A logic-algebraic tool for reasoning with Knowledge-Based Systems

TL;DR

This paper introduces a logic-algebraic framework for reasoning with propositional knowledge bases, utilizing polynomial derivatives and algebraic inference rules, with proofs of soundness and completeness and practical applications.

Contribution

It presents a novel algebraic inference rule inspired by algebraic geometry for propositional reasoning, along with foundational proofs and applications.

Findings

The inference rule is sound and refutationally complete.

The algebraic approach enables new reasoning techniques for propositional logic.

Applications demonstrate practical utility of the algebraic tools.

Abstract

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on polynomials (on residue rings) which is used to design a new inference rule of algebro-geometric inspiration. Soundness and (refutational) completeness of the rule are proved. Some applications of the tools introduced in the paper are shown.