Author:
Dušan Guller
Affiliation:
Comenius University, Slovak Republic
Keyword(s):
Hyperresolution, Product Logic, Automated Deduction, Fuzzy Logics, Many-valued Logics.
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:
We provide the foundations of automated deduction in the propositional product logic.
Particularly, we generalise the hyperresolution principle for the propositional product logic.
We propose translation of a formula to an equivalent satisfiable finite order clausal theory,
which consists of order clauses - finite sets of order literals of the augmented form: e1 @ e2
where e1 is either a truth constant, 0, 1, or a conjunction of powers of propositional atoms, and @ is a connective from =, <.
= and < are interpreted by the equality and strict linear order on [0,1], respectively.
We devise a hyperresolution calculus over order clausal theories, which is refutation sound and complete for the finite case.
By means of the translation and calculus, we solve the deduction problem T |= phi for a finite theory T and a formula phi.