Generalized Horn Clause Programs

This paper considers, in a general setting, an axiomatic basis for Horn clause logic programming. It characterizes a variety of \Horn-clause-like" computations, arising in contexts such as deductive databases, various abstract interpretations, and extensions to logic programming involving E-uniication, quantitative deduction, and inheritance, in terms of two simple operators , and discusses algebraic properties these operators must satisfy. It develops xpoint and model-theoretic semantics in this generalized setting, and shows that the xpoint semantics is well-deened and coincides with the model-theoretic semantics. This leads to a generalized notion of a Horn clause logic program that captures a variety of xpoint computations proposed in different guises, and allows concise expression in the logic programming idiom of several programs that involve aggregate operations.

[1]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[2]  Robert A. Kowalski,et al.  The Semantics of Predicate Logic as a Programming Language , 1976, JACM.

[3]  I. Anderson,et al.  Graphs and Networks , 1981, The Mathematical Gazette.

[4]  William A. Kornfeld.  Equality for Prolog , 1983, IJCAI.

[5]  Christoph Walther,et al.  Unification in Many-Sorted Theories , 1984, ECAI.

[6]  Roberto Barbuti,et al.  On the Integration of Logic Programming and Functional Programming , 1984, SLP.

[7]  Michael J. Maher,et al.  A Theory of Complete Logic Programs with Equality , 1984, J. Log. Program..

[8]  Hisao Tamaki,et al.  Semantics of a Logic Programming Language with a Reducibility Predicate , 1984, SLP.

[9]  Hisao Tamaki,et al.  Enumeration of Success Patterns in Logic Programs , 1983, Theor. Comput. Sci..

[10]  José Meseguer,et al.  EQLOG: Equality, Types, and Generic Modules For Logic Programming , 1986, Logic Programming: Functions, Relations, and Equations.

[11]  Hassan Aït-Kaci,et al.  Logic and inheritance , 1986, POPL '86.

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

[13]  Jean H. Gallier,et al.  SLD-Resolution Methods for Horn Clauses with Equality Based on E-Unification , 1986, SLP.

[14]  Giorgio Levi,et al.  The Relation between Logic and Functional Languages: A Survey , 1986, J. Log. Program..

[15]  M. H. van Emden,et al.  Quantitative Deduction and its Fixpoint Theory , 1986, J. Log. Program..

[16]  Tobias Nipkow,et al.  Unification in Boolean Rings , 1986, CADE.

[17]  Eugene Wong,et al.  An Algebraic Approach to Recursive Inference , 1986, Expert Database Conf..

[18]  Hassan Aït-Kaci,et al.  LOGIN: A Logic Programming Language with Built-In Inheritance , 1986, J. Log. Program..

[19]  Heikki Mannila,et al.  Flow Analysis of Prolog Programs , 1987, SLP.

[20]  Suzanne W. Dietrich,et al.  Extension Tables: Memo Relations in Logic Programming , 1987, SLP.

[21]  Laurent Vieille,et al.  A Database-Complete Proof Procedure Based on SLD-Resolution , 1987, ICLP.

[22]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[23]  Saumya K. Debray,et al.  Automatic Mode Inference for Logic Programs , 1988, J. Log. Program..

[24]  D. S. Parker.  Partial Order Programming. , 1989 .

[25]  Giorgio Levi,et al.  Declarative Modeling of the Operational Behavior of Logic Languages , 1989, Theor. Comput. Sci..

[26]  Michael J. Maher,et al.  Déjà Vu in Fixpoints of Logic Programs ∗ , 1989 .

[27]  Maurice Nivat,et al.  Resolution of Equations in Algebraic Structures , 1989 .

[28]  J. Goguen,et al.  Order-Sorted Equational Computation , 1989 .

[29]  Manuel V. Hermenegildo,et al.  Determination of Variable Dependence Information through Abstract Interpretation , 1989, NACLP.

[30]  François Bry,et al.  Query Evaluation in Recursive Databases , 1990 .

[31]  Sergio Greco,et al.  Minimum and maximum predicates in logic programming , 1991, PODS '91.

[32]  S. Sudarshan,et al.  Aggregation and Relevance in Deductive Databases , 1991, VLDB.

[33]  Raghu Ramakrishnan,et al.  Magic Templates: A Spellbinding Approach To Logic Programs , 1991, J. Log. Program..

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

[35]  Roberto Giacobazzi,et al.  A Generalized Semantics for Constraint Logic Programs , 1992, Fifth Generation Computer Systems.

[36]  Kim Marriott,et al.  Denotational abstract interpretation of logic programs , 1994, TOPL.

[37]  Michael Codish,et al.  Bottum-up abstract interpretation of logic programs , 1992 .

[38]  Agostino Cortesi,et al.  Optimal Groundness Analysis Using Propositional Logic , 1996, J. Log. Program..