems[END_REF][START_REF] Rescher | The role of rhetoric in rational argumentation[END_REF] and applied to decision making (e.g. [START_REF] Bonet | Arguing for decisions: A qualitative model of decision making[END_REF][START_REF] Fox | Safe and sound -artificial intelligence in hazardous applications[END_REF]), deductive argumentation and defeasible logic programming [START_REF] Amgoud | Final review and report on formal argumentation system[END_REF][START_REF] Prakken | An abstract framework for argumentation with structured arguments[END_REF] or for modelling different types of dialogues including negotiation or explanation (e.g. [START_REF] Kraus | Reaching agreements through argumentation: A logical model and implementation[END_REF][START_REF] Sycara | Persuasive argumentation in negotiation[END_REF][START_REF] Arioua | Formalizing explanatory dialogues[END_REF][START_REF] Arioua | A dialectical proof theory for universal acceptance in coherent logic-based argumentation frameworks[END_REF]). In the reminder of this paper we will focus on using argumentation for decision making. Originally, in order to capture a large class of problems, an argument [START_REF] Dung | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games[END_REF] was seen as abstract entity. This abstraction poses problems when aiming to apply argumentation in practice for decision making. While an argument is intuitively understood as a statement for or against an action, the attack relation is much harder to discern. How is the attack relation obtained? Is it declared, deduced or computed? On which rationale is it defined? How should it be interpreted? Does it have a human-intuitive interpretation or a machine interpretation?

Against this background, in this paper we focus on the following research question: "How to define an attack relation for argumentative decision making in socio-economic systems?" Since the added value of argumentation lies in its principled interaction with the user we evaluate the potential answers to the above research question with the users. More precisely we propose three kinds of attacks that could be defined in the context of a precise application (packaging selection) and see how the non computer science experts evaluate, against a given set of decision tasks, each of these attacks.

The salient point of the paper lies in the fact that it represents, to the best knowledge of the authors, the first study in argumentation research that addresses the problem of attack modelling in practice. This is a significant problem since the structure of the argumentation graph is directly dictated by the attacks. Moreover, such structure plays a fundamental role in how difficult reasoning over the argumentation graph is [START_REF] Gaggl | Benchmark selection at iccma[END_REF][START_REF] Yun | A structural benchmark for logical argumentation frameworks[END_REF].

The paper is structured as follows. After a recall on modelling choices in Section 2, the packaging case study is presented in Section 3. The experimental protocol of the paper is proposed in Section 4 and its results discussed in Section 5.

Argumentation primer

Argumentation is a reasoning model based on the construction and evaluation of conflicting arguments [START_REF] Dung | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games[END_REF]. An argumentation process follows three main steps: (1) constructing arguments and counter-arguments via attacks, (2) evaluating the acceptability of the arguments using semantics defined on the resulting argumentation framework of step [START_REF] Amgoud | Final review and report on formal argumentation system[END_REF], and (3) obtaining the justified conclusions based on the set of acceptable arguments of step [START_REF] Amgoud | Using arguments for making and explaining decisions[END_REF]. These notions are formalised below (argumentation framework, acceptability semantics). Please note that for introducing acceptability semantics (in this paper we only considered the preferred semantics) we need to introduce three additional notions i.e. conflict-freeness, defence and admissibility. -B is conflict-free if and only if ∃a i , a j ∈ B such that (a i , a j ) ∈ R; -B defends an argument a i ∈ B if and only if for each argument a j ∈ A, if (a j , a i ) ∈ R, then ∃a k ∈ B such that (a k , a j ) ∈ R; a conflict-free set B of arguments is admissible if and only if B defends all its elements.

A preferred extension is a maximal (with respect to set inclusion) admissible set of arguments.

In the above framework, an argument is abstract and can be differently instantiated according to various contexts [START_REF] Walton | A classification system for argumentation schemes[END_REF]. In general, an argument gives a reason for believing a claim, or for doing an action and it is commonly seen as a set of statements composed of one (or more) premise(s) and a conclusion linked by a logical relation. In decision making, arguments can be intuitively understood as being statements to support, contradict, or explain opinions or decisions [START_REF] Amgoud | Using arguments for making and explaining decisions[END_REF]. More precisely, in decisional argumentation frameworks [START_REF] Ouerdane | Argumentation theory and decision aiding[END_REF], the argument definition is provided with additional features: the decision (also referred to as action, option or alternative) and the goal (also referred to as target). In some studies arguments are also associated with specific actors. An application of a decision-oriented argumentation framework to a real-life problem concerning food policy can be found in [START_REF] Bourguet | An artificial intelligencebased approach to deal with argumentation applied to food quality in a public health policy[END_REF], where a recommendation regarding the provision of whole-grain bread was analyzed a posteriori. In that case, each argument is associated with the action it supports. Based on the above rationale, in this paper, the structure for argument modelling is defined as a tuple composed of a target (a goal), a conclusion inferred from the target choice (i.e. considering / or not this target will imply that the following condition will hold), an aligning of the argument with respect to the target (i.e. if the condition holds in the presence or absence of the target) and a priority rank. Formally: Definition 3. An argument is a tuple a = (T, C, A, R) where:

-T is the target of the argument; -C is the conclusion of the argument; -A ∈ {f or, against} is the alignment of the argument (i.e. for or against); -R ∈ N is the rank of the argument.

For any argument a, we denote by Target(a) the target of the argument, Conclusion(a) the conclusion of the argument a, Alignment(a) the alignment of a and Rank(a) the rank of the argument. In Table 1 the set of arguments considered in our experimentation is given for illustrative purposes. More details about the use case scenario and the experimentation protocol will be provided in the next section.

In structured argumentation (e.g. logic based argumentation frameworks where arguments are obtained as instantiations over an inconsistent knowledge base) three kinds of attacks have been defined: undercut, rebut and undermine. [START_REF] Besnard | Elements of argumentation[END_REF]. The intuition of these attacks is either to counter the premise of the opposing argument (the undercut), the conclusion (the rebut) or the logical step that allowed the inference between premise and conclusion (undermine). In abstract argumentation the set of attacks is simply considered as given. A particular aspect to be considered is when the argumentation framework is enhanced with a set of preferences (in this paper the preferences over arguments are cardinal and expressed as ranks). Classically, when preferences are present the attack relation can be modified in order to take into account the induced precedence. In this paper, since the considered definition of the attack places our work between structured and abstract argumentation (i.e. we impose some structure on the argument given the decision task at hand but do not logically formalise the target and the conclusion), we need to decide how the attack is defined. Following the above intuition, attacking an argument could be achieved by raising doubts about its acceptability and (i) questioning its target, (ii) questioning the alignment with respect to the target, or (iii) using the argument rank. Formally, we consider the following three attack relations R 1 , R 2 and R 3 : Definition 4. Let a, b ∈ A be two arguments. We say that: Let us consider again the arguments of Table 1. We have that (a1, a2) ∈ R 1 since T arget(a1) = W C and T arget(a2) = P RL. Furthermore, we have that (a1, a21) ∈ R 2 since T arget(a1) = T arget(a21) = W C and Alignment(a1) = f or and Alignment(a21) = against. Finally, we have that (a1, a2) ∈ R 3 since Rank(a1) ≤ Rank(a2).

-(a, b) ∈ R 1 iff T arget(a) = T arget(b); -(a, b) ∈ R 2 iff
All of the 3 attacks can be a priori justified from examples as being intuitive, and have been in the literature (see e.g. [START_REF] Bourguet | An artificial intelligencebased approach to deal with argumentation applied to food quality in a public health policy[END_REF][START_REF] Yun | Arguing About End-of-Life of Packagings: Preferences to the Rescue[END_REF]). Our objective here is to propose an a posteriori and experimental evaluation, which has not been proposed. In this evaluation, we will consider several criteria: (i) adequation to human spontaneous way of reasoning; (ii) human interpretability of the results; (iii) added-value of computarization for the human. Adequation to human spontaneous way of reasoning will be used as the prime criterion to assert intuitiveness.

Case study

In the framework of the Pack4Fresh agri-food research project supported by the INRA and CIRAD research institutes, a study was launched to design optimized innovative food packagings.

Food packagings play an crucial part in the food market, since they perform multiple functions: marketing appeal, information about the provenance of the products, nutrition facts, food preservation as long as possible associated with food waste reduction, logistic practicality such as the possibility to stack the products for instance. However, food packagings also have harmful effects, in particular on the environment, since it generates waste material and requires energy-intensive manufacturing, etc. At the present time, active research is ongoing to design and develop new-generation, biobased, biodegradable, "intelligent" food packagings. It is mainly focused on technical aspects of packaging, such as properties of the materials used, matter flows through the packaging material, etc. Yet, to be acceptable and usable, these new-generation packagings have to take into account the characteristics expected or appreciated by the users at all levels of the food supply chain (production, transportation, distribution, storage, consumption, etc.). Hence the importance of explicitly identifying these expectations, as exhaustively as possible, starting from cases of (i) existing packagings and (ii) simple systems, excluding in particular labelling information and advanced preservation properties such as modified atmosphere.

Pursuing this objective, in this study it was decided to focus on the case of strawberry packagings, because of the local accessibility of this product and its properties as a perishable product, subject to much wastage by consumers due to bad habits. The following four existing alternatives were considered and the aim of the study was to best identify and analyze the pros and cons of each of them:

-A opened plastic container without lid or plastic film (OPC).

-A opened wooden container without lid or plastic film (WC).

-A plastic container with a rigid lid (PRL).

-A plastic container with a plastic film (PPF).

In order to determine the viewpoints and needs of the wider class of consumers w.r.t. the four previous packagings, a web survey was developed. The survey was given to a representative (with regard to age and socio-professional category) sample of 840 persons. As an example, the questions asked by the survey were of the form: "Do you think that this packaging has a harmful effect on the strawberries?". The possible answers were "Yes", "No" or "Neutral".

In a first step, a pretreatment of neutral answers was performed. Questions with an important part of neutral answers were eliminated and not exploited at all in the rest of the study. Therefore, we considered the ratio of neutral answers should be less than in the case where answers would have been obtained randomly, i.e. less than 1/3.

Then in a second step we extracted statements from the survey representing the general viewpoint of the consumers w.r.t. the packaging as follows. For a given question, let n 1 be the number of "Yes" answers and n 2 the number of "No" answers. If the ratio n 1 /(n 1 + n 2 ) is superior to a given threshold α, a positive statement is extracted. Conversely, if the ratio n 2 /(n 1 + n 2 ) is superior to α, a negative statement is extracted. Otherwise no statement was extracted. The higher the ratio, the prior the rank of the statement is. Again we set α at 2/3 to ensure the results are statistically different from answers that would have been obtained randomly (i.e. α ≈ 0.5). For instance, for the given assertion of whether "the open wooden containers are recyclable", the number of "Yes" answers of the survey participants is 658, whereas the number of "No" answers is 45. We have 658/(658 + 45) > 2/3, thus a positive statement for the open wooden container in the form: "The consumers think that the opened wooden container is recyclable" is extracted. The same question concerning the plastic container with the plastic film provided 165 "Yes" answers and 370 "No" answers. Since we have 370/(165 + 370) > 2/3, a negative statement against the plastic container with the plastic film, of the form: "The consumers think that the plastic container with the plastic film is not recyclable", is extracted.

These statements were transformed into arguments as shown in Table 1. The different kinds of attacks as defined in the previous section were computed. The resulting three argumentation frameworks (sharing the set of arguments) were the inputs for the experimentation protocol described in the next section.

Experimentation protocol

The experimentation was composed of 3 groups (A,B and C) of 7, 8 and 10 persons respectively, all experts in agri-food research but not necessarily experts in packaging conception. Each group rigorously followed the experimentation's framework described in Figure 1. The difference in the group sizes is an experimental constraint due to logistic reasons. Although reduced, the experiment size is conform to ratio requirements [START_REF] Marugán | Decision-Making Management[END_REF] which recommend a minimum number of observations (here participants) equivalent to the number of entries (here arguments).

These three groups were first shown a textual description of the use-case. Then, they were asked to grade the 4 packagings by giving them a score between 1 and 4 (see Figure 2). In Figure 2, the blue bar above W C A means that in group A, there were In the formula above, N umberP ersons(p, i) represents the number of persons that gave the score i to the packaging p. Please note the smaller the score of a packaging, the better that packaging is. In Figure 2, the aggregated score of each packaging in each group is enclosed in square brackets. The detailed analysis of the results is as follows:

-In group A, the WC is considered the "best" packaging (score 12), the PRL is second (score 13). It is followed by the OPC (score 20) and the PPF at the last place (score 21).

-In group B, the WC is obviously the "best" packaging (score 6), it is followed by the OPC (score 12) and the PRL (score 15). The all agree to give the PPF the last place (score 24). -In group C, the WC is the "best" packaging (score 11), the PRL is second (score 21).

It is followed by the OPC (score 28) and the PPF is at the last place (score 38).

From the above we can conclude that, before the experiment, the three groups relatively agree on the ranking of packagings: WC > PRL > OPC > PPF (for groups A and C) and WC > OPC > PRL > PPF (for group B).

The experiment we held out for each group was as follows:

-For group A, we considered the argumentation graph AS = (A, R) where A is the set of arguments of Table 1 with Alignment(a) = f or for each a ∈ A and R = R 1 .

They were shown the following list of preferred extensions:

• ε P P F = {a9} • ε OP C = {a6, a10, a13, a18}
• ε P RL = {a2, a4, a8, a12, a17}

• ε W C = {a1, a3, a5, a7, a11, a14, a15, a16, a19, a20}

In this case, one preferred extension of the argumentation graph corresponds to one packaging and contains all the arguments that are in favor of this option. -For group B, we considered the argumentation graph AS = (A, R) where A is the set of arguments of Table 1 and R = R 2 . They were shown the following list of preferred extensions:

• ε 1 = {a2, a4, a6, a8, a10, a12, a13, a17, a18, a21, a22}

• ε 2 = {a2, a4, a6, a8, a9, a10, a12, a13, a17, a18, a21}

• ε 3 = {a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20} • ε 4 = {a1, a2, a3, a4, a5, a6, a7, a8, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a22}

In this case, one extension cannot contain the arguments for and against one packaging at the same time. Here, ε 1 contains the arguments for PRL, the arguments for OPC, the arguments against WC and the arguments against PPF, ε 2 contains the arguments for PRL, the arguments for OPC, the arguments for PPF and the arguments against WC, ε 3 contains all the arguments for a packaging and ε 4 contains the arguments for PRL, the arguments for OPC, the arguments for WC and the arguments against PPF. -For group C, we considered the argumentation graph AS = (A, R) where A is the set of arguments of Table 1 with Alignment(a) = f or for each a ∈ A and R = R 3 . They were shown the following list of preferred extensions ε W C = {a1, a3, a5, a7, a11, a14, a15, a16, a19, a20}, that contains all the arguments for the wooden container.

After conducting the argumentation experiment and showing them the resulting extensions, the participants were asked again to grade the four packagings by giving them a score between 1 and 4 (see Figure 3). Aggregated scores are given in square brackets and the detailed analysis of the results is as followed:

-In group A, the WC is considered the "best" packaging (score 7), the PRL is second (score 14), third is the OPC (score 21) and the PPF (score 28) is at the last place. Interesting enough, every participant agreed to this ranking. -In group B, the OPC is the "best" packaging (score 8), it is followed by the PRL (score 10) and WC get the third place (score 16). The PPF is ranked last (score 22). -In group C, the WC is the "best" packaging (score 8), the OPC is second (score 18).

It is followed by the PRL (score 20) and the PPF is at the last place (score 27). Once the scoring of packagings was completed, we reunited the three groups (A,B and C) and proceeded with a group debate. Each group explained its approach and revealed their rankings on packagings. We then asked the three groups to grade again the four packagings by giving them a score between 1 and 4 (see Figure 4). Aggregated scores are given in square brackets and the detailed analysis of the results is as followed:

-In group A, the WC is considered the "best" packaging (score 6), the PRL is second (score 12), third is the OPC (score 18) and the PPF is at the last place (score 24). -In group B, the WC is the "best" packaging (score 9), it is followed by the OPC (score [START_REF] Sycara | Persuasive argumentation in negotiation[END_REF]) and PRL at the second/third place (score 19). The PPF is ranked last (score 24). -In group C, the WC is the "best" packaging (score 10), the PRL is second (score 23).

It is followed by the OPC (score 25) and the PPF is at the last place (score 35).

Discussion

Let us summarise the different rankings expressed in this paper in Table 2. From this table we can conclude that the argumentation method of group A does not change the ranking of packagings. The argumentation method of group B seems to be misleading as we can see great changes in the ranking after the experiment which are then revised after the debate. It seems like the argumentation method of group C has some minor effect on the ranking since P RL > OP C before the experiment and OP C > P RL after. One interesting result is that the ranking on packagings is similar before the experiment and after the debate. To go further, let us consider in more detail the ranking statistics as well as the individual comments obtained in each group.

If we examine the statistics of Figures 2 to 4, we can make the following observations. In Figure 2, at the beginning of the experiment before applying the argumentation methods, the global ranking (mixing the answers of the three groups) is clearly W C > P RL > OP C > P P F , however the three groups show some nuances in their profiles. Group A shows a clear view about which 2 packagings should be ranked third and last, but seems to be hesitating about how to discriminate between WC and PPF for ranks first and second. Group B shows a clear view of which packaging should be ranked first and last (respectively WC and PPF) but seems more doubtful on the discrimination between the intermediate rankings (PRL or OPC), since the ranking be-tween PRL and OPC is close to ex aequo in this group. Group C offers a quite categoric ranking with little exceptions with W C > P RL > OP C > P P F . Since all participants have the same information, the variations observed between the three groups are due to individual differences in interpretation.

In Figure 3, after the experiment applying the different argumentation methods, the differences in the profiles of the three groups become much deeper. Group A provides an answer with no ambiguity with the unanimous ranking W C > P RL > OP C > P P F . Thus, this group seems to have gained confidence in their initial answer by applying the argumentation method. Group B, on the contrary, has a much more confused opinion than before the experiment. Indeed, its ranking number one has changed in favour of the packagings that have no negative arguments (OPC and PRL). Its ranking number 2 is now distributed on all the packaging options. WC, which was initially ranked first, has become number 3 because of its negative argument. Only the last ranking, PPF, which also has negative argument, is unchanged. Group C has gained confidence in their initial first rank WC, since 100% of the participants now rank WC first. Their last ranking, PPF, is also confirmed. However ranks 2 and 3 tend to be inversed, with OPC coming before PRL. This can be explained by the prior ranks of the arguments associated with OPC, these ranks being further examined by this group.

In Figure 4, after the debate common to the three groups, the final opinions tend to be more consensual, each group retrieving additional information from the other two experimentations. Hence, the first rank for WC and the last rank for PPF are majoritary in all the groups. Ranks 2 and 3 between OPC and PRL are more controversial, taking into consideration that PRL has more positive arguments, that none of them has negative arguments, but that OPC has prior-ranked arguments.

Moreover, comments given by the participants allow to provide complementary analysis. At the beginning of the experiment before applying the argumentation methods, the comments show that the participants intuitively perform the ranking by seeking a balance between a great number of positive arguments and restricted occurrences of negative arguments, e.g.: "The wooden packaging has lots of positive arguments but also a strong negative argument since it is harmful to strawberries. Thus, the plastic packaging with a rigid lid comes first since it does not have any negative arguments.". "There is a lot of positive arguments and no negative arguments for the plastic container with a rigid lid; The wooden container seems to be ranked second despite of having more positive arguments because of the presence of negative arguments (possibility to smell, harmful effects, etc.)". "I compare the options w.r.t. the number of positive and negative arguments.".

After the experiment, each groups provides interpretations according to the method used. In group A the ranking is reduced to a counting method: "We sort according to the number of arguments. There is a bigger extension for the wooden container.". Group B expresses the difficulty in interpreting the extensions which mix arguments from all packaging options: "There is no possible choice because of the large number of extensions. However, the plastic open container and the plastic container with a rigid lid appear in all the 4 extensions which means that we can prioritise them.". Group C identifies the method is more suitable to compute the best choice than to rank the op-tions, since the output contains only one extension here: "The only extension available. The answers for the wooden container are stronger, there is no knowledge on the other packagings".

Based on the observations above, we can conclude on the strong and weak points of each attack definition:

by separating the positive arguments associated with a given option into a distinguished extension, R 1 allows to rank the options by simply counting the number of arguments in each extension, which is what the participants intuitively perform before the experiment. However, R 1 does not take into account negative arguments, whereas the participants intuitively do; -R 2 takes into account the bipolar aspect of decision making by considering both positive and negative arguments, as participants intuitively do. But having positive and negative arguments for a option in separate extensions, and even more mixing arguments from different options in the same extension, is misleading and practically impossible to interprete by the participants; the added-value of R 3 is to take into account and highlight the prioritization of arguments, which at first glance is not natural to the participants and thus useful to computerize. However the non-symmetric attack relation it provides does not guarantee to keep one extension per option, which is relevant for the selection of best alternatives but leads to a lack of knowledge for the participants about the ranking of the other alternatives.

Conclusion

In this paper we have introduced an experimental study of a packaging conception use case for strawberries. The aim of the experiment was to investigate how the different attack relations behave on a decision making argumentation framework used by non computer science experts. As seen from our results we can infer that the R 1 attack showed to be the most intuitive and easy to use one, whereas R 2 was the closest to the bipolar way of reasoning naturally adopted by the participants by considering both positive and negative arguments, and R 3 seemed to provide the most added-value in computerizing the approach by performing computations with priority ranks. [START_REF] Yun | Arguing About End-of-Life of Packagings: Preferences to the Rescue[END_REF] may be cited as an attempt to combine several of these advantages through a preference-based ranking approach. From the experiment analysed in the present paper, the decision mechanism could be done by an algorithm in order to simulate human experts taking into account attack relations. Obviously from our results, such an algorithm should be primarily based on R 1 and possibly refined using R 3 then R 2 .

Let us conclude this paper with one last remark. Further data are available for analysis in the context of this use case as the consumer survey was complemented by interviews with scientists experts of packaging technologies and with actors of the distribution industry (wholesalers, quality managers, etc.). While in this paper we focus on consumers' answers, in order to study the intuitiveness impact of the attack definition in a delimitated case involving only one category of stakeholders, integrating the various stakeholder opinions is ongoing current work.

Definition 1 .

 1 (Dung's argumentation framework). An argumentation framework is a pair AF = (A, R) where A is a set of arguments and R ⊆ A × A is an attack relation. An argument a attacks an argument a if and only if (a, a ) ∈ R. Definition 2. (Conflict-free, Defense, Admissibility). Let an argumentation framework AF = (A, R) and B ⊆ A. Then:

  T arget(a) = T arget(b) and Alignment(a) = Alignment(b); -Let be a partial order on arguments, (a, b) ∈ R 3 iff T arget(a) = T arget(b), Alignment(a) = Alignment(b) = f or and Rank(a) ≤ Rank(b).

Fig. 1 : 4 Fig. 2 :

 142 Fig. 1: Timeline of the experiment conducted

OP C A [ 21 ] 1 Fig. 3 :

 2113 Fig. 3: Scoring for each group after the argumentation methods

4 Fig. 4 :

 44 Fig. 4: Scoring for each group after the debate

Table 1 :

 1 List of arguments of the experimentation use case.

	Name Target Conclusion	Alignment Rank
	a1 W C shock_resistant	f or	14
	a3 W C taste_preservation	f or	8
	a5 W C can_smell_product	f or	1
	a7 W C can_see_product	f or	9
	a11 W C incites_to_eat	f or	4
	a14 W C ambiant_preservation	f or	18
	a15 W C ref rigerator_preservation f or	19
	a16 W C have_aerations	f or	3
	a19 W C protect_environment	f or	6
	a20 W C reusable	f or	13
	a21 W C harmf ul_ef f ect	against	22
	a2 P RL shock_resistant	f or	15
	a4 P RL taste_preservation	f or	20
	a8 P RL can_see_product	f or	5
	a12 P RL incites_to_eat	f or	16
	a17 P RL have_aerations	f or	17
	a9 P P F can_see_product	f or	10
	a22 P P F N OT _reusable	against	21
	a6 OP C can_smell_product	f or	7
	a10 OP C can_see_product	f or	2
	a13 OP C incites_to_eat	f or	12
	a18 OP C have_aerations	f or	11

Table 2 :

 2 Overview of the results

Acknowledgements

The authors acknowledge the participants to the ECIDCM 2016 training school. We also acknowledge the support of the Pack4Fresh project. Many thanks to Patrice Buche for his insights and help with the experimental set up.


Zhanjie Wang

Hiroyuki Kokawa

Ryutaro Maeda

EPITAXIAL PZT FILMS DEPOSITED BY PULSED LASER DEPOSITION FOR MEMS APPLICATION

Pb(Zr 0.52 Ti 0.48 )O 3 (PZT) thin films were in situ deposited by pulsed laser deposition (PLD) on Pt/Ti/SiO 2 /Si substrates using a template layer derived by a sol-gel method. A 0.15-µm-thick PZT layer with (111)-preferred orientation was first deposited onto Pt/Ti/SiO 2 /Si substrates using the sol-gel method, and than a PZT layer was in situ deposited by PLD on the above-mentioned PZT layer. The crystalline phases and the preferred orientations of the PZT films were investigated by X-ray diffraction analysis.

Surface and cross-sectional morphologies were observed by scanning electron microscopy and transmission electron microscopy. The electrical properties of the films were evaluated by measuring their P-E hysteresis loops and dielectric constants. The preferred orientation of the films can be controlled using the template layer derived by the sol-gel method. The deposition temperature required to obtain the perovskite phase in this process is approximately 460°C, and is significantly lower than that in the case of direct film deposition by PLD on the Pt/Ti/SiO 2 /Si substrates.

INTRODUCTION

Lead zirconate titanate (Pb(Zr x Ti 1-x )O 3 : PZT) thin films have developed rapidly in recent years, because of their excellent ferroelectric, pyroelectric and piezoelectric properties. A large number of potential applications of PZT thin films in nonvolatile ferroelectric random access memories (FeRAMs) [START_REF] Auciello | The physics of ferroelectric memories[END_REF] and microelectro-mechanical systems (MEMS) [START_REF] Spearing | Materials issues in micro electro mechanical systems (MEMS)[END_REF], such as membrane-type micropumps [START_REF] Polla | Ferroelectric thin films in microelectricmechanical systems applications[END_REF], atomic force microscopy (AFM) cantilevers [START_REF] Chu | Microfabricated dynamic scanning force microscope using a three dimensional piezoelectric T-shape actuator[END_REF][START_REF] Chu | Novel multibridge-structured piezoelectric microdevice for scanning force microscopy[END_REF] and microscanning mirror devices [START_REF] Tsaur | Resonant-typed microscanners fabricated by hybrid PZT deposition process on SOI wafers[END_REF], have been reported. PZT films have been studied for more than one decade, and most of them are for FeRAMs less than 0.5 µm in thickness [START_REF] Ramesh | Science and technology of ferroelectric films and heterostructures for nonvolatile ferroelectric memories[END_REF]. However, for use in AFM cantilevers and microscanning mirror devices, a highquality 3-µm-thick PZT film on an electrode/substrate is desirable to obtain a larger displacement [START_REF] Chu | Novel multibridge-structured piezoelectric microdevice for scanning force microscopy[END_REF][START_REF] Tsaur | Resonant-typed microscanners fabricated by hybrid PZT deposition process on SOI wafers[END_REF]. Many fabrication techniques, such as the sol-gel method, pulsedlaser deposition (PLD) and jet print deposition, have been used to fabricate PZT films for microactuators [START_REF] Maeda | Deposition and Patterning Technique for Realization of Pb(Zr 0.52 , Ti 0.48 )O 3 Thick Film Micro Actuator[END_REF]. However, it is not easy to obtain thick PZT films with good electrical properties due to crack formation and the volatility of lead and lead oxide in films. In our previous work, we successfully fabricated crack-free PZT films of 3 µm thickness on Pt/Ti/SiO 2 /Si substrates using the solgel method [START_REF] Wang | Preparation and characterization of sol-gel derived PZT thin films for micro actuators[END_REF]. However, a deposition of 3 µm requires more than 20 repetitions of the coating and firing procedures, which increases the risk of contamination and leads to Pb diffusion between the PZT layer and Pt/Ti bottom electrodes [START_REF] Wang | Effect of bottom electrodes on microstructures and electrical properties of sol-gel derived Pb(Zr 0.53 Ti 0.47 )O 3 thin films[END_REF]. On the other hand, PLD is a promising technique for thick-PZT-film fabrication, because it offers the advantage of a high deposition rate (approximately -3 µm/h). In PLD, films can be crystallized by two different processing methods; namely, they can be crystallized in situ as they are deposited on hot substrates, or they can be deposited amorphously at lower substrate temperatures (or room temperature) and then crystallized by postdepositional annealing. To obtain wellcrystallized PZT films on Pt/Ti/SiO 2 /Si substrates, substrate temperatures (in the case of in situ deposition) or postannealing temperatures (in the case of films deposited at room temperature) in the range of 600 -750°C are required [START_REF] Horwitz | In situ deposition of epitaxial Pb(Zr x Ti 1-x )O 3 thin films by pulsed laser deposition[END_REF][START_REF] Roy | Excimer laser ablated lead zirconate titanate thin films[END_REF][START_REF] Verardi | In situ growth of ferroelectric lead zirconate-titanate thin films on Si substrates by pulsed Nd: YAG laser deposition[END_REF][START_REF] Zheng | Excimer laser deposition of c-axis oriented Pb(Zr, Ti)O 3 thin films on silicon substrates with direct-current glow discharge[END_REF]. In our previous work, we also successfully fabricated crack-free PZT films of 2 µm thickness on Pt/Ti/SiO 2 /Si substrates by PLD at room temperature, which were crystallized by subsequent annealing at 750°C [START_REF] Wang | Effect of Pb Content in Target on Electrical Properties of Laser Ablation Derived PZT Thin Films[END_REF]. However, the temperature of postdeposition annealing in PLD is 750°C, which is significantly higher than that in the sol-gel method (600°C). Thus the evaporation of lead and lead oxide from the surface of films at elevated temperatures is more acute than that in the case of the sol-gel process and leads to the formation of a thin pyrochlore layer on the surface of PZT films [START_REF] Wang | Microstructure and Electrical Properties of Lead Zirconate Titanate Thin Films Deposited by Excimer Laser Ablation[END_REF]. A hybrid process consisting of the sol-gel method and PLD is effective for obtaining thick PZT films with good properties, because it integrates the advantages of the sol-gel method and PLD [START_REF] Wang | Preparation of lead zirconate titanate thin films derived by hybrid processing: sol-gel method and laser ablation[END_REF]. In our previous work, we found that the temperature of postdeposition annealing in the hybrid process is lower Zhanjie Wang, Hiroyuki Kokawa and Ryutaro Maeda Epitaxial PZT films deposited by pulsed laser deposition for MEMS application than that in the case of direct film deposition by PLD on a Pt/Ti/SiO 2 /Si substrate, and the preferred orientation of the film obtained by the hybrid process can be controlled using the layer deposited by the sol-gel method. PZT films fabricated by the hybrid process exhibit better ferroelectric properties than those directly deposited by the PLD process [START_REF] Wang | Preparation and Characterization of Lead Zirconate Titanate Thin Films Derived by Hybrid Processing: Sol-Gel Method and Pulsed Laser Deposition[END_REF]. However, in the hybrid process, PLD is performed at room temperature and the postprocess of amorphously deposited PZT films are still required, so that an in situ deposition technique is also desirable. Hence, in this study, PZT thin films were in situ grown on Pt/Ti/SiO 2 /Si substrates by the hybrid process consisting of the sol-gel method and PLD. The crystalline phases and preferred orientations, as well as the microstructures of PZT films were investigated. On the basis of the experimental results, the mechanism of the in situ growth of PZT films in the hybrid process is discussed.

EXPERIMENTAL PROCEDURE

Pt/Ti/SiO 2 /Si substrates were prepared by sputtering 0.05 µm of titanium and 0.15 µm of platinum on oxidized (1.8 µm of SiO 2 ) silicon substrates.

First, a thin PZT layer was deposited on Pt/Ti/SiO 2 /Si(100) substrates using the sol-gel method. The precursor solution was prepared from lead acetate [Pb(CH 3 COO) 2 ], zirconium-n-propoxide [Zr(C 3 H 7 O) 4 ] and titanium tetraisopropoxide [Ti((CH 3 ) 2 CHO) 4 ]. 2-propanol [(CH 3 ) 2 CHOH] was used as the solvent. The solution composition was controlled at a ratio of Pb : Ti : Zr = 1.2 : 0.48 : 0.52. The PZT films were fabricated on Pt/Ti/SiO 2 /Si substrates using a spin coater operated at 2600 rpm for 20 s and 4000 rpm for 40 s. Before coating, the precursor solution was passed though 0.45 µm nylon filters. The coated films were dried at 250°C for 20 min and then finally annealed at 600°C for 30 min to crystallize the films into a perovskite-type structure with a (100)-preferred orientation. The preferred orientation of the PZT films deposited by the sol-gel method can be easily controlled by varying pyrolysis temperature [START_REF] Liu | Nucleation-or Growth-Controlled Orientation Development in Chemically Derived Ferroelectric Lead Zirconate Titanate (Pb(Zr x Ti 1-x )O 3 , x=0.4) Thin Films[END_REF][START_REF] Liu | Sequence of phase formation in chemically derived ferroelectric lead zirconate titanate Pb(Zr 0.4 Ti 0.6 )O 3 thin films[END_REF][START_REF] Law | Effect of pyrolysis temperature on the characteristics of PZT films deposited by the sol-gel method[END_REF]. We also found that varying pyrolysis temperature in the heattreatment process can affect the preferred orientation of PZT films derived by the sol-gel method: 250°C favored a (111)-preferred orientation and 400°C favored a (100)preferred orientation [START_REF] Wang | Rffect of heat treatment on Preferred Orientation of Sol-Gel deposited PZT Thin films[END_REF]. The thickness of the PZT layer deposited by the sol-gel method was approximately 130 nm.

Second, a PZT film of approximately 0.6 µm thickness was deposited by PLD on the above-mentioned PZT layer at a substrate temperature of 460°C. Figure 1 shows the pulsed laser deposition system, which is composed of a laser source and a deposition chamber with a substrate holder for 3 inch wafers. The substrate holder could be rotated for uniform deposition. Light from a KrF excimer laser (wavelength: 248 nm) was introduced through a quartz SUPRASIL II window. The pumping system was composed of rotary and turbomolecular pumps and the chamber could be evacuated to 10 -7 Torr at room temperature. The distance from the target to the substrate was approximately 10 cm. The targets used were dense ceramic pellets of Pb (Zr 0.45 Ti 0.55 ) O 3 with 20 wt% excess PbO, and their surfaces were polished with emery paper of grades up to #2000 prior to each PLD process. In our previous work, we found that the addition of at least 20 wt% excess PbO to the PZT target is required to obtain a single perovskite phase [START_REF] Wang | Effect of Pb Content in Target on Electrical Properties of Laser Ablation Derived PZT Thin Films[END_REF]. We also found that PZT films fabricated from a target with a Zr/Ti ratio of 45/55 exhibit good electric properties and their compositions are close to that of the morphotropic phase boundary (52/48) Fig. 1 Schematic of the pulsed laser deposition system. Zhanjie Wang, Hiroyuki Kokawa and Ryutaro Maeda Epitaxial PZT films deposited by pulsed laser deposition for MEMS application [START_REF] Wang | Effect of Zr/Ti Ratio in Targets on Electrical Properties of Lead Zirconate Titanate Thin Films Derived by Pulsed Laser Deposition on Template layer[END_REF][START_REF] Wang | Crystal structure and microstructure of lead zirconate titanate (PZT) thin films with various Zr/Ti ratios grown by hybrid processing[END_REF]. Hence, in this work, we fabricated PZT films using a target of Pb(Zr 0.45 Ti 0.55 )O 3 with 20 wt% excess PbO. Before starting the deposition, the vacuum chamber was evacuated up to 10 -7 Torr and then filled with oxygen up to 200 mTorr. PZT films were deposited at a substrate temperature of 460°C for 30 min so that PZT films of approximately 0.6-µm-thickness were obtained. The deposition conditions for the PZT films are summarized in Table1.

The crystalline structure of the PZT films was examined by X-ray diffractometer (XRD, Rigaku RINT2000, CuKa radiation) analysis. The surface and cross-sectional morphology of the films were observed by scanning electron microscopy (FE-SEM, JSM-6500F). Crosssectional TEM specimens were prepared by conventional grinding and polishing. The specimens were ground and polished to a thickness of 20 µm, and were then further thinned to perforation by Ar-ion milling using a Gatan precision ion polishing system (PIPS). The microstructures of the films were studied by transmission electron microscopy (FE-TEM, HF2000, HITACHI). The Pt/Ti film was used as a bottom electrode, and a Pt film (size: 1.5mm in diameter) was deposited by sputtering to form the top electrode. The P-E hysteresis loop of these films was measured using a standard ferroelectric test system (Radiant Technologies RT-60A), and the dielectric constants and loss value of these films were measured at 1 kHz using an impedance analyzer (Hewlett-Packard, HP4192A).

RESULTS AND DISCUSSIN

Crystalline phases and preferred orientations of the PZT films

Figure 2(a) shows the XRD pattern of the PZT layer deposited by the sol-gel method, which was dried at 250°C for 20 min and then finally annealed at 600°C for 30 min. The PZT layer mainly consists of the perovskite phase with a (111)-preferred orientation, and no peak of the pyrochlore phase was detected in the PZT layer. These results are in good agreement with those of our previous study [START_REF] Wang | Rffect of heat treatment on Preferred Orientation of Sol-Gel deposited PZT Thin films[END_REF]. Varying pyrolysis temperature in the heattreatment process can influence the preferred orientation of the PZT films obtained by the sol-gel method: 250°C favored a (111)-preferred orientation and 400°C favored a (100)-preferred orientation.

Figure 2(b) shows the XRD pattern of the PZT film deposited by the hybrid process on the (111)-oriented PZT layer. The film had a pure perovskite phase with a sharp and prominent diffraction peak of (111) planes. In comparison with that in Fig. 2(a), the XRD pattern of the PZT film deposited by the hybrid process is similar to that of the layer deposited by the sol-gel method. These results indicate that the grains of the perovskite phase in the layer deposited by the sol-gel method grew in situ during PLD at the substrate temperature of 460°C. In the case of PLD at room temperature in the hybrid process, we found that the lower PZT layer deposited by the sol-gel method acted as a seed layer for the crystallization of the upper PZT layer deposited by PLD during postdeposition annealing [START_REF] Wang | Growth of lead zirconate titanate thin films by hybrid processing: sol-gel method and pulsed-laser deposition[END_REF]. To clarify the solid-phase epitaxial effect between the PZT layers deposited by the sol-gel method and PLD, the cross-sectional microstructure of the PZT films were studied by TEM described below.

Zhanjie Wang, Hiroyuki Kokawa and Ryutaro Maeda Epitaxial PZT films deposited by pulsed laser deposition for MEMS application

On the other hand, in the case of direct film deposition by PLD on the Pt/Ti/SiO 2 /Si substrates, to obtain wellcrystallized PZT films, higher substrate temperatures in the range of 650 -750°C are required [START_REF] Horwitz | In situ deposition of epitaxial Pb(Zr x Ti 1-x )O 3 thin films by pulsed laser deposition[END_REF][START_REF] Roy | Excimer laser ablated lead zirconate titanate thin films[END_REF][START_REF] Verardi | In situ growth of ferroelectric lead zirconate-titanate thin films on Si substrates by pulsed Nd: YAG laser deposition[END_REF][START_REF] Zheng | Excimer laser deposition of c-axis oriented Pb(Zr, Ti)O 3 thin films on silicon substrates with direct-current glow discharge[END_REF]. However, a pure perovskite phase can be obtained by PLD at a substrate temperature of 460°C by the hybrid process (Fig. 2(b)). It is clear that the PZT layer deposited by the solgel method decreases the deposition temperature to obtain the perovskite phase during PLD.

2 S E M and TEM observation of microstructure of the PZT films

Figure 3 shows the surface morphology of the PZT films fabricated by the hybrid process at the substrate temperature of 460°C. The film has a spherulite grain structure and most of the grains are approximately 250 nm in size. The cross-sectional morphology of the PZT films fabricated by the hybrid process is shown in Fig. 4. As can be seen, the film was grown as a columnar microstructure extending through its thickness, and no boundary between the PZT layers deposited by the sol-gel method and PLD can be observed. This suggests that the adherence of the layers deposited by the sol-gel method and PLD is very good. Figure 5 shows the microstructure of the PZT films fabricated by the hybrid process at the substrate temperature of 460°C. According to the thickness of the layer deposited by the sol-gel method, the interface between the layers deposited by the sol-gel method and PLD can be assumed and is denoted by the arrows. The film showed a polycrystalline columnar grain structure, and no defects, such as pores are observed at the interface between the layers deposited by the sol-gel method and PLD. The result also indicates that perovskite grains in the PZT layer deposited by the sol-gel method grew in situ during PLD at a substrate temperature of 460°C. Taking this result together with XRD spectra shown in Fig 2, we conclude that the solid-phase epitaxial effect between the PZT layers deposited by the sol-gel method and PLD decreases the deposition temperature to obtain the perovskite phase during PLD, and causes the films to exhibit the same preferred orientation as that of the layer deposited by the sol-gel method.

3 Electrical properties of the PZT films

The dielectric constant and loss value measurements of the films fabricated by the hybrid process were carried out at a frequency of 1 kHz using an impedance analyzer. The dielectric constant and the loss value were approximately 900 and 0.05, respectively. The ferroelectricity of the PZT Zhanjie Wang, Hiroyuki Kokawa and Ryutaro Maeda Epitaxial PZT films deposited by pulsed laser deposition for MEMS application films fabricated by the hybrid process was investigated by observing the P-E hysteresis loop (Fig. 6). The average remanent polarization P r and the coercive field E c are 15 µC/cm 2 and 45 kV/cm, respectively. We also tried to determine the ferroelectric properties of the PZT films fabricated directly on Pt/Ti/SiO 2 /Si substrates by PLD at the substrate temperatures of 460°C and 550°C. However, no hysteresis loops were obtained from these films, because they consist of mainly the pyrochlore phase, which is a nonferroelectric phase. It is clear that the hybrid process is effective for obtaining PZT films with good properties at lower deposition temperature.

CONCLUSIONS

Pb(Zr x Ti 1-x )O 3 (PZT) thin films were in situ-deposited on Pt/Ti/SiO 2 /Si substrates at a substrate temperature of 460°C by the hybrid process consisting of the sol-gel method and pulsed-laser deposition (PLD). The crystalline structure and preferred orientation of the PZT films were examined by XRD analysis. The microstructures of the films were studied by TEM. XRD analysis indicated that the preferred orientation of PZT films could be controlled using the layer deposited by the sol-gel method. TEM image showed that the film had a polycrystalline columnar microstructure extending through its thickness. These results indicate that the solid-phase epitaxial effect between the PZT layers deposited by the sol-gel method and PLD decreases the deposition temperature, thereby obtaining the perovskite phase during PLD, and causes the films to exhibit the same preferred orientation as the layer deposited by the sol-gel method.

Fig. 3

 3 Fig. 3 Surface SEM image of PZT films fabricated by hybrid process at substrate temperature of 460°C.

Fig. 2

 2 Fig. 2 XRD patterns of (100)-preferred PZT films: a) fabricated by the sol-gel method, b) fabricated by PLD on the sol-gel layer at substrate temperature of 460°C. Pv: perovskite phase.

Fig. 5

 5 Fig. 5 Cross-sectional TEM image of PZT films fabricated by hybrid process at substrate temperature of 460°C.

Fig. 6 P

 6 Fig.6P-E hysteresis loop of PZT film fabricated by hybrid processing at a substrate temperature of 460°C.

Fig. 4

 4 Fig. 4 Cross-sectional SEM image of PZT films fabricated by hybrid process at substrate temperature of 460°C.

Table 1

 1 Conditions of pilsed-laser deposition of the PZT thin films


Bruno Yun
email: yun@lirmm.fr

Madalina Croitoru
email: croitoru@lirmm.fr

Srdjan Vesic
email: vesic@cril.fr

Pierre Bisquert
email: pierre.bisquert@inra.fr

DAGGER: Datalog+/-Argumentation Graph GEneRator

We introduce DAGGER: a generator for logic based argumentation frameworks instantiated from inconsistent knowledge bases expressed using Datalog+/-. The tool allows to import a knowledge base in DLGP format and the generation and visualisation of the corresponding argumentation graph. Furthermore, the argumentation framework can also be exported in the Aspartix format.

THE DAGGER'S TIMELINESS

This demonstration paper will present DAGGER, a Datalog+/- [START_REF] Calì | A general datalogbased framework for tractable query answering over ontologies[END_REF] Argumentation Graph GEneRator. We place ourselves in the context of multi agent argumentation systems [START_REF] Minh | On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games[END_REF], and, more precisely, logic-based argumentation systems, i.e. argumentation systems that employ arguments built over a logical knowledge base (KB). When reasoning about inconsistent logical KBs, one has to deploy reasoning mechanisms that are not following the classical logical inference. This is due to the fact that, in classical logic, falsum implies everything. Alternative reasoning techniques are therefore needed in order to make sense of such KBs. Argumentation is one reasoning under inconsistency technique, that allows to build arguments and attacks over an inconsistent data. The arguments represent the various logical consequences one can draw from consistent subsets of the KB. The attacks capture the inconsistency between the different pieces of knowledge. The set of arguments and the corresponding set of attacks is referred to as an argumentation framework (AF). AFs are visually represented using a directed graph where the nodes represent the arguments and the directed edges the attacks between the arguments [START_REF] Minh | On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games[END_REF].

Classically, reasoning with argumentation systems consists of finding the maximal sets of arguments that (1) are not attacking each other and (2) defend themselves (as a group) from all incoming attacks. Such sets are called extensions. An argument is skeptically accepted if it is in all extensions and credulously accepted if it is in only one extension. In the graph theory, such reasoning task is translated into finding and intersecting all the graph's stables.

While a lot of theoretical work in the past 23 years has focused, amongst others, on optimising the extension finding procedures [START_REF] Sarah | A Comprehensive Analysis of the cf2 Argumentation Semantics: From Characterization to Implementation[END_REF][START_REF] Lagniez | CoQuiAAS: A Constraint-Based Quick Abstract Argumentation Solver[END_REF], on the investigation of various extension notions [START_REF] Baroni | An introduction to argumentation semantics[END_REF] or on the investigation of desirable properties of logic based instantiations [START_REF] Amgoud | Postulates for logic-based argumentation systems[END_REF][START_REF] Modgil | The ASPIC+ framework for structured argumentation: a tutorial[END_REF], there are few tools that allow to generate an AF from a given KB [START_REF] Thimm | The Tweety Library Collection for Logical Aspects of Artificial Intelligence and Knowledge Representation[END_REF]. Furthermore, the few available tools for reasoning using argumentation over inconsistent KBs do not allow for further interoperability (allowing their output to be used by other tools).

A workflow that will allow a knowledge engineer to (1) input a KB in a commonly used format and then (2) generate, (3) visualise or (4) export the argumentation graph are very useful for practical argumentation. Such scenario could be used when a non expert wants to reason, using argumentation, over a KB in a particular domain ([4, 18, 19], etc.). It could also be useful for investigating the theoretical properties of the generated AF. Given the fact that certain graph theoretical properties could radically improve the extension computation efficiency [START_REF] Yun | A Structural Benchmark for Logical Argumentation Frameworks[END_REF] such visualisation could be a useful tool for argumentation specialists. Last, please note that, even when the KB is modestly large, the corresponding argumentation graph can become truly immense [START_REF] Yun | A Structural Benchmark for Logical Argumentation Frameworks[END_REF]. In this case, allowing tool interoperability that will directly load a logically generated argumentation graph into efficient solvers [START_REF] Lagniez | CoQuiAAS: A Constraint-Based Quick Abstract Argumentation Solver[END_REF][START_REF] Thimm | The Tweety Library Collection for Logical Aspects of Artificial Intelligence and Knowledge Representation[END_REF] can make the difference between time out errors and obtaining a result.

USING THE DAGGER

We propose the DAGGER tool that assists domain experts and argumentation developers in the specification, visualisation and/or export of logic based AFs built over the Datalog+/-language.

Agent Techniques: Logic Argumentation

Let us first make a note about the logical language used in this paper. Existential rules (whom computationally decidable subclasses are referred to as Datalog+/-) have been intensively investigated on the Semantic Web for their generalisation w.r.t. Description Logic fragments [START_REF] Thomazo | Conjunctive Query Answering Under Existential Rules -Decidability, Complexity, and Algorithms[END_REF]. It has been shown that using argumentation techniques over inconsistent existential rules KBs yields extensions logically equivalent to the maximally consistent subsets [START_REF] Croitoru | What Can Argumentation Do for Inconsistent Ontology Query Answering?[END_REF] of the KB (called repairs [START_REF] Lembo | Inconsistency-Tolerant Semantics for Description Logics[END_REF]). Using argumentation over existential rules has been shown to be of practical interest over existing repair based approaches [START_REF] Hecham | An empirical evaluation of argumentation in explaining inconsistency tolerant query answering[END_REF]. Argumentation for handling inconsistency tolerant semantics enhance the human interaction [START_REF] Arioua | DALEK: A Tool for Dialectical Explanations in Inconsistent Knowledge Bases[END_REF], are used in food science applications [START_REF] Arioua | A Dialectical Proof Theory for Universal Acceptance in Coherent Logic-Based Argumentation Frameworks[END_REF][START_REF] Arioua | DALEK: A Tool for Dialectical Explanations in Inconsistent Knowledge Bases[END_REF] or allow for alternative computation methods [START_REF] Yun | An Argumentation Workflow for Reasoning in Ontology Based Data Access[END_REF]. Such techniques have been shown to have further implications w.r.t. human reasoning and bias detection [START_REF] Bisquert | Substantive Irrationality in Cognitive Systems[END_REF].

An existential rule KB K = (F , R, N ) is composed of a finite set of facts F (such as {packaдinд(A)} representing the fact that the individual A is a packaging), a set of rules R (such as {∀x (packaдinд(x ) ∧ has (x, PlasticFilm) → pollute (x ))} representing the implication that a packaging that has a plastic film is polluting the environement) and a set of negative constraints N (such as {∀x (pollute (x ) ∧protectEnv (x ) → ⊥)} representing the impossibility to both protect the environment and pollute it). The constraints are used to express negative knowledge about the world. In the considered setting, rules and constraints act as an ontology used to "access" different data sources. Therefore, we suppose that the set of rules is compatible with the set of negative constraints, i.e. the union of those two sets is satisfiable [START_REF] Lembo | Inconsistency-Tolerant Semantics for Description Logics[END_REF].

Starting from an inconsistent KB (composed of a set of facts and an ontology containing positive and negative rules), using the AF of [START_REF] Croitoru | What Can Argumentation Do for Inconsistent Ontology Query Answering?[END_REF] we generate the arguments and the attacks corresponding to the KB. An argument [START_REF] Croitoru | What Can Argumentation Do for Inconsistent Ontology Query Answering?[END_REF] in Datalog+/-is composed of a minimal (w.r.t. set inclusion) set of facts called support and a set of facts entailed from the support called the conclusion. The Skolem chase coupled with the use of decidable classes of Datalog+/-ensures the finiteness of the AF proposed (following from [START_REF] Baget | On rules with existential variables: Walking the decidability line[END_REF]). The attack considered is the undermining [START_REF] Croitoru | What Can Argumentation Do for Inconsistent Ontology Query Answering?[END_REF]: a attacks b iff the union of the conclusion of a and an element of the support of b entails a negative constraint. Please note that the attack is not symmetric which ensures the fact that the set of naive extensions is different from the sets of stable and preferred extensions.

The AF above outputs a set of extensions equivalent to the repairs [START_REF] Bienvenu | On the Complexity of Consistent Query Answering in the Presence of Simple Ontologies[END_REF][START_REF] Lembo | Inconsistency-Tolerant Semantics for Description Logics[END_REF] of the KB (i.e. the maximum consistent set of facts).

DAGGER Architecture

The layered architecture of the DAGGER tool is shown in Figure 1 and it is detailed as follows:

• High level: This layer is mainly composed of the graphical user interface (GUI) that is used for the different interactions.

It has a text area that allows to enter a KB expressed in the DGLP format (i.e. the formal for expressing existential rules). • Mid level: This layer is composed of the logical model: KBs and AFs. • Low level: This layer is composed of the computational tools that allow the computation of the arguments, the attacks (via the Graal library) and the repairs (i.e. the extensions). The information flow passes from the high level to the low level through the intermediate level using the different communication channels between modules.

Usability Scenarios

We consider three usability scenarios of DAGGER. All of these scenarios are easily employed using DAGGER. Scenario 1. First, we consider the task of a non computer science specialist inputting an inconsistent KB of his expertise and wanting to find the maximally consistent point of views one can consider. For instance, let us consider the KB of Example 2.1. Please note that tools for assisting non domain experts in building such KBs without computer expertise exists [START_REF] Chein | Graph-based Knowledge Representation -Computational Foundations of Conceptual Graphs[END_REF].

Example 2.1. Let K = (F , R, N ) be a KB with: In this KB, a packaging A with a plastic film is said to protect the environment. However, since the possession of a plastic film leads to pollution, this KB is thus inconsistent. Finding maximally consistent point of views (or repairs) consists in computing all maximal subsets of F that do not trigger a negative constraint of F . Here, we have three repairs: {packaдinд(A), has (A, PlasticFilm)}, {packaдinд(A), protectEnv (A)} and {has (A, PlasticFilm), protectEnv (A)}. Scenario 2. Second, we consider an argumentation specialist looking for graph based structural properties of argumentation graphs instantiated with particular KBs. For instance, let K be a KB with three facts a(m), b (m), c (m), no rules and only containing one binary negative constraint ∀x (b (x ) ∧ c (x ) → ⊥). By generating the graph representation one might observe that the graph is symmetrical thus satisfying certain restrictions over its extensions [START_REF] Amgoud | An argumentation system for defeasible reasoning[END_REF]. However, if one considers a ternary negative constraint that is added to the KB (i.e. ∀x (a(x ) ∧ b (x ) ∧ c (x ) → ⊥)), one can observe that the structure of the graph changes and it is no longer symmetric (and thus the properties of [START_REF] Amgoud | An argumentation system for defeasible reasoning[END_REF] do not hold anymore). Scenario 3. Third, we consider a KB composed of 7 facts, 2 rules and 1 negative constraints. Generating the graph over such a KB will yield a graph of 383 arguments and 32768 attacks. Non optimised tools will not be able to handle these large graphs for a computationally expensive operation such as finding all its stables. However, ASPARTIX solvers based on SAT [START_REF] Lagniez | CoQuiAAS: A Constraint-Based Quick Abstract Argumentation Solver[END_REF] will generate all extensions in less than 1 seconds. This is why one can use the export feature for such computations.

Figure 1 :

 1 Figure 1: The 3-layer structure of DAGGER.

Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018), M. Dastani, G. Sukthankar, E. André, S. Koenig (eds.), July 10-15, 2018, Stockholm, Sweden. © 2018 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.


Bruno Yun
email: yun@lirmm.fr

Madalina Croitoru
email: croitoru@lirmm.fr

Pierre Bisquert
email: pierre.bisquert@inra.fr

Srdjan Vesic
email: vesic@cril.fr

Graph Theoretical Properties of Logic Based Argumentation Frameworks Extended Abstract

Argumentation frameworks instantiated from logical language allow for argument generation over real knowledge. We present some graph theoretical properties of argumentation graphs obtained from an inconsistent knowledge base expressed using existential rules.

RESEARCH CONTEXT

The contribution of this paper is to provide a complete characterisation of argumentation frameworks constructed from KBs solely composed of factual knowledge and negative constraints. This result can be used for designing argumentation solvers [START_REF] Cerutti | Computing Preferred Extensions in Abstract Argumentation: A SAT-Based Approach[END_REF] that perform better in the presence of symmetries [START_REF] Lagniez | CoQuiAAS: A Constraint-Based Quick Abstract Argumentation Solver[END_REF] or for generating realistic benchmarks [START_REF] Yun | Are Ranking Semantics Sensitive to the Notion of Core?[END_REF]. In this short paper, for lack of space, we illustrate the contribution of the paper via a running example. We also focus on the simple case where the knowledge base does not contain any positive rules. Negative rules, expressing incompatibilities, are allowed. Please refer to [START_REF] Yun | Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results[END_REF] for the formalisation of the paper results.

Let us consider a knowledge base composed of four facts representing a possible instance of the famous Incompatible Food Triad where one is requested to find three foods (or drinks) for which any pair will taste good together, but all three together will not. The triad Beer, 7Up, and Whiskey was given as a solution with the statement that beer with 7Up makes Shandy, beer with whiskey makes a boilermaker (beer cocktail) and whiskey with 7Up is a 7 and 7, but the three together would "make you sick".

Therefore, we cannot have at the same time a 7Up, a whiskey and a beer in a single cup (this is a negative constraint). Since the negative constraint is applicable to the facts, this knowledge base is inconsistent. The arguments generated over this knowledge base (there are 13 of them) are composed of a support and a conclusion, such that the conclusion is logically entailed by the support. The arguments are represented in Table 1.

a 1 ({whiskey(ssc)}, {whiskey(ssc)}) a 2 ({soda(7U p)}, {soda(7U p)}) a 3 ({whiskey(ssc), soda(7U p)}, {whiskey(ssc), soda(7U p)}) a 4 ({beer (lb)}, {beer (lb)}) a 5 ({whiskey(ssc), beer (lb)}, {whiskey(ssc), beer (lb)}) a 6 ({soda(7U p), beer (lb)}, {soda(7U p), beer (lb)})

a 7 ({cup(c)}, {cup(c)}) a 8 ({whiskey(ssc), cup(c)}, {whiskey(ssc), cup(c)}) a 9 ({soda(7U p), cup(c)}, {soda(7U p), cup(c)}) a 10 ({whiskey(ssc), soda(7U p), cup(c)}, {whiskey(ssc), soda(7U p), cup(c)}) a 11 ({beer (lb), cup(c)}, {beer (lb), cup(c)}) a 12 ({whiskey(ssc), beer (lb), cup(c)}, {whiskey(ssc), beer (lb), cup (c)
}) a 13 ({soda(7U p), beer (lb), cup(c)}, {soda(7U p), beer (lb), cup(c)}) Table 1: Arguments of the running example

The inconsistency is captured via the attacks that are defined as follows: an argument a i attacks an argument a j if and only if the conclusion of a i with only one element of the support of a j is sufficient to trigger a negative constraint. For example, a 3 attacks argument a 5 because the conclusion of a 3 , {whiskey(ssc), soda(7U p)}, is inconsistent with beer (lb) of the support of a 5 .

The set of arguments and attacks can be visually represented using a directed graph where the nodes are labeled with the arguments and the attack relation is depicted via the edges. In Figure 1 below, the argumentation graph of this knowledge base is shown.

STRUCTURAL PROPERTIES OF ARGUMENTATION GRAPHS

The structural properties we propose in this paper enable us to have a general grasp of the layout of the generated graph. Indeed, we show the existence and describe three kinds of strongly connected components and some repetitive patterns in such graphs. Furthermore, we explicit the exponential number of arguments with respect to specific facts in the knowledge base. These structural properties are details as follows:

• Number of isolated nodes (nodes that are not attacked and that do not attack other arguments). This number is linked to the number of facts that are not in any minimal inconsistent set (free facts). A minimal inconsistent set is an inconsistent subset of facts of the knowledge base that becomes consistent as soon as at least one element is removed. We showed in [START_REF] Yun | Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results[END_REF] that the number of isolated nodes is exactly equal to 2 k -1 where k is the number of free facts. This property is responsible for the exponential explosion of the graph size as seen in [START_REF] Yun | A Structural Benchmark for Logical Argumentation Frameworks[END_REF]. For instance, in our running example, there is only one minimal inconsistent set ({whiskey(ssc), soda(7U p), beer (lb)}) and thus only one free fact (cup(c)). Therefore, we conclude that there is one isolated node (a 7 ) as represented in Figure 1. Please note that if we add two more free facts to the running example, we now have 55 arguments and 576 attacks. represented in Figure 2. The graph G ′ composed of the arguments {a 1 , . . . , a 6 , a 8 , . . . , a 13 } (the grey nodes in Figure 1) and the corresponding attacks is a 2-copy graph of G. Given an argumentation graph with isolated nodes (thus coming from a knowledge base K with at least one free facts), the graph G obtained by removing the isolated nodes has the property that it is a 2 k -copy graph of the graph obtained from the previously mentioned knowledge base K without free facts where k is the number of free facts [START_REF] Yun | Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results[END_REF].

•
For example, if we remove the free fact cup(c), we obtain the argumentation graph of Figure 2. Since we have one free fact, we know that this graph is a 2-copy graph of the subgraph in grey in Figure 1. • Strongly connected components (SCCs). In a directed graph a SCC is a subgraph such that for every two arguments a, b of this subgraph, there is a sequence of attacks (or path) from a to b. There are three kinds of SCCs in the argumentation graphs of [START_REF] Yun | Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results[END_REF]. The first kind is the isolated nodes. By definition, each isolated node is a SCC by itself since it does not attack any other argument. The second kind of SCCs is composed of arguments of the form (X , X ) such that, for all minimal inconsistent sets of facts C, X does not contain a subset of C of size |C -1| (this represent the arguments that are attacked but do not attack other arguments).

For example, the argument a 11 in Figure 1 does not contain any subset of size 2 of the only minimal inconsistent set {whiskey(ssc), soda(7U p), beer (lb)}. Therefore, it is attacked by a 10 and a 3 but it does not attack other arguments. It is a SCC by itself. Last but not least, all the other arguments that are not in the two aforementioned classes represent a SCC where each argument attacks all the other arguments. For example, the set of arguments E = {a 3 , a 5 , a 6 , a 10 , a 12 , a 13 } is such that for every a i , a j ∈ E, i j we have a i ↔ a j . Please note that the investigation of structural results of argumentation graphs computed over existential rules is of practical interest. Indeed, a similar instantiation [START_REF] Arioua | Logic-based argumentation with existential rules[END_REF] was used in the domain of food science in order to explain to non experts the outcome of inconsistent tolerant query answering results [START_REF] Arioua | DALEK: A Tool for Dialectical Explanations in Inconsistent Knowledge Bases[END_REF]. Based on the logical equivalence between repair semantics and argumentation semantics [START_REF] Croitoru | What Can Argumentation Do for Inconsistent Ontology Query Answering?[END_REF], the added value of argumentation over classical techniques was demonstrated in practice (see [START_REF] Hecham | An empirical evaluation of argumentation in explaining inconsistency tolerant query answering[END_REF]).

7 Figure 1 :

 71 Figure 1: Argumentation framework corresponding to the running example

  Presence of repetitive patterns in subgraphs. A k-copy graph of a graph G is a graph G ′ with k times more arguments. Each argument is copied k times and the attacks in G ′ satisfy (1) if a attacks b in G then a attacks all the k copies of b in G ′ and (2) if c is a copy of a in G ′ then c has the same attackers and attacks the same arguments as a. For instance, let G be the graph with six arguments (b 1 , . . . , b 6 )

6 Figure 2 :

 62 Figure 2: A graph G with six arguments and nine attacks

Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018), M. Dastani, G. Sukthankar, E. André, S. Koenig (eds.), July 10-15, 2018, Stockholm, Sweden. © 2018 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.

The authors acknowledge the support of the H2020 CORDIS NoAW project (project ID 688338). Srdjan Vesic benefited from the support of the project AMANDE ANR-13-BS02-0004 of the French National Research Agency (ANR).