Possibilistic Boolean games: strategic reasoning under incomplete information

Boolean games offer a compact alternative to normal-form games, by encoding the goal of each agent as a propositional formula. In this paper, we show how this framework can be naturally extended to model situations in which agents are uncertain about other agents' goals. We first use uncertainty measures from possibility theory to semantically define (solution concepts to) Boolean games with incomplete information. Then we present a syntactic characterization of these semantics, which can readily be implemented, and we characterize the computational complexity

Prime Forms in Possibilistic Logic

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized prime implicant. We first consider several desirable properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime implicant in possibilistic logic do not satisfy all of these properties. We then provide a novel definition of prioritized prime implicant, which is a set of weighted literals that may be inconsistent. We show that the prioritized prime implicants satisfy all the desirable properties. Finally, we discuss the problem of computing prioritized prime implicants of a possibilistic knowledge base

Prime Forms in Possibilistic Logic

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized prime implicant. We first consider several desirable properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime implicant in possibilistic logic do not satisfy all of these properties. We then provide a novel definition of prioritized prime implicant, which is a set of weighted literals that may be inconsistent. We show that the prioritized prime implicants satisfy all the desirable properties. Finally, we discuss the problem of computing prioritized prime implicants of a possibilistic knowledge base

The Basic Principles of Uncertain Information Fusion. An organized review of merging rules in different representation frameworks

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

An Analysis of Sum-Based Incommensurable Belief Base Merging

International audienceDifferent methods have been proposed for merging multiple and potentially conflicting informations. Sum-based operators offer a natural method for merging commensurable prioritized belief bases. Their popularity is due to the fact that they satisfy the majority property and they adopt a non cautious attitude in deriving plausible conclusions. This paper analyses the sum-based merging operator when sources to merge are incommensurable, namely they do not share the same meaning of uncertainty scales. We first show that the obtained merging operator can be equivalently characterized either in terms of an infinite set of compatible scales, or by a well-known Pareto ordering on a set of models. We then study different families of compatible scales useful for merging process. This paper also provides a postulates-based analysis of our merging operators