This paper presents a tool for constructing and evaluating deductive mathematical proofs using formal argumentation called CLEAR (Constructing and evaLuating dEductive mAthematical pRoofs). This tool has a twofold objective: (i) allows students to construct deductive proofs collaboratively using a structured argumentative debate; and (ii) helps instructors to evaluate these proofs and all intermediary steps in order to provide constructive feedbacks to students. This paper focuses on objective (i) and presents results of an experimental study conducted with undergraduate students. The behavior of students during the construction of deductive proofs is analyzed to show whether formal argumentation frameworks allow students to build deductive proofs and measure students' acceptance of CLEAR.

Also in Volume 305: Computational Models of Argument (IOS Press)

In long lifespan software systems, specification documents can be outdated or even missing. Developing new software releases or checking whether some user requirements are still valid becomes challenging in this context. This challenge can be addressed by extracting high-level observable capabilities of a system by mining its source code and the available source-level documentation. This paper presents feature extraction and traceability (FEAT), an approach that automatically extracts topoi, which are summaries of the main capabilities of a program, given under the form of collections of code functions along with an index. FEAT acts in two steps: first, clustering: by mining the available source code, possibly augmented with code-level comments, hierarchical agglomerative clustering groups similar code functions. In addition, this process gathers an index for each function. Second, entry point selection: functions within a cluster are then ranked and presented to validation engineers as topoi candidates. We implemented FEAT on top of a general-purpose test management and optimization platform and performed an experimental study over 15 open-source software projects amounting to more than 1 M lines of codes proving that automatically discovering topoi is feasible and meaningful on realistic projects.

We introduce a preferences-based itemset mining framework. Preferences are encoded by a penalty function over the transactions in a database. We define an itemset mining problem where we associate to each transaction a penalty value. This problem consists in generating the frequent itemsets with a maximum penalty threshold. We then provide a propositional satisfiability based encoding. We extend the previous problem with a penalty function over items, where we use two maximum penalty thresholds, over the transactions and over the items. In this setting, computing the optimum itemsets corresponds to computing Pareto front. The experimental evaluation on real world data shows the feasibility of our approach.

Preferences can be expressed as wishes, constraints or both. Generally, wishes and constraints do not complement each other. A different reasoning principle is applied to rank-order the set of options depending on whether preferences refer to wishes or constraints. Consequently, these two types of preferences have been characterized by two separate sets of postulates offering a normative view of the preferences. This paper provides a complementary study. In particular an empirical analysis has been conducted in order to assess human endorsement of the normative view of wishes and constraints. Results showed that single postulates are highly endorsed by humans. However the latter showed more or less strong endorsement w.r.t. patterns of postulates. US laypersons and French participants in the experiment showed different behaviors.

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e., finding hypotheses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.

Intelligent 'services' are increasingly used on e-commerce platforms to provide assistance to customers. Numerous preference elicitation methods developed in the literature are now employed for this purpose. However, it is commonly known that there is a real bottleneck in preference handling as concerns the elicitation of preferences because it does not cater to the wide range of preference representation languages available. Thus, as a first step in developing a decision-support tool using an AI based on such languages, this paper describes a preliminary study conducted to address this issue. We propose a method of eliciting real-time user preferences expressed in natural language (NL) which can be formally represented using comparative preference statements complying with different semantics, and provide a proof of concept to demonstrate its feasibility. Since we develop NL resources to detect preference semantics, we also make a comparative study with existing resources to underline the peculiarities of our model.

Various formalisms for representing and reasoning about temporal information with qualitative constraints have been studied in the past three decades. The most known are definitely the Point Algebra (PA) and the Interval Algebra (IA) proposed by Allen. In this paper, for both calculi, we study a particular problem that we call minimal consistency problem (MinCons). Given a temporal qualitative constraint network (TQCN) and a positive integer k, this problem consists in deciding whether or not this TQCN admits a solution using at most k distinct points on the line. On the one hand, we prove that this problem is NP-complete for both PA and IA, in the general case. On the other hand, we show that for TQCNs defined on the convex relations, MinCons is polynomial. For these TQCNs, we give a polynomial method allowing to obtain compact scenarios.

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalize conventional acceptance, and we present the concept of a conditional acceptance function.

Argumentation is a reasoning model based on constructing arguments, determining potential conflicts between arguments and determining acceptable arguments. Dung's argumentation theory is an abstract framework based on a binary defeat relation between arguments. Due to this abstract representation, it has been instantiated in different ways. In particular, preference-based argumentation frameworks take into account a preference relation over arguments together with a (non necessarily symmetric) attack relation. We show that preference-based argumentation frameworks faithfully instantiate Dung's framework only when the attack relation is symmetric. Moreover the latter condition prevents undesirable results. We also promote a higher impact of preferences in preference-based argumentation frameworks and propose different ways to rank-order sets of acceptable arguments.

This paper is centered on the problem of merging (possibly conflicting) information coming from different sources. Though this problem has attracted much attention in propositional settings, propositional languages remain typically not expressive enough for a number of applications, especially when spatial information must be dealt with. In order to fill the gap, we consider a (limited) first-order logical setting, expressive enough for representing and reasoning about information modeled as half-spaces from metric affine spaces. In this setting, we define a family of distance-based majority merging operators which includes the propositional majority operator ΔdH,Σ. We identify a subclass of interpretations of our representation language for which the result of the merging process can be computed and expressed as a formula.

Recently, Dung's argumentation has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another one. We construct an argumentation framework with varied-strength defeats from a preference-based argumentation framework with an intensity degree in the preference relation. We also consider the case when the preference over the arguments is constructed from a valued logic.

We address the problem of merging qualitative constraints networks (QCNs). We point out a merging algorithm which computes a consistent QCN representing a global view of the input set of (possibly conflicting) QCNs. This algorithm is generic in the sense that it does not depend on a specific qualitative formalism. The efficiency of our method comes from the fact that it merges locally the constraints of the input QCNs bearing on the same pairs of variables. We define several constraint merging operators in a way to ensure that the induced QCNs merging operator satisfies some expected properties from a logical standpoint.

The paper proposes a new approach to the handling of preferences expressed in a compact way under the form of conditional statements. These conditional statements are translated into classical logic formulas associated with symbolic levels. Ranking two alternatives then leads to compare their respective amount of violation with respect to the set of formulas expressing the preferences. These symbolic violation amounts, which can be computed in a possibilistic logic manner, can be partially ordered lexicographically once put in a vector form. This approach is compared to the ceteris paribus-based CP-net approach, which is the main existing artificial intelligence approach to the compact processing of preferences. It is shown that the partial order obtained with the CP-net approach fully agrees with the one obtained with the proposed approach, but generally includes further strict preferences between alternatives (considered as being not comparable by the symbolic level logic-based approach). These additional strict preferences are in fact debatable, since they are not the reflection of explicit user's preferences but the result of the application of the ceteris paribus principle that implicitly, and quite arbitrarily, favors father node preferences in the graphical structure associated with conditional preferences. Adding constraints between symbolic levels for expressing that the violation of father nodes is less allowed than the one of children nodes, it is shown that it is possible to recover the CP-net-induced partial order. Due to existing results in possibilistic logic with symbolic levels, the proposed approach is computationally tractable. Key words: preference, priority, partial order, CP-net, possibilistic logic.

From a knowledge representation point of view, it may be interesting to distinguish between (i) what is potentially possible because it is not inconsistent with the available knowledge on the one hand, and (ii) what is actually possible because it is reported from observations on the other hand. Such a distinction also makes sense when expressing preferences, to point out positively desired choices among merely tolerated ones. Possibility theory provides a representation framework where this distinction can be made in a graded way. The two types of information can be encoded by two types of constraints expressed in terms of necessity measures and in terms of so-called guaranteed possibility functions. These two set-functions are min-decomposable with respect to conjunction and disjunction, respectively. This gives birth to two forms of possibilistic logic bases, where clauses (resp., phrases) are weighted in terms of a necessity measure (resp., a guaranteed possibility function). By application of a minimal commitment principle, the two bases induce a pair of possibility distributions at the semantic level, for which a consistency condition should hold to ensure that what is claimed to be actually possible is indeed not impossible. The paper provides a survey of this bipolar representation framework, including the use of conditional measures, or the handling of comparative context-dependent constraints. The interest of the framework is stressed for expressing preferences, as well as in the representation of “if–then” rules in terms of examples and counterexamples. © 2008 Wiley Periodicals, Inc.

Bipolar preferences distinguish between negative preferences inducing what is acceptable by complementation and positive preferences representing what is really satisfactory. This article provides a review of the main logics for preference representation. Representing preferences in a bipolar logical way has the advantage of enabling us to reason about them, while increasing their expressive power in a cognitively meaningful way. In the article, we first focus on the possibilistic logic setting and then discuss two other logics: qualitative choice logic and penalty logic. Finally, an application of bipolar preferences querying systems is outlined. © 2008 Wiley Periodicals, Inc.

Preferences, which control our decisions in the daily life, have been widely studied and analyzed in computer science. In artificial intelligence, preferences are used in many domains such as decision theory, learning, etc. Several representations and reasoning techniques of preferences were proposed. One of these representations is the non-monotonic logic of preferences characterized by the ability to express several interpretations of preferences simultaneously. In relational databases, preferences are used for the personalization of queries to reduce the volume of data presented to the user by offering only the information that interests him. There, preferences are typically specified using binary preference relations among tuples. Binary preference relations are defined by preference formulas which can be embedded into classical relational queries. This paper is intended to discuss the encoding of relational database preference queries in the framework of the non-monotonic logic of preferences. We show that this framework allows the representation of binary preference relations that are asymmetric orders. In addition, it provides several mechanisms to manipulate preference queries efficiently.

In this paper we consider the extension of non-monotonic preference logic with the distinction between controllable (or endogenous) and uncontrollable (or exogenous) variables, which can be used for example in agent decision making and deliberation. We assume that the agent is optimistic about its own controllable and pessimistic about its uncontrollable, and we study ways to merge these two distinct dimensions. We also consider complex preferences, such as optimistic preferences conditional on an uncontrollable, or optimistic preferences conditional on a pessimistic preference

This paper proposes a first comparative study of the expressive power of two approaches to the representation of preferences: conditional preferences networks (CP-nets) and a logical preference representation framework, namely possibilistic logic. It is shown that possibilistic logic, using a method for handling symbolic priority weights, can always provide complete preorders compatible with the partial CP-net order. Although CP-nets provide an intuitive appealing setting for expressing preferences, possibilistic logic appears to be somewhat more flexible for that purpose.