Abstract Argumentation has become an essential tool in AI, allowing the representation of knowledge with only a set of arguments and a binary relation between arguments, the attack relation. Since the seminal work presented in 1995 by Dung, many extensions have been proposed in order to enrich this very simple framework by the addition of a second type of interaction, the support relation, and by the use of higher-order or collective interactions. In parallel, several links have been exhibited and studied between Logics and Abstract Argumentation, showing that these two domains are closely interrelated. Among these works, one can find several logical encodings of abstract argumentation frameworks. Nevertheless, these encodings are very often built ad hoc and only for some given frameworks. The aim of this paper is to propose a generic logical encoding covering several families of abstract argumentation frameworks, from Dung’s framework to the most enriched framework using higher-order and collective evidential supports and attacks.

In the field of pattern mining, a negative sequential pattern is specified by means of a sequence consisting of events to occur and of other events, called negative events, to be absent. For instance, containment of the pattern a ¬b c arises with an occurrence of a and a subsequent occurrence of c but no occurrence of b in between. This article is to shed light on the ambiguity of such a seemingly intuitive notation and we identify eight possible semantics for the containment relation between a pattern and a sequence. These semantics are illustrated and formally studied, in particular we propose dominance and equivalence relations between them. Also we prove that support is anti-monotonic for some of these semantics. Some of the results are discussed with the aim of developing algorithms to extract efficiently frequent negative patterns.

Rule learning is a data analysis task consisting of extracting rules to generalize examples. For a data scientist, some generalizations called here admissible generalizations, make more sense. We explore formal properties of admissible generalizations. A formalization for generalization of examples is proposed that allows to express rule admissibility. Some admissible generalizations are captured by topological operators. We examine selecting supersets of examples that induce these operators and we define classes of such choice functions. This formalization is particularly developed in the case of numerical attributes. Classes of such functions are associated with notions of generalization and they are used to comment some behaviours of the CN2 algorithm.

Ranking-based semantics are a way of assessing the acceptability of arguments in an abstract argumentation framework, by providing a ranking on arguments. This paper aims at going towards a generalization of the construction of such semantics, by investigating subsumption and incompatibility cases that may arise when principles that may enter into their composition are combined.

An original method for the extraction of one maximal subset of a set of Boolean clauses that must be satisfiable with possibly mutually contradictory assumptive contexts is motivated and experimented. Noticeably, it performs a direct computation and avoids the enumeration of all subsets that are satisfiable with at least one of the contexts. The method applies for subsets that are maximal with respect to inclusion or cardinality.

An argument is seen as reason in favour of a claim. It is made of three parts: a set of premises representing the reason, a conclusion representing the supported claim, and a connection showing how the premises lead to the conclusion. Arguments are frequently exchanged by human agents in natural language (spoken or written) in discussion, debate, negotiation, persuasion, etc. They may be very different in that their three components may have various forms. In this paper, we propose a language for representing such arguments. We show that it is general enough to capture the various forms of arguments encountered in natural language, and that it is possible to represent attack and support relations between arguments as formulas of the same language.

This paper is intended to lay down the basic foundations of logic-based argumentation for reasoning about bounded resources. First, a simple variant of Boolean logic is introduced, allowing us to reason about consuming resources. An adapted tableau method is presented as a means for automated reasoning in the logic. Then, the main concepts of logic-based argumentation are revisited in this framework.

We are interested by argumentation systems which build their arguments from a propositional knowledge base (KB), and evaluate them using Dung's acceptability semantics. We start by showing that such systems are infinite, i.e. from a finite KB, an infinite set of arguments and an infinite set of attacks among them are generated. While the construction of arguments under propositional logic is costly even in the finite case, the fact that those systems are infinite makes them completely useless. Then, we provide a procedure which, given an argumentation system, computes its finite sub-system, called core. A core considers a finite subset of arguments and a finite subset of attacks, and returns all the results of the original system. This means that a finite subset of arguments is sufficient to draw all the expected conclusions from a KB.

In this paper, we examine logical formalisms with respect to contradictions and related notions. We deal with virtually any kind of logical formalisms, including those that fail to have any connective. We investigate various properties, especially paraconsistency. Among the topics discussed are ways of specifying contradictions and, more generally, inconsistency, as well as a few criteria for paraconsistency. We further explore logical formalisms that overlap with fragments of classical logic, and provide a couple of formal results for them. A number of options about inconsistency are also discussed throughout the text, insisting on how contradictions can be specified either directly, or by way of reference to a fragment of classical logic. Importantly, the concept of undesirable conclusions is given a formal account, which is applied to most of the issues involved in this paper. A noticeable point is that we take into account not only features of the language, depending on the formalism, but also some aspects of inference, most notably the so-called Identity.

We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We introduce a simple logical language which makes it possible to express that a fact causes another fact and that a fact explains another fact. We present a set of formal inference patterns from causal statements to explanation statements. We introduce an elementary ontology which gives greater expressiveness to the system while staying close to propositional reasoning. We provide an inference system that captures the patterns discussed, in a datalog (limited predicate) framework.

This paper is centered on a family of propositional multivalued logics, based on bilattices. The semantics of such logics relies on a set of “truth values,” with two orderings that give the set a bilattice structure. Many interesting inference relations can be defined on these grounds, especially paraconsistent ones and/or nonmonotonic ones. The focus is laid on Belnap's fundamental bilattice logic FOUR, with four “epistemic truth values,” which proves sufficient for the purpose of inference. We show how the bilattice can be associated with a second biordinal structure, which no longer is bilatticial but bipolar. We show how additional inference relations in the logic FOUR can be obtained by exploiting the two preorders associated with this structure. © 2008 Wiley Periodicals, Inc.

The problem of combining pieces of information issued from several sources can be encountered in various fields of application. This paper aims at presenting the different aspects of information fusion in different domains, such as databases, regulations, preferences, sensor fusion, etc., at a quite general level. We first present different types of information encountered in fusion problems, and different aims of the fusion process. Then we focus on representation issues which are relevant when discussing fusion problems. An important issue is then addressed, the handling of conflicting information. We briefly review different domains where fusion is involved, and describe how the fusion problems are stated in each domain. Since the term fusion can have different, more or less broad, meanings, we specify later some terminology with respect to related problems, that might be included in a broad meaning of fusion. Finally we briefly discuss the difficult aspects of validation and evaluation. © 2001 John Wiley & Sons, Inc.

In this paper, we elaborate the idea that contexts provide an important and meaningful notion in default reasoning. We demonstrate this by looking at Reiter's default logic that has been the prime candidate for formalizing consistency-based default reasoning ever since its introduction in 1980. This results in a new context-based approach to default logic, called contextual default logic. The approach extends the notion of a default rule and supplies each default extension with a context. In particular, contextual default logic provides a unified framework for default logics. That is, it allows for embedding existing variants of default logic along with more traditional approaches like the closed world assumption. Since this is accomplished in a homogeneous way, we gain additional expressiveness by combining the diverse approaches. A key advantage of contextual default logic is that it provides a syntactical instrument for comparing existing default logics in a unified setting. In particular, the approach reveals that existing default logics mainly differ in the way they deal with an explicit or implicit underlying context.

We introduce a uniform semantical framework for various default logics in terms of Kripke structures. This possible worlds approach provides a simple but meaningful instrument for comparing existing default logics in a unified setting. The possible w

Paraconsistent logics are examined as an approach to knowledge representation devoted to the formalization of reasoning in the presence of contradictions. the adequacy of paraconsistent logics in such a perspective is described both on a general level and on a more specific level: discussion involves representative examples as well as special features (in the form of logical principles) of some significant paraconsistent logics. There is also a comparison of the paraconsistent logics approach with two alternative approaches, namely belief revision and non-monotonic logics. © 1994 John Wiley & Sons, Inc.