A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language.Expand

This paper presents a logic programming language, called L, that also contains both function variables and A-abstractions, but certain restriction are placed on occurrences of function variables, so an implementation of LA does not need to implement full higher-order unification.Expand

λProlog is a logic programming language that extends Prolog by incorporating notions of higher-order functions, λ-terms, higher-order unification, polymorphic types, and mechanisms for building… Expand

Forum is presented, a logic programming presentation of all of linear logic that modularly extends the languages /spl lambda/Prolog, Lolli, and LO, and greatly extends the expressiveness of these other logic programming languages.Expand

This paper presents Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO, and specifies in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency.Expand

This paper uses a higher-order logic to describe a generalization to first-order Horn clauses, and shows that the familiar operational and least fixpoint semantics can be given to these clauses.Expand

This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment of logic programming.Expand

This paper is able to prove a strengthen form of the firstorder interpolation theorem as well as provide a correct description of Skolem functions and the Herbrand Universe.Expand

This paper shows that the unification of simply typed ‚-terms modulo the rules of fl- and ·-conversions can be coded as a query of the logic programming language L‚ in a natural and clear fashion.Expand

Using ideas from proof-theory, co-agents are introduced and it is shown that they can specify some testing equivalences for πo, the “propositional” fragment of the π-calculus, which lacks restriction and value passing.Expand