Author:
Dušan Guller
Affiliation:
Comenius University, Slovak Republic
Keyword(s):
The DPLL procedure, Automated deduction, Gödel logic, Many-valued logics.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Systems
;
Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic
;
Soft Computing
Abstract:
In the paper, we investigate the satisfiability and validity problems of a formula in the propositional Gödel logic. Our approach is based on the translation of a formula to an equivalent CNF one which contains literals of the augmented form: either a or a→b or (a→b)→b, where a, b are propositional atoms or the propositional constants 0, 1. A CNF formula is further translated to an equisatisfiable finite order clausal theory which consists of order clauses, finite sets of order literals of the forms a ≖ b or a ≺ b. ≖ and ≺ are interpreted by
the equality and strict linear order on [0,1], respectively. A variant of the DPLL procedure for deciding the satisfiability of a finite order clausal theory is proposed. The DPLL procedure is proved to be refutation sound and complete. Finally, we reduce the validity problem of a formula (tautology checking) to the unsatisfiability of a finite order clausal theory.