Prime Implicate Generation in Equational Logic

Abduction and prime implicates, from propositional logic to equational logic

Contents Motivations 4 1 State of the art for prime implicate generation in propositional logic 6 1.1 Abduction and prime implicates in propositional logic .

Quantifier-Free Equational Logic and Prime Implicate Generation

Prime Implicates and Prime Implicants in Modal Logic

The purpose of this paper is to extend the notions of prime implicates and prime implicants to the basic modal logic K. We consider a number of different potential definitions of clauses and terms for K, which we evaluate with respect to their syntactic, semantic, and complexity-theoretic properties. We then continue our analysis by comparing the definitions with respect to the properties of th...

A Rewriting Strategy to Generate Prime Implicates in Equational Logic

Generating the prime implicates of a formula consists in finding its most general consequences. This has many fields of application in automated reasoning, like planning and diagnosis, and although the subject has been extensively studied (and still is) in propositional logic, very few have approached the problem in more expressive logics because of its intrinsic complexity. This paper presents...

Prime Implicate Normal Form for ALC Concepts

In this paper, we present a new normal form for concept expressions in the description logic ALC which is based on a recently introduced notion of prime implicate. We show that concepts in prime implicate normal form enjoy a number of desirable properties which make prime implicate normal form interesting from the viewpoint of knowledge compilation. In particular, we prove that subsumption betw...