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Sémantique algébrique ďun système logique basé sur un ensemble ordonné fini
Author(s) -
Nour Abir
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450404
Subject(s) - mathematics , decidability , gödel's completeness theorem , algebraic semantics , algebraic logic , completeness (order theory) , partially ordered set , algebraic number , discrete mathematics , universal algebra , propositional calculus , first order logic , corollary , classical logic , algebra over a field , pure mathematics , mathematical analysis
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.