Foundations of Equational Logic Programming

✍ Scribed by Steffen Hölldobler (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1989
• Tongue: English
• Leaves: 259
• Series: Lecture Notes in Computer Science 353 : Lecture Notes in Artificial Intelligence
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Introduction....Pages 1-14
Preliminaries....Pages 15-23
Equational Logic Programming....Pages 24-64
Universal Unification....Pages 65-75
SLDE-Resolution....Pages 76-84
Paramodulation....Pages 85-173
Universal Unification by Complete Sets of Transformations....Pages 174-200
Lazy Resolution and Complete Sets of Inference Rules for Horn Equational Theories....Pages 201-207
Conclusion....Pages 208-230

✦ Subjects

Artificial Intelligence (incl. Robotics); Mathematical Logic and Formal Languages; Programming Languages, Compilers, Interpreters