An abstract axiomatization of the notion of entropy

We present an abstract axiomatization of generalized entropy using the notion of ordinal number and the new concept of systemic set of equivalence relations. The aximoatization applies to arbitrary sets and extends previous results obtained for the finite case.

Characterization of Database Dependencies with FCA and Pattern Structures

International audienceIn this review paper, we present some recent results on the characterization of Functional Dependencies and variations with the formalism of Pattern Structures and Formal Concept Analysis. Although these dependencies have been paramount in database theory, they have been used in different fields: artificial intelligence and knowledge discovery, among others

Counting for satisfiability by inverting resolution

10.1007/s10462-004-4329-2Artificial Intelligence Review224339-366AIRV

Feedback Set Problems

. This paper is a short survey of feedback set problems. It will be published in Encyclopedia of Optimization, Kluwer Academic Publishers, 2000. 1. INTRODUCTION In recent years feedback set problems have been the subject of growing interest. They have found applications in many fields, including deadlock prevention [89], program verification [78], and Bayesian inference [2]. Therefore, it is natural that in the past few years there have been intensive efforts on exact and approximation algorithms for these kinds of problems. Exact algorithms have been proposed for solving the problems restricted to special classes of graphs as well as several approximation algorithms with provable bounds for the cases that are not known to be polynomially solvable. The most general feedback set problem consists in finding a minimum-weight (or minimum cardinality) set of vertices (arcs) that meets all cycles in a collection C of cycles in a graph (G,w), where w is a nonnegative function defined on th..