Foundations of Equational Logic Programming

Steffen Hölldobler

ISBN 10: 354051533X / ISBN 13: 9783540515333

Editore: Springer Berlin Heidelberg, 1989

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Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9783540515333

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Titolo: Foundations of Equational Logic Programming

Casa editrice: Springer Berlin Heidelberg

Data di pubblicazione: 1989

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

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.

Contenuti:

Preliminaries.- Equational Logic Programming.- Universal Unification.- SLDE-Resolution.- Paramodulation.- Universal Unification by Complete Sets of Transformations.- Lazy Resolution and Complete Sets of Inference Rules for Horn Equational Theories.- Conclusion.