The Semantics of Nominal Logic Programs

Nominal logic programming is a form of logic programming with “concrete” names and binding, based on nominal logic, a theory of α-equivalence founded on swapping and freshness constraints. Previous papers have employed diverse characterizations of the semantics of nominal logic programs, including operational, denotational, and proof-theoretic characterizations; however, the formal properties and relationships among them have not been fully investigated. In this paper we give a uniform and improved presentation of these characterizations and prove appropriate soundness and completeness results. We also give some applications of these results.

[1]  J. Cheney,et al.  A sequent calculus for nominal logic , 2004, LICS 2004.

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

[3]  Jan Maluszy¿ski.  Constraint Logic Programming with Hereditary Harrop Formulas , 1997 .

[4]  Michael J. Maher,et al.  The Semantics of Constraint Logic Programs , 1998, J. Log. Program..

[5]  James Cheney,et al.  Completeness and Herbrand theorems for nominal logic , 2006, Journal of Symbolic Logic.

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

[7]  James Cheney.  Equivariant Unification , 2005, RTA.

[8]  Christian Urban,et al.  alpha-Prolog: A Logic Programming Language with Names, Binding and a-Equivalence , 2004, ICLP.

[9]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[10]  James Cheney,et al.  The Complexity of Equivariant Unification , 2004, ICALP.

[11]  Andrei Voronkov,et al.  Orienting rewrite rules with the Knuth-Bendix order , 2003, Inf. Comput..

[12]  Frank Pfenning,et al.  Higher-Order Logic Programming as Constraint Logic Programming , 1993, PPCP.

[13]  Andrew M. Pitts,et al.  A First Order Theory of Names and Binding , 2001 .

[14]  Dale Miller,et al.  A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification , 1991, J. Log. Comput..

[15]  Gopalan Nadathur,et al.  Uniform Proofs as a Foundation for Logic Programming , 1991, Ann. Pure Appl. Log..

[16]  Christian Urban,et al.  Nominal logic programming , 2006, TOPL.

[17]  Christian Urban,et al.  Avoiding Equivariance in Alpha-Prolog , 2005, TLCA.

[18]  James Cheney.  A Simpler Proof Theory for Nominal Logic , 2005, FoSSaCS.

[19]  Yike Guo,et al.  Constraint Logic Programming in the Sequent Calculus , 1994, LPAR.

[20]  Christian Urban,et al.  Nominal unification , 2004, Theor. Comput. Sci..