Possibilistic reasoning with partially ordered beliefs

International audienceThis paper presents the extension of results on reasoning with totally ordered belief bases to the partially ordered case. The idea is to reason from logical bases equipped with a partial order expressing relative certainty and to construct a partially ordered deductive closure. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent in the partially ordered one. At the syntactic level we can either use a language expressing pairs of related formulas and axioms describing the properties of the ordering, or use formulas with partially ordered symbolic weights attached to them in the spirit of possibilistic logic. A possible semantics consists in assuming the partial order on formulas stems from a partial order on interpretations. It requires the capability of inducing a partial order on subsets of a set from a partial order on its elements so as to extend possibility theory functions. Among different possible definitions of induced partial order relations, we select the one generalizing necessity orderings (closely related to epistemic entrenchments). We study such a semantic approach inspired from possibilistic logic, and show its limitations when relying on a unique partial order on interpretations. We propose a more general sound and complete approach to relative certainty, inspired by conditional modal logics, in order to get a partial order on the whole propositional language. Some links between several inference systems, namely conditional logic, modal epistemic logic and non-monotonic preferential inference are established. Possibilistic logic with partially ordered symbolic weights is also revisited and a comparison with the relative certainty approach is made via mutual translations

"Minimal defence": a refinement of the preferred semantics for argumentation frameworks

Dung's abstract framework for argumentation enables a study of the interactions between arguments based solely on an ``attack'' binary relation on the set of arguments. Various ways to solve conflicts between contradictory pieces of information have been proposed in the context of argumentation, nonmonotonic reasoning or logic programming, and can be captured by appropriate semantics within Dung's framework. A common feature of these semantics is that one can always maximize in some sense the set of acceptable arguments. We propose in this paper to extend Dung's framework in order to allow for the representation of what we call ``restricted'' arguments: these arguments should only be used if absolutely necessary, that is, in order to support other arguments that would otherwise be defeated. We modify Dung's preferred semantics accordingly: a set of arguments becomes acceptable only if it contains a minimum of restricted arguments, for a maximum of unrestricted arguments.Comment: 8 pages, 3 figure

Научно-технический семинар «Повышение эксплуатационной надежности линейной части магистральных газопроводов газотранспортной системы Украины»

С 11 по 15 марта 2002 г. Научно-технический комплекс «Институт электросварки им. II. О. Па-топа» Национальной Академии наук Украины совместно с ДК «Укртрансгаз» провели научно-технический семинар «Повышение эксплуатационной надежности линейной части магистральных газопроводов газотранспортной системы Украины». Семинар прошел в рамках Проекта Программы развития ООН «Обмен технологической информацией в Украине для поддержки экономических реформ»

Symbolic Possibilistic Logic: Completeness and Inference Methods

International audienceThis paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic

Change in abstract bipolar argumentation systems (SUM 2015)

International audienceAn argumentation system can undergo changes (addition or removal of arguments/interactions), particularly in multiagent systems. In this paper, we are interested in dynamics of abstract bipolar argumentation systems, i.e. argumentation systems using two kinds of interaction: attacks and supports. We propose change characterizations that use and extend previous results defined in the case of Dung abstract argumentation systems

Bipolarity in argumentation graphs: Towards a better understanding

Edited by Benferhat Salem, Philippe LerayInternational audienceDifferent abstract argumentation frameworks have been used for various applications within multi-agents systems. Among them, bipolar frameworks make use of both attack and support relations between arguments. However, there is no single interpretation of the support, and the handling of bipolarity cannot avoid a deeper analysis of the notion of support.In this paper we consider three recent proposals for specializing the support relation in abstract argumentation: the deductive support, the necessary support and the evidential support. These proposals have been developed independently within different frameworks. We restate these proposals in a common setting, which enables us to undertake a comparative study of the modellings obtained for the three variants of the support. We highlight relationships and differences between these variants, namely a kind of duality between the deductive and the necessary interpretations of the support