New Graphical Model for Computing Optimistic Decisions in Possibility Theory Framework

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the other represents agent's preferences. We show that computing an optimal optimistic decision comes down to compute the inconsistency degree of the union of the two possibilistic bases augmented with a given decision

Multiple agent possibilistic logic

International audienceThe paper presents a ‘multiple agent’ logic where formulas are pairs of the form (a, A), made of a proposition a and a subset of agents A. The formula (a, A) is intended to mean ‘(at least) all agents in A believe that a is true’. The formal similarity of such formulas with those of possibilistic logic, where propositions are associated with certainty levels, is emphasised. However, the subsets of agents are organised in a Boolean lattice, while certainty levels belong to a totally ordered scale. The semantics of a set of ‘multiple agent’ logic formulas is expressed by a mapping which associates a subset of agents with each interpretation (intuitively, the maximal subset of agents for whom this interpretation is possibly true). Soundness and completeness results are established. Then a joint extension of the multiple agent logic and possibilistic logic is outlined. In this extended logic, propositions are then associated with both sets of agents and certainty levels. A formula then expresses that ‘all agents in set A believe that a is true at least at some level’. The semantics is then given in terms of fuzzy sets of agents that find an interpretation more or less possible. A specific feature of possibilistic logic is that the inconsistency of a knowledge base is a matter of degree. The proposed setting enables us to distinguish between the global consistency of a set of agents and their individual consistency (where both can be a matter of degree). In particular, given a set of multiple agent possibilistic formulas, one can compute the subset of agents that are individually consistent to some degree

OPTIMISTIC DECISION MAKING USING AN APPROXIMATE GRAPHICAL MODEL

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Algorithms for quantitative-based possibilistic lightweight ontologies

International audienceno abstrac

Using Syntactic Possibilistic Fusion for Modeling Optimal Optimistic Qualitative Decision

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Uncertain lightweight ontologies in a product-based possibility theory framework.

International audienceThis paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages, to the product-based possibility theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based possibility theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem. The last part of the paper provides an encoding of the problem of computing inconsistency degree in product-based possibility DL-Lite as a weighted set cover problem and the use of a greedy algorithm to compute an approximate value of the inconsistency degree. This encoding allows us to provide an approximate algorithm for answering instance checking queries in product-based possibilistic DL-Lite. Experimental studies show the quality of the approximate algorithms for both inconsistency degree computation and instance checking querie

An Integer 0-1 Linear Programming Approach for Computing Inconsistency Degree in Product-Based Possibilistic DL-Lite.

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Logique possibiliste multi-agents : Validité et Complétude

Cet article présente le résultat de la complétude et de la correction de la logique possibiliste multi-agents. La logique possibiliste multi-agents est une extension de la logique possibiliste. Elle manipule des formules de la forme (a, α/A) tels que a est une formule propositionnelle, α ∈ [0, 1] et A un sous-ensemble d’agents. En effet, les propositions sont associées à la fois aux degrés de certitude et aux ensembles d’agents. La logique possibiliste multi-agents permet d’exprimer que : au moins tous les agents qui sont dans l’ensemble A croient que la formule a est vraie a au moins un degré α

Reasoning with Multiple-Agent Possibilistic Logic

International audienceIn multiple-agent logic, a formula is in the form of (a, A) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form (a,α/A) expressing that all agents in set A believe at least at some level α that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms