Franz KurfeB. Parallelism in Logic

Transcription

1 Franz KurfeB Parallelism in Logic

2 Artificial Intelligence Kiinstliche Intelligenz edited by Wolfgang Bibel and Walther von Hahn Artificial Intelligence aims for an understanding and the technical realization of intelligent behaviour. The books of this series are meant to cover topics from the areas of knowledge processing, knowledge representation, expert systems, communication of knowledge (language, images, speach, etc.), AI machinery as well as languages, models of biological systems, and cognitive modelling. In English: Automated Theorem Proving by Wolfgang Bibel Parallelism in Logic by Franz Kurfel3 Relative Complexities of First Order Calculi by Elmar Eder In German: Die Wissensreprasentationssprache OPS 5 by Reinhard Krickhahn and Bernd Radig Prolog by Ralf Cordes, Rudolf Kurse, Horst Langend6rfer and Heinrich Rust LISP by Rudiger Esser and Elisabeth Feldmar Logische Grundlagen der KiinstIichen Intelligenz by Michael R. Genesereth and Nils 1. Nilsson Wissenbasierte Echtzeitplanung by Jtirgen Dorn Modulare Regelprogrammierung by Siegfried Bocionek Automatisierung von Terminierungsbeweisen by Christoph Walther Logische und Funktionale Programmierung by Ulrich Furbach

3 Franz KurfeB Parallelism in Logic Its Potential for Performance and Program Development II Vleweg

4 Die Deutsche Bibliothek - CIP-Einheitsaufnahme Kurfess, Franz: Parallelism in logic: its potential for performance and program development / Franz Kurfess. - Braunschweig: Vieweg, 1991 (Artificial intelligence) AMS Subject Classification: 03 B 70,68 N 05, 68 M 20,68 Q 10,68 T 25 Verlag Vieweg P. O. Box Wiesbaden. FR Germany Vieweg is a subsidiary company of the Bertelsmann Publishing International. All rights reserved Friedr. Vieweg & Sohn Verlagsgesellschaft mbh, Braunschweig 1991 No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise, without prior permission of the copyright holder. Cover design: L. Markgraf, Wiesbaden ISBN-13: e-isbn-13: DOl: /

5 Preface The work described in this book is the outcome of the author's contributions to the design of a parallel inference machine in the Artificial Intelligence / Intellektik Group at the Computer Science Department of the Technical University in Munich. It is the revised version of a doctoral dissertation, submitted to the Technical University under the same title in The research was carried out in the framework of the European ESPRIT programme, project 415: "Parallel Architectures and Languages for Advanced Information Processing - A VLSI-directed Approach", with Philips Research Laboratories, Eindhoven, The Netherlands, as main contractor, and Nixdorf Computer AG, Paderborn, Germany, as subcontractor for subproject F. Out of the many people who helped me to accomplish this work, I owe the most to Prof. Dr. W. Bibel, who founded the Intellektik Group in Munich, initiated its participation in ESPRIT 415, and hired me for this project although my exposure to logic was rather limited at that time. My thesis advisor, Prof. E. Jessen, deserves a lot of gratitude for his superb supervision and constant encouragement, especially after Prof. Bibelleft Munich; without his help, it would have taken me even longer to complete this work. Many more people contributed to the research described here; an overview can be found in the back of the book (p. 269). My final thanks go to Catharine 0 'Shaughnessy for her patience and support, especially during the final stage. Berkeley, March 1991 Franz K urfeb

6 Abstract This book discusses the potential of parallelism in logic programming and its exploitation on parallel architectures. Whereas the state of the art is almost exclusively restricted to an exploitation of ANDor OR-parallelism, a variety of categories of parallelism is discussed with respect to different levels of a logical formula (formula, clause, literal, term) and different ways to evaluate it. This discussion is based on formal specifications of the categories using the language UNITY (Chandy and Misra, 1988). As an outcome of these investigations, a proposal is made to capture both the specification of parallel problems with logic, as well as the exploitation of parallelism in the evaluation of a logic formula or program: Modularity allows structuring of logic programs in an appropriate way, and meta-evaluation can be used to control the evaluation process on a parallel system. This combination yields a consistent programming framework with a wide scope ranging from program specification and verification to implementation and execution on parallel archi tectures. Finally, the suitability of a specific evaluation mechanism for parallel architectures is investigated. The spanning setter concept is derived from the connection method (Bibel, 1987) and relies on a statical analysis of the formula to achieve largely independent computation units suited for execution on parallel computer systems. The potential of parallelism in logic reaches far beyond the exploitation of AND- and OR-parallelism usually found in attempts to parallelize PROLOG. Moderate language enhancements and an appropriate evaluation mechanism offer a programming framework with strong expressiveness and efficient execution, without sacrificing the cleanliness of the underlying theoretical foundations.

7 Contents 1 Introduction Logic Parallelism Parallelism and Logic Relevance of the Work Organization of the Book Foundations Logic: The Connection Method Parallelism: UNITY and Processes Model Elimination A Language: Lop Conclusions 64 3 State of the Art Parallel Logic Systems Conclusions Parallelism in Logic Chapter Organization Variations on Parallelism Overview Multitasking Modularity Precision.. 120

8 4.7 Competition Spanning Sets Reductions o R-Parallelism Routes AND-Parallelism Term Parallelism Distributed Representation Conclusions: Parallelism in Logic A Parallel Logic Language: MMLOP Overview Syntax Semantics Examples Computational Model A Computational Model for MMLop Architecture Overview Architecture.... Spanning Setters.... Mappings to Parallel Architectures Unification Conclusions: Spanning Setters and Parallel Architectures255 8 Conclusions Foundations State of the Art Parallelism in Logic MMLOP: A Parallel Logic Programming Language Computational Model Architecture V1l1

9 List of Figures 2.1 A predicate logic formula and its matrix notation The matrix with connections The matrix with copies Program COMPLEMENTARY PATHS Program COMPLEMENTARY PATHS A model elimination tableau Program PROVER Program EXTENSION Program EXTREE Program REDUCTION Program EXTENSION Program PROVER-2a Program PROVER-2b PROLOG and Lop notation The Syntax of Lop An interpretation for Lop Fanning of a Lop formula The Space of Parallelism in Logic Program TASK-EXEC Program TASK-LOGIC Program MODULE-EXECl Program MODULE-EXEC Program PRECISION Program CALCULI

10 4.8 Program STRATEG Program STRATRBF Program STRATBDF Program SPASE Program TAUTOLOGY Program SUBSUMPTION Program RESTRICTED UNIT RESOLUTION Program PURITY REDUCTION Program ISOLATED CONNECTION REDUCTION Program OR Program ROUTES Program AND/OR Program TERM Program FORWARD A computational model for MMLop Anatomy of a spanning setter A team of spanning setters Functional structure of spanning setters Bus-connected spanning setters Transputer-based node Transputer system Transputer tree Massively parallel system Dag representation of terms Root connection First forward Second forward Melted dag Program SYNC-UNIF 254 x

11 List of Tables 3.1 Extended Warren Abstract Machine 3.2 ANDORRA AQUARIUS / PPP AURORA CONCURRENT PROLOG 3.6 DELTA PROLOG GUARDED HORN CLAUSES 3.8 PARLOG. 3.9 PARTHEO 3.10 PEPSys 3.11 PIM 3.12 POPE 4.1 Multitasking 4.2 Modularity 4.3 Precision 4.4 Calculi 4.5 Strategies 4.6 Find Connections 4.7 Construction of Spanning Sets 4.8 Unification Spanning Sets 4.10 Tautology Reduction 4.11 Subsumption 4.12 Factorization

12 4.13 Restricted Unit Resolution Purity Isolated Connection Reduction Reductions OR-Parallelism Routes AND-Parallelism Forwarding Chaining Occur Check Bottom-up Separability Function Call Distributed Representation Parallel phenomena and their description: Coarse grain Parallel phenomena and their description: Medium grain Parallel phenomena and their description: Fine grain Features of parallel architectures Bus-based system Transputer-based system Massively parallel system. 249 Xll