A logic programming system for nonmonotonic reasoning

The evolution of logic programming semantics has included the introduction of a new explicit form of negation, beside the older implicit (or default) negation typical of logic programming. The richer language has been shown adequate for a spate of knowledge representation and reasoning forms.The widespread use of such extended programs requires the definition of a correct top-down querying mechanism, much as for Prolog wrt. normal programs. One purpose of this paper is to present and exploit a SLDNF-like derivation procedure, SLX, for programs with explicit negation under well-founded semantics (WFSX) and prove its soundness and completeness. (Its soundness wrt. the answer-sets semantics is also shown.) Our choice ofWFSX as the base semantics is justi-fied by the structural properties it enjoys, which are paramount for top-down query evaluation.Of course, introducing explicit negation requires dealing with contradiction. Consequently, we allow for contradiction to appear, and show moreover how it can be removed by freely changing the truth-values of some subset of a set of predefined revisable literals. To achieve this, we introduce a paraconsistent version ofWFSX, WFSXp, that allows contradictions and for which our SLX top-down procedure is proven correct as well.This procedure can be used to detect the existence of pairs of complementary literals inWESXp simply by detecting the violation of integrity rulesf ←L, -L introduced for eachL in the language of the program. Furthermore, integrity constraints of a more general form are allowed, whose violation can likewise be detected by SLX.Removal of contradiction or integrity violation is accomplished by a variant of the SLX procedure that collects, in a formula, the alternative combinations of revisable literals' truth-values that ensure the said removal. The formulas, after simplification, can then be satisfied by a number of truth-values changes in the revisable, among “true,” “false”, and “undefined”. A notion of minimal change is defined as well that establishes a closeness relation between a program and its revisions. Forthwith, the changes can be enforced by introducing or deleting program rules for the revisable literals.To illustrate the usefulness and originality of our framework, we applied it to obtain a novel logic programming approach, and results, in declarative debugging and model-based diagnosis problems.

[1]  Frank Teusink,et al.  A Proof Procedure for Extended Logic Programs , 1993, ILPS.

[2]  Gerd Wagner,et al.  A Database Needs Two Kinds of Negation , 1991, MFDBS.

[3]  José Júlio Alferes,et al.  Non-Monotonic Reasoning with Logic Programming , 1993, J. Log. Program..

[4]  Marianne Winslett,et al.  Reasoning about Action Using a Possible Models Approach , 1988, AAAI.

[5]  John W. Lloyd,et al.  A Basis for Deductive Database Systems II , 1986, J. Log. Program..

[6]  Michael Gelfond,et al.  Compiling Circumscriptive Theories into Logic Programs , 1989, NMR.

[7]  Johan de Kleer Focusing on Probable Diagnoses , 1991, AAAI.

[8]  José Júlio Alferes,et al.  Contradiction: When Avoidance Equals Removal - Part II , 1993, ELP.

[9]  José Júlio Alferes,et al.  Diagnosis and Debugging as Contradiction Removal , 1993, LPNMR.

[10]  José Júlio Alferes,et al.  Top-Down Query Evaluation for Well-Founded Semantics with Explicit Negation , 1994, ECAI.

[11]  Paolo Mancarella,et al.  Generalized Stable Models: A Semantics for Abduction , 1990, ECAI.

[12]  Robert A. Kowalski,et al.  Logic for problem solving , 1982, The computer science library : Artificial intelligence series.

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

[14]  Raymond Reiter On Asking What a Database Knows , 1990 .

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

[16]  David Scott Warren,et al.  A Goal-Oriented Approach to Computing the Well-Founded Semantics , 1993, J. Log. Program..

[17]  José Júlio Alferes,et al.  SLX - A Top-down Derivation Procedure for Programs with Explicit Negation , 1994, ILPS.

[18]  Teodor C. Przymusinski Extended Stable Semantics for Normal and Disjunctive Programs , 1990, ICLP.

[19]  autoepistemic Zogic Logic programming and negation : a survey , 2001 .

[20]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[21]  Marianne Winslett,et al.  A model-based belief revision system , 1994, Journal of Automated Reasoning.

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

[23]  Gerd Wagner,et al.  Logic Programming with Strong Negation and Inexact Predicates , 1991, J. Log. Comput..

[24]  José Júlio Alferes,et al.  Belief, Provability, and Logic Programs , 1995, J. Appl. Non Class. Logics.

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

[26]  John W. Lloyd,et al.  A Basis for Deductive Database Systems , 1985, J. Log. Program..

[27]  José Júlio Alferes,et al.  Diagnosis and Debugging as Contradiction Removal in Logic Programs , 1993, EPIA.

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

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

[30]  Wolfgang Nejdl,et al.  Choosing Observations and Actions in Model-Based Diagnosis/Repair Systems , 1992, KR.

[31]  Jürgen Dix,et al.  A Framework for Representing and Characterizing Semantics of Logic Programs , 1992, KR.

[32]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[33]  Krzysztof R. Apt,et al.  On the Safe Termination of PROLOG Programs , 1989, ICLP.

[34]  Robert A. Kowalski,et al.  Linear Resolution with Selection Function , 1971, Artif. Intell..

[35]  Edward Joseph McCluskey Algebraic minimization and the design of two-terminal contact networks , 1956 .

[36]  David Scott Warren,et al.  Query evaluation under the well-founded semantics , 1993, PODS.

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

[38]  Danny De Schreye,et al.  SLDNFA: An Abductive Procedure for Normal Abductive Programs , 1992, JICSLP.

[39]  José Júlio Alferes,et al.  The Extended Stable Models of Contradiction Removal Semantics , 1991, EPIA.

[40]  Wolfgang Nejdl,et al.  Diamon: a model-based troubleshooter based on qualitative reasoning , 1993, IEEE Expert.

[41]  Michael Gelfond,et al.  Representing Actions in Extended Logic Programming , 1992, JICSLP.

[42]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[43]  B. Wuthrich On updates and inconsistency repairing in knowledge bases , 1993, Proceedings of IEEE 9th International Conference on Data Engineering.

[44]  Teodor C. Przymusinski Static semantics for normal and disjunctive logic programs , 1995, Annals of Mathematics and Artificial Intelligence.

[45]  P. Legay,et al.  WELL!: An Evaluation Procedure for All Logic Programs , 1990, ICDT.

[46]  José Júlio Alferes,et al.  Debugging by Diagnosing Assumptions , 1993, AADEBUG.

[47]  Gerd Wagner,et al.  Neutralization and Preemtion in Extended Logic Programs , 1993, LPAR.

[48]  José Júlio Alferes,et al.  Well Founded Semantics for Logic Programs with Explicit Negation , 1992, ECAI.

[49]  Michael Gelfond,et al.  Logic Programs with Classical Negation , 1990, ICLP.

[50]  Luís Moniz Pereira,et al.  REVISE: An Extended Logic Programming System for Revising Knowledge Bases , 1994, KR.

[51]  Raymond Reiter,et al.  Towards a Logical Reconstruction of Relational Database Theory , 1982, On Conceptual Modelling.

[52]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[53]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[54]  Chitta Baral,et al.  Logic Programming and Knowledge Representation , 1994, J. Log. Program..

[55]  José Júlio Alferes,et al.  Derivation Procedures for Extended Stable Models , 1991, IJCAI.

[56]  José Júlio Alferes,et al.  Contradiction: When Avoidance Equals Removal - Part I , 1993, ELP.

[57]  Gerd Wagner Reasoning with Inconsistency in Extended Deductive Databases , 1993, LPNMR.

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

[59]  José Júlio Alferes,et al.  On Logic Program Semantics with Two Kinds of Negation , 1992, JICSLP.

[60]  Robert A. Kowalski,et al.  Legislation as Logic Programs , 1992, Logic Programming Summer School.

[61]  Robert A. Kowalski,et al.  The treatment of negation in logic programs for representing legislation , 1989, ICAIL '89.

[62]  José Júlio Alferes,et al.  Contradiction Removal within Well Founded Semantics , 1991, LPNMR.

[63]  José Júlio Alferes Semantics of logic programs with explicit negation , 1993 .

[64]  Robert A. Kowalski,et al.  Problems and Promises of Computational Logic , 1990 .

[65]  Marianne Winslett,et al.  Immortal: A Model-Based Belief Revision System , 1991, KR.

[66]  Divesh Srivastava,et al.  Query Restricted Bottom-Up Evaluation of Normal Logic Programs , 1992, JICSLP.

[67]  Raymond Reiter On Closed World Data Bases , 1977, Logic and Data Bases.

[68]  Bernhard Nebel,et al.  Belief Revision: Syntax based approaches to belief revision , 1992 .

[69]  D. C. Dashfield HER MAJESTY'S STATIONERY OFFICE , 1954 .