Contributions to the Theory of Logic Programming

Hom clauses of first-order predicate logic can be regarded as a high-level programming language when SLD-resolution, a special-purpose resolution theorem prover, is used as interpreter. Consequently, the semantics of Hom clauses can be studied both by model-theoretic and fixpoint methods (in the sense of Scott). This possibility is exploited here by identifying the least (greatest) fixpoint with a least (greatest) model. Successful termination of SLD-resolution is characterized by least fupoints. A semantic characterization of finite failure of SLD-resolution is given, which coincides with the greatest fixpoint only for a special case of clauses. It is shown that nondeterministic flowchart schemata of bounded nondeterminacy are modeled by this special case; the connection between finite failure and greatest fixpoint is then used to give a semantic characterization of termination, blocking, and nontermination of such flowchart schemata.

[1]  Andrzej Blikle.  Proving Programs by Sets of Computations , 1974, MFCS.

[2]  Keith L. Clark.  Predicate logic as a computational formalism , 1979 .

[3]  David Harel.  On the Total Correctness of Nondeterministic Programs , 1981, Theor. Comput. Sci..

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

[5]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[6]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

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

[8]  M. H. van Emden.  Verification Conditions as Programs , 1976, ICALP.

[9]  Raymond Reiter.  On Closed World Data Bases / 119 on Closed World Data Bases , .

[10]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[11]  M. H. van Emden,et al.  Computation and Deductive Information Retrieval , 1977, Formal Description of Programming Concepts.

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

[13]  Donald W Loveland,et al.  Automated theorem proving: a logical basis , 1978, Fundamental studies in computer science.

[14]  Howard Arden Blair.  The recursion-theoretic complexity of the fixed-point semantics of definite sentences , 1980 .

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

[16]  Alain Colmerauer,et al.  Metamorphosis Grammars , 1978, Natural Language Communication with Computers.