Abstract

In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems the use of a set of constants constitutes a fundamental tool. We have introduced in [8] a logic system called equation image without this kind of constants but limited to the case that T is a finite poset. We have proved a completeness result for this system w.r.t. an algebraic semantics. We introduce in this paper a Kripke-style semantics for a subsystem equation image of equation image for which there existes a deduction theorem. The set of “possible worldsr is enriched by a family of functions indexed by the elements of T and satisfying some conditions. We prove a completeness result for system equation image with respect to this Kripke semantics and define a finite Kripke structure that characterizes the propositional fragment of logic equation image. We introduce a reational semantics which has the advantage to allow an interpretation of the propositionnal logic equation image using only binary relations. We treat also the computational complexity of the satisfiability problem of the propositional fragment of logic equation image.