Enhancing global SLS-resolution with loop cutting and tabling mechanisms

Abstract Global SLS-resolution is a well-known procedural semantics for top–down computation of queries under the well-founded model. It inherits from SLDNF-resolution the linearity property of derivations, which makes it easy and efficient to implement using a simple stack-based memory structure. However, like SLDNF-resolution it suffers from the problem of infinite loops and redundant computations. To resolve this problem, in this paper we develop a new procedural semantics, called SLTNF-resolution , by enhancing Global SLS-resolution with loop cutting and tabling mechanisms. SLTNF-resolution is sound and complete w.r.t. the well-founded semantics for logic programs with the bounded-term-size property, and is superior to existing linear tabling procedural semantics such as SLT-resolution.

[1]  Teodor C. Przymusinski.  The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics , 1990, Fundam. Inform..

[2]  Jürgen Dix,et al.  Transformation-based bottom-up computation of the well-founded model , 1996, Theory and Practice of Logic Programming.

[3]  Alan van Gelser.  Negation as failure using tight derivations for general logic programs , 1989 .

[4]  Kenneth Kunen,et al.  Negation in Logic Programming , 1987, J. Log. Program..

[5]  Jürgen Dix,et al.  Characterizations of the Disjunctive Well-founded Semantics: Confluent Calculi and Iterated Gcwa , 1997 .

[6]  Allen Van Gelder,et al.  Negation as Failure using Tight Derivations for General Logic Programs , 1988, J. Log. Program..

[7]  Miroslaw Truszczynski,et al.  On the Problem of Computing the Well-Founded Semantics , 2000, Computational Logic.

[8]  Gopal Gupta,et al.  A Simple Scheme for Implementing Tabled Logic Programming Systems Based on Dynamic Reordering of Alternatives , 2001, ICLP.

[9]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[10]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Peter Buneman,et al.  Semistructured data , 1997, PODS.

[13]  Kenneth A. Ross,et al.  A procedural semantics for well founded negation in logic programs , 1989, J. Log. Program..

[14]  Neng-Fa Zhou,et al.  Parameter passing and control stack management in Prolog implementation revisited , 1996, TOPL.

[15]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[16]  Teodor C. Przymusinski,et al.  Soundness and Completeness of Partial Deductions for Well-Founded Semantics , 1992, LPAR.

[17]  Jürgen Dix,et al.  On the equivalence of the static and disjunctive well-founded semantics and its computation , 2001, Theor. Comput. Sci..

[18]  Theresa Swift.  Tabling for non‐monotonic programming , 2004, Annals of Mathematics and Artificial Intelligence.

[19]  Li-Yan Yuan,et al.  SLT-Resolution for the Well-Founded Semantics , 2004, Journal of Automated Reasoning.

[20]  Konstantinos Sagonas,et al.  XSB as an efficient deductive database engine , 1994, SIGMOD '94.

[21]  Robert A. Kowalski,et al.  Predicate Logic as Programming Language , 1974, IFIP Congress.

[22]  Divesh Srivastava,et al.  Bottom-Up Evaluation and Query Optimization of Well-Founded Models , 1995, Theor. Comput. Sci..

[23]  Juliana Freire,et al.  The XSB Programmer's Manual Version 1.7.1 , 1994 .

[24]  David Scott Warren,et al.  Efficient Top-Down Computation of Queries under the Well-Founded Semantics , 1995, J. Log. Program..

[25]  Jack Minker.  Foundations of deductive databases and logic programming , 1988 .

[26]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[27]  Hisao Tamaki,et al.  OLD Resolution with Tabulation , 1986, ICLP.

[28]  Roland N. Bol,et al.  Tabulated Resolution for the Well-Founded Semantics , 1993, J. Log. Program..

[29]  Neng-Fa Zhou,et al.  Efficient fixpoint computation in linear tabling , 2003, PPDP '03.

[30]  Juliana Freire,et al.  The XSB Programmer’s Manual , 1800 .

[31]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[32]  K. A. Ross,et al.  Tabled Evaluation with Delaying for General Logic Programs , 1996 .

[33]  Neng-Fa Zhou,et al.  Semi-naive evaluation in linear tabling , 2004, PPDP '04.

[34]  Krzysztof R. Apt,et al.  An Analysis of Loop Checking Mechanisms for Logic Programs , 1991, Theor. Comput. Sci..

[35]  Danny De Schreye,et al.  Termination of Logic Programs: The Never-Ending Story , 1994, J. Log. Program..

[36]  Qiang Yang,et al.  A dynamic approach to characterizing termination of general logic programs , 2003, TOCL.

[37]  Shinichi Morishita,et al.  An Extension of Van Gelder's Alternating Fixpoint to Magic Programs , 1996, J. Comput. Syst. Sci..

[38]  Miroslaw Truszczynski,et al.  On the problem of computing the well-founded semantics , 2001, Theory Pract. Log. Program..

[39]  Johann Eder,et al.  Logic and Databases , 1992, Advanced Topics in Artificial Intelligence.

[40]  Teodor C. Przymusinski.  Every logic program has a natural stratification and an iterated least fixed point model , 1989, PODS.

[41]  Li-Yan Yuan,et al.  Linear tabulated resolution based on Prolog control strategy , 2000, Theory and Practice of Logic Programming.

[42]  David Scott Warren,et al.  Memoing for logic programs , 1992, CACM.

[43]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[44]  Li-Yan Yuan,et al.  Implementation of a Linear Tabling Mechanism , 2001, J. Funct. Log. Program..