Sémantique algébrique ďun système logique basé sur un ensemble ordonné fini

✍ Scribed by Abir Nour

• Book ID: 102942663
• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 592 KB
• Volume: 45
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19990450404

✦ Synopsis

Abstract

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.