On the Semantics and Automated Deduction for PLFC, a Logic of Possibilistic Uncertainty and Fuzziness

TL;DR

This paper formalizes PLFC, an extension of possibilistic logic with fuzzy constants, and develops a sound resolution calculus and proof procedure for automated deduction in this uncertain, fuzzy setting.

Contribution

It introduces a formal semantics and a resolution-based proof system for PLFC, enabling automated reasoning with fuzzy constants and fuzzy quantifiers.

Findings

Defined a many-valued semantics for fuzzy constants.

Developed a sound resolution calculus for PLFC.

Proposed a novel proof procedure using most general substitutions.

Abstract

Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a proof procedure based on a refutation complete resolution-style calculus. Recently, a syntactical extension of first order Possibilistic logic (called PLFC) dealing with fuzzy constants and fuzzily restricted quantifiers has been proposed. Our aim is to present steps towards both the formalization of PLFC itself and an automated deduction system for it by (i) providing a formal semantics; (ii) defining a sound resolution-style calculus by refutation; and (iii) describing a first-order proof procedure for PLFC clauses based on (ii) and on a novel notion of most general substitution of two literals in a resolution step. In contrast to standard Possibilistic logic semantics, truth-evaluation of formulas with fuzzy constants are many-valued instead of boolean, and consequently an extended notion of possibilistic uncertainty is also needed.