## Foundations of Equational Logic Programming"Equations 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."--Publisher's web site. |

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### Contents

Introduction | 1 |

Preliminaries | 15 |

Universal Unification | 65 |

Copyright | |

4 other sections not shown

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### Common terms and phrases

applied atom axiom of reflexivity canonical term rewriting complete lattice computed answer substitution conditional term rewriting congruence relation corollary correct answer substitution Definition derivation E-consequence of EP,LP E-interpretation E-unsatisfiable EP-resolution equa equational clause equational logic program equational program EP example consider exists a refutation find a refutation finite Furthermore Gallier goal clause ground confluent ground instance ground terms Hence Herbrand E-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 multiset normal form occurring paramodulation step program clause PROLOG proof proposition refutation of EPu{«=F refutations with respect removal of trivial resolution rule resp rewrite rule selected subgoal selection function set of EP-unifiers SLD-resolution strong completeness term rewriting system theorem tion transformation rules trivial equations unification problem unifier variable elimination variable occurrence variant wrt Hp