Author:
Dušan Guller
Affiliation:
Comenius University, Slovak Republic
Keyword(s):
Product Logic, DPLL Procedure, Many-valued Logics, Automated Deduction.
Related
Ontology
Subjects/Areas/Topics:
Approximate Reasoning and Fuzzy Inference
;
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Systems
;
Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic
;
Soft Computing
Abstract:
In the paper, we investigate the deduction problem of a formula from a finite theory in the propositional Product logic
from a perspective of automated deduction.Our approach is based on the translation of a formula to an equivalent satisfiable finite order clausal theory,
consisting of order clauses. An order clause is a finite set of order literals of the form $\varepsilon_1\diamond \varepsilon_2$
where $\varepsilon_i$ is either a conjunction of propositional atoms or the propositional constant $\gz$ (false) or $\gu$ (true), and
$\diamond$ is a connective either $<$ or $=$. $<$ and $=$ are interpreted by the equality and standard strict linear order on $[0,1]$, respectively.
A variant of the DPLL procedure, operating over order clausal theories, is proposed.
The DPLL procedure is proved to be refutation sound and complete for finite order clausal theories.