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

Gradient-prolongation commutativity and graph theory

This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very important, since it characterizes the gradients of coarse nodal functions in the coarse edge function space. They will be expressed using graph theory and they provide techniques to compute approximation bases at each level.Comment: 6 page

Trust-based belief change

International audienceWe propose a modal logic that supports reasoning about trust-based belief change. The term trust-based belief change refers to belief change that depends on the degree of trust the receiver has in the source of information

Discounting in Strategy Logic

Discounting is an important dimension in multi-agent systems as long as we want to reason about strategies and time. It is a key aspect in economics as it captures the intuition that the far-away future is not as important as the near future. Traditional verification techniques allow to check whether there is a winning strategy for a group of agents but they do not take into account the fact that satisfying a goal sooner is different from satisfying it after a long wait. In this paper, we augment Strategy Logic with future discounting over a set of discounted functions D, denoted SLdisc[D]. We consider "until" operators with discounting functions: the satisfaction value of a specification in SLdisc[D] is a value in [0, 1], where the longer it takes to fulfill requirements, the smaller the satisfaction value is. We motivate our approach with classical examples from Game Theory and study the complexity of model-checking SLdisc[D]-formulas.Comment: Extended version of the paper accepted at IJCAI 202

Compatible Coarse Nodal and Edge Elements Through Energy Functionals

23 pagesInternational audienceWe propose new algorithms for the setup phase of algebraic multigrid AMG) solvers for linear systems coming from edge element discretization. The construction of coarse levels is performed by solving an optimization problem with a Lagrange multiplier method: we minimize the energy of coarse bases under a constraint linking coarse nodal and edge element bases. On structured meshes, the resulting AMG method and the geometric multigrid method behave similarly as preconditioners. On unstructured meshes, the convergence rate of our method compares favorably with the AMG method of Reitzinger and Schöberl

GDL Meets ATL: A Logic for Game Description and Strategic Reasoning

National audienceThis paper presents a logical framework that extends the Game Description Language with coalition operators from Alternating-time Temporal Logic and prioritised strategy connectives. Our semantics is built upon the standard state transition model. The new framework allows us to formalise van Benthem’s game-oriented principles in multi-player games, and formally derive Weak Determinacy and Zermelo’s Theorem for two-player games. We demonstrate with a real-world game how to use our language to specify a game and design a strategy, and how to use our framework to verify a winning/no-losing strategy. Finally, we show that the model-checking problem of our logic is in 2EXPTIME with respect to the size of game structure and the length of formula, which is no worse than the model-checking problem in ATL