Sémantique algébrique ďun système logique basé sur un ensemble ordonné fini

In order to modelize the reasoning of an intelligent agent represented by a poset T , H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems called L ′ T without this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness theorem of the L ′ T system with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between the L ′ T logic and the intuitionistic and classical logics.