Badran Raddaoui

MUS-based generation of arguments and counter-arguments

Most of the approaches of computational argumentation define an argument as a pair consisting of premises and a conclusion, where the latter is entailed by the former. However, the matter of computing arguments and counter-arguments remains largely unsettled. We propose here a method to compute arguments and counter-arguments in the context of propositional logic, by using the concept of a MUS (Minimally Unsatisfiable Subset). The idea relies on the fact that reduction ad absurdum is valid in propositional logic: 〈Φ,α〉 is an argument induced from a knowledge base Δ iff Φ ⋃ {¬α} is inconsistent. Therefore, if Φ ⋃ {¬α} is a MUS of Δ ⋃ {¬α} that contains ¬α then 〈Φ,α〉 is an argument from Δ. Not only do we present an algorithm that generates arguments, we also present an algorithm generating the complete argumentation tree induced by a given argument. We include a report on computational experimentations with both algorithms.

Measuring inconsistency through minimal proofs

Measuring the degree of inconsistency of a knowledge base provides important context information for making easier inconsistency handling. In this paper, we propose a new fine-grained measure to quantify the degree of inconsistency of propositional formulae. Our inconsistency measure uses in an original way the minimal proofs to characterize the responsibility of each formula in the global inconsistency. We give an extension of such measure to quantify the inconsistency of the whole base. Furthermore, we show that our measure satisfies the important properties characterizing an intuitive inconsistency measure. Finally, we address the problem of restoring consistency using an inconsistency measure.

On Measuring Inconsistency Using Maximal Consistent Sets

An important problem in knowledge-based systems is inconsistency handling. This problem has recently been attracting a lot of attention in AI community. In this paper, we tackle the problem of evaluating the amount of conflicts in knowledge bases, and provide a new fine grained inconsistency measure, denoted MCSC, based on maximal consistent sets. In particular, it is suitable in systems where inconsistency results from multiple consistent sources. We show that our measure satisfies several rational postulates proposed in the literature. Moreover, we provide an encoding in integer linear programming for computing MCSC.

Prime implicates based inconsistency characterization

Measuring inconsistency is recognized as an important issue for handling inconsistencies [5, 6]. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.

A Conditional Logic-Based Argumentation Framework

The goal of this paper is twofold. First, a logic-based argumentation framework is introduced in the context of conditional logic, as conditional logic is often regarded as an appealing setting for knowledge representation and reasoning. Second, a concept of conditional contrariety is defined that covers usual inconsistency-based conflicts and puts in light a specific form of conflicts that often occurs in real-life: when an agent asserts an If then rule, it can be argued that additional conditions are actually needed to derive the conclusion.

On an MCS-based inconsistency measure

An important problem in knowledge-based systems is inconsistency handling. This problem has recently been attracting a lot of attention in AI community. In this paper, we tackle the problem of evaluating the amount of conflicts in knowledge bases, and provide a new fine grained inconsistency measure, denoted I MCC , based on maximal consistent sets (MCSes). The main idea consists in quantifying the inconsistency of a knowledge base by considering that all its consistent pieces of information are possible. Furthermore, we provide an epistemic interpretation of our inconsistency measure using the multimodal logic S5 . Then, we show that I MCC satisfies several state-of-the-art postulates. Moreover, we provide an encoding in integer linear programming for computing our inconsistency measure, which is defined from the set of MCSes. We also propose a Partial Max-SAT encoding, which allows us to avoid the computation of the MCSes. Finally, we provide a comparison between I MCC and two related existing inconsistency measures. A new fine grained inconsistency measure is proposed.A multi-agent consensus based interpretation of the proposed measure.Integer linear programming and Partial Max-SAT models are introduced for computing the proposed measure.

Argumentation Framework Based on Evidence Theory

In many fields of automated information processing it becomes crucial to consider imprecise, uncertain or inconsistent pieces of information. Therefore, integrating uncertainty factors in argumentation theory is of paramount importance. Recently, several argumentation based approaches have emerged to model uncertain data with probabilities. In this paper, we propose a new argumentation system called evidential argumentation framework that takes into account imprecision and uncertainty modeled by means of evidence theory. Indeed, evidence theory brings new semantics since arguments represent expert opinions with several weighted alternatives. Then, the evidential argumentation framework is studied in the light of both Smets and Demspter-Shafer interpretations of evidence theory. For each interpretation, we generalize Dung’s standard semantics with illustrative examples. We also investigate several preference criteria for pairwise comparison of extensions in order to select the ones that represent potential solutions to a given decision making problem.

Computing Inconsistency Using Logical Argumentation

Measuring the degree of conflict of a knowledge base can help us to deal with inconsistencies. Several semantic and syntax based approaches have been proposed separately. In this paper, we use logical argumentation as a field to compute the inconsistency measure for propositional formulae. We show using the complete argumentation tree that our family of measures is able to express finely the inconsistency of a formula following their context and allows us to distinguish between formulae. We extend our measure to quantify the degree of inconsistency of set of formulae and give a general formulation of the inconsistency using some logical properties.

On the Characterization of Inconsistency: A Prime Implicates Based Framework

Measuring inconsistency is recognized as an important issue for handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named dominance, rarely satisfied by syntactic measures. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.

A SAT-Based Framework for Overlapping Community Detection in Networks

In this paper, we propose a new approach to detect overlapping communities in large complex networks. We first introduce a parametrized notion of a community, called k -linked community, allowing us to characterize node/edge centered k-linked community with bounded diameter. Such community admits a node or an edge with a distance at most \(\frac{k}{2}\) from any other node of that community. Next, we show how the problem of detecting node/edge centered k-linked overlapping communities can be expressed as a Partial Max-SAT optimization problem. Then, we propose a post-processing strategy to limit the overlaps between communities. An extensive experimental evaluation on real-world networks shows that our approach outperforms several popular algorithms in detecting relevant communities.