Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Representation and duality of the untyped lambda-calculus in nominal lattice and topological semantics, with a proof of topological completeness

We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is necessary)

An Object-oriented Formal Notation: Executable Specifications in Clay = Una notación formal orientada a objetos : especificaciones ejecutables con Clay

This thesis presents Clay, a stateless object-oriented formal notation. Clay is class-based, has a nominal type system that integrates algebraic types and inheritance, has equality, method overriding with Scandinavian semantics, dynamic binding, and a rather permissive overloading. The type system of Clay is used to reject illegal specifications, and also to help guide the translation schemes that define the Clay semantics and the generation of executable prototypes. Clay has a first-order semantics that gives an interpretation in first-order logic of the main object-oriented constructions: inheritance, defining classes by cases, overloading, dynamic binding and static equality. Furthermore, the use of the concrete syntax of an automatic theorem prover (Prover9/Mace4) has allowed mechanising both, the Clay's meta-theory and specifications. For example, some of the theorems about Clay in this thesis have been proved semi-automatically. The thesis presents also a compilation scheme of Clay specifications into Prolog programs. Code can be generated from implicit specifications, even recursive ones, something hard to find in other tools. My implementation takes advantage of various logic programming techniques in order to achieve reasonable efficiency: constraints, constructive negation, Lloyd-Topor transforms, incremental deepening search, etc. A Clay compiler is also contributed, a tool that goes beyond the mathematical presentation of the translations into first-order logic and the synthesis of logic programs. I have built a compiler that supports syntax analysis of modular Clay specifications, type checking, translation of Clay specifications into first-order theories in Prover9/Mace4, and synthesis of executable Prolog prototypes

Tense and the Logic of Change

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic

Anaphora and the Logic of Change

This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim