Prime Implicate Generation in Equational Logic

Prime Implicate Generation in Equational Logic

We present an algorithm for the generation of prime implicates in equational logic, that is, of the most general consequences of formulæ containing equations and disequations between first-order terms. This algorithm is defined by a calculus that is proved to be correct and complete. We then focus on the case where the considered clause set is ground, i.e., contains no variables, and devise a s...

Quantifier-Free Equational Logic and Prime Implicate Generation

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 .

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...

A New Algorithm for Incremental Prime Implicate Generation

Traditional algorithms for prime implicate generation [Quine, 1952; McCluskey, 1956; Tison, 1967; Kean and Tsiknis, 1990; de Kleer, 1992] require the input formulas to be first transformed into a CNF formula. This process, however, requires exponential time in the worst case and can result in an exponential blow up of the input size. Such cases occur frequently when the problem domains are best...