HANDBOOK OF LOGIC IN ARTIFICIAL INTELLIGENCE AND LOGIC PROGRAMMING

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1 HANDBOOK OF LOGIC IN ARTIFICIAL INTELLIGENCE AND LOGIC PROGRAMMING Volume 5 Logic Programming Edited by DOV M. GABBAY and C. J. HOGGER Imperial College of Science, Technology and Medicine London and J. A. ROBINSON Syracuse University, New York CLARENDON PRESS OXFORD 1998

2 vu Contents List of contributors XIV Introduction: Logic and Logic Programming Languages Michael J. O'Donnell 1 1 Introduction Motivation A notational apology 3 2 Specifying logic programming languages Semantic systems and semantic consequences Query Systems, questions and answers Examples of logic programming languages 15 3 Implementing logic programming languages Proof systems Soundness and completeness of proof systems Programming systems Soundness and completeness of programming systems Proof-theoretic foundations for logic programming 56 4 The uses of semantics Logical semantics vs. denotational semantics Logical semantics vs. initial/final-algebra and Herbrand semantics \ 58 Equational Logic Programming Michael J. O'Donnell 69 1 Introduction to equational logic programming Survey of prerequisites, Motivation for programming with equations Outline of the chapter 74 2 Proof systems for equational logic Inferential proofs Term rewriting proofs The confluence property and the completeness of term rewriting 81 3 Term rewriting proof strategies 96

3 viii CONTENTS 3.1 Complete and outer most complete rewriting sequences Sequentiality analysis and optimal rewriting Algorithms and data structures to implement equational languages Ill 4.1 Data structures to represent terms Ill 4.2 Pattern-matching and sequencing methods Driving procedures for term rewriting Compiling efficient code from equations Parallel implementation Extensions to equational logic programming Incremental infinite input and output Solving equations Indeterminate evaluation in subset logic Relational rewriting 151 Proof Procedures for Logic Programming Donald W. Loveland and Gopalan Nadathur Building the framework: the resolution procedure The resolution procedure Linear resolution refinements The logic programming paradigm Horn clause logic programming A framework for logic programming Abstract logic programming languages Extending the logic programming paradigm A language for hypothetical reasoning Near-Horn Prolog Conclusion...> The Role of Abduction in Logic Programming A. C. Kakas, R. A. Kowalski and F. Toni Introduction Abduction in logic Integrity constraints Applications Knowledge assimilation Default reasoning viewed as abduction Negation as failure as abduction Logic programs as abductive frameworks An abductive proof procedure for LP An argumentation-theoretic interpretation 263

4 CONTENTS ix 4.4 An argumentation-theoretic interpretation of the abductive proof procedure Abductive logic programming Generalized stable model semantics An abductive proof procedure for ALP An argumentation-theoretic interpretation of the abductive proof procedure for ALP Computation of abduction through TMS Simulation of abduction Abduction through deduction from the completion Abduction and constraint logic programming Extended logic programming Answer set semantics Restoring consistency of answer sets Rules and exceptions in LP (Extended) Logic Programming without Negation as Failure An argumentation-theoretic approach to ELP A methodology for default reasoning with explicit negation ELP with abduction An abstract argumentation-based framework for default reasoning... : Abduction and truth maintenance Justification-based truth maintenance Assumption-based truth maintenance Conclusions and future work 307 Semantics for Disjunctive and Normal Disjunctive Logic Programs \ Jorge Lobo, Jack Minker and Arcot Rajasekar Introduction Positive consequences in logic programs Definite logic programming Disjunctive logic programming Negation in logic programs Negation in definite logic programs Negation in disjunctive'logic programs Normal or general disjunctive logic programs Stratified definite logic programs Stratified disjunctive logic programs Well-founded and generalized well-founded logic programs 346

5 x CONTENTS 4.4 Generalized disjunctive well-founded semantics Summary Addendum 349 Negation as Failure, Completion and Stratification J. C. Shepherdson Overview/introduction Negation as failure, the closed world assumption and the Clark completion Incompleteness of NF for comp(p) Floundering, an irremovable source of incompleteness Cases where SLDNF-resolution is complete for comp(p) Semantics for negation via special classes of model Semantics for negation using non-classical logics Constructive negation: an extension of negation as failure Concluding remarks Main body Negation in logic programming Negation as failure; SLDNF-resolution The closed world assumption, CWA(P) The Clark completion, comp(p) 374 ^ 2.5 Definite Horn clause programs..." 384 ' 2.6 Three-valued logic Cases where SLDNF-resolution is complete for comp(p): hierarchical, stratified and call-consistent programs Semantics for negation in terms of special classes of models Constructive negation; an extension of negation as failure Modal and autoepistemic logic Deductive calculi for negation as failure, 409 Meta-Programming in Logic Programming P. M. Hill and J. Gallagher Introduction Theoretical foundations Applications Efficiency improvements Preliminaries 427

6 CONTENTS xi 2 The non-ground representation The representation Reflective predicates Meta-programming in Prolog The ground representation The representation Reflective predicates The language Godel and meta-programming Self-applicability Separated meta-programming Amalgamated meta-programming Ambivalent logic Dynamic meta-programming Constructing programs Updating programs The three wise men problem Transforming and specializing programs Specialization of meta-programs Logic program specialization Specialization and compilation Self-applicable program specializers Applications of meta-program specialization Higher-Order Logic Programming Gopalan Nadathur and Dale Miller Introduction " A motivation for higher-order features A higher-order logic The language, Equality between terms \ The notion of derivation A notion of models Predicate variables and the subformula property Higher-order Horn clauses The meaning of computations Restriction to positive terms Provability and operational semantics Towards a practical realization The higher-order unification problem V derivations Designing an actual-interpreter Examples of higher-order programming A concrete syntax for programs 549

7 xii CONTENTS 7.2 Some simple higher-order programs Implementing tactics and tacticals A comparison with functional programming Using A-terms as data structures ' " ' Implementing an interpreter for Horn clauses Dealing with functional programs as data A limitation of higher-order Horn clauses Hereditary Harrop formulas : Universal quantifiers and implications in goals Recursion over structures with binding Conclusion 584 Constraint Logic Programming: A Survey Joxan Jaffar and Michael J. Maher Introduction Constraint languages Logic Programming CLP languages Synopsis Notation and terminology Constraint domains Logical semantics Fixedpoint semantics Top-down execution Soundness and completeness results 615 7, Bottom-up execution Concurrent constraint logic programming Linguistic extensions Shrinking the computation tree \ Complex constraints ' User-defined constraints Negation Preferred solutions Algorithms for constraint solving Incrementality Satisfiability (non-incremental) ' Satisfiability (incremental) Entailment Projection Backtracking Inference engine Delaying/wakeup of goals and constraints Abstract machine 651

8 CONTENTS xiii 11.3 Parallel implementations Modelling of complex problems Analysis and synthesis of analog circuits Options trading analysis Temporal reasoning Combinatorial search problems Cutting stock DNA sequencing Scheduling Chemical hypothetical reasoning Propositional solver Further applications 675 Transformation of Logic Programs Alberto Pettorossi and Maurizio Proietti Introduction A preliminary example Transformation rules for logic programs Syntax of logic programs Semantics of logic programs Unfold/fold rules Correctness of the transformation rules Reversible transformations A derived goal replacement rule The unfold/fold proof method > Correctness results for definite programs _ Correctness results for normal programs Strategies for transforming logic programs Basic strategies Techniques which use basic strategies > Overview of other techniques Partial evaluation and program specialization Related methodologies for program development 771 Index 789

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