Foundations of Equational Logic ProgrammingEquations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, many proposals have been made to integrate equational, functional, and logic programming. This book presents the foundations of equational logic programming. After generalizing logic programming by augmenting programs with a conditional equational theory, the author defines a unifying framework for logic programming, equation solving, universal unification, and term rewriting. Within this framework many known results are developed. In particular, a presentation of the least model and the fixpoint semantics of equational logic programs is followed by a rigorous proof of the soundness and the strong completeness of various proof techniques: SLDE-resolution, where a universal unification procedure replaces the traditional unification algorithm; linear paramodulation and special forms of it such as rewriting and narrowing; complete sets of transformations for conditional equational theories; and lazy resolution combined with any complete set of inference rules for conditional equational theories. |
Contents
Introduction | 1 |
Equational Logic Programming | 24 |
Universal Unification | 65 |
Copyright | |
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Common terms and phrases
applied atom axiom of reflexivity canonical term rewriting complete set computed answer substitution congruence relation correct answer substitution Definition disagreement set E-interpretation E-model EP-resolution EP,LP equa equational clause equational logic program example consider exists a refutation find a refutation finite Furthermore goal clause ground confluent ground terms Hence Herbrand model Herbrand universe Horn clauses Horn equational theories induction hypothesis inference rules innermost redex instantiation and paramodulation lazy narrowing lazy resolution least fixpoint lifting lemma logical E-consequence modulation multiset normal form occur check occurring program clause proof proposition refutation of EPU{F refutations with respect removal of trivial resp rewrite rule RU{F selected subgoal selection function set of transformations SLD-resolution strong completeness term decomposition term rewriting system theorem tion transformation rules trivial equations unconditional term rewriting unification problem unifier universal unification procedures variable elimination variable occurrence variant wrt f wrt ip