Jérôme Mengin

On Decision Problems Related to the Preferred Semantics for Argumentation Frameworks

Argumentation is a form of reasoning, in which two agents cooperate in order to establish the validity of a given argument; this argument could be used to deduce some conclusion of interest. In this article, we look at the credulous and the sceptical decision problems under Dung’s preferred semantics, that is, the problems of deciding if an argument belongs to one or to every preferred extension of an argumentation framework. We present two proof theories for the credulous decision problem and an algorithm which computes one of them. We show how these proof theories can be used for the sceptical decision problem in two particular cases of argumentation frameworks and we give an algorithm which answers that problem in the general case.

Chapter 6 Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion

Abstract This short paper intends first to emphasize the basic distinction between gradual truth and uncertainty, and its relevance when dealing with classification. Then, the representation capabilities of first-order possibilistic logic are pointed out, before briefly providing some hints, which may be of interest for dealing with uncertainty and handling some fuzzy features in description logic.

Preferred Extensions of Argumentation Frameworks: Query Answering and Computation

The preferred semantics for argumentation frameworks seems to capture well the intuition behind the stable semantics while avoiding several of its drawbacks. Although the stable semantics has been thoroughly studied, and several algorithms have been proposed for solving problems related to it, it seems that the algorithmic side of the preferred semantics has received less attention. In this paper, we propose algorithms, based on the enumeration of some subsets of a given set of arguments, for the following tasks: 1) deciding if a given argument is in a preferred extension of a given argumentation framework; 2) deciding if the argument is in all the preferred extensions of the framework; 3) generating the preferred extensions of the framework.

Learning Ordinal Preferences on Multiattribute Domains: The Case of CP-nets

A recurrent issue in decision making is to extract a preference structure by observing the user’s behavior in different situations. In this paper, we investigate the problem of learning ordinal preference orderings over discrete multiattribute, or combinatorial, domains. Specifically, we focus on the learnability issue of conditional preference networks, or CP-nets, that have recently emerged as a popular graphical language for representing ordinal preferences in a concise and intuitive manner. This paper provides results in both passive and active learning. In the passive setting, the learner aims at finding a CP-net compatible with a supplied set of examples, while in the active setting the learner searches for the cheapest interaction policy with the user for acquiring the target CP-net.

Uniform Interpolation by Resolution in Modal Logic

The problem of computing a uniform interpolant of a given formula on a sublanguage is known in Artificial Intelligence as variable forgetting. In propositional logic, there are well known methods for performing variable forgetting. Variable forgetting is more involved in modal logics, because one must forget a variable not in one world, but in several worlds. It has been shown that modal logic K has the uniform interpolation property, and a method has recently been proposed for forgetting variables in a modal formula (of mu-calculus) given in disjunctive normal form. However, there are cases where information comes naturally in a more conjunctive form. In this paper, we propose a method, based on an extension of resolution to modal logics, to perform variable forgetting for formulae in conjunctive normal form, in the modal logic K.

On Sceptical Versus Credulous Acceptance for Abstract Argument Systems

At a high level of abstraction, many systems of argumentation can be represented by a set of abstract arguments, and a binary relation between these abstract arguments describing how they contradict each other. Acceptable sets of arguments, called extensions, can be defined as sets of arguments that do not contradict one another, and attack all their attackers. We are interested in this paper in answering the question: is a given argument in all extensions of an argumentation system? In fact, what is likely to be useful in AI systems is not a simple yes/no answer, but some kind of well-argued answer, called a proof: if an argument is in every extension, why is it so? Several authors have described proofs that explain why a given argument is in at least one extension. In this paper, we show that a proof that an argument is in every extension can be a proof that some meta-argument is in at least one extension of a meta-argumentation system: this meta-argumentation system describes relationships between sets of arguments of the initial system.

Logical Connectives for Nonmonotonicity: A Choice Function-Based Approach

Several semantics for logics that model defeasible inference are based on the idea that not all models of a set F of classical formulas should be considered, but only some of them, the preferred ones. Recently, Daniel Lehmann proved that a very general family of nonmonotonic inference relations can be obtained by using choice functions, that pick some of the models of a given set of logical formulas. However, in this setting the choice function is fixed. This paper describes a semantics where the choice function is defined by formulas: instead of associating a set of models with each formula of the language, we associate a choice function which picks some models. The choice functions are defined for atomic formulas first, and then inductively for every formula, using for each connective a corresponding operator for combining choice functions. We show that this approach generalises classical logic: the choice function associated to a classical formula ϕ is the function that picks, from a set of models M , the elements of M that satisfy ϕ in the classical sense. We then describe operations on choice functions that correspond to connectives meaning for example: “p if it is consistent” or “p prior to q”.