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A MultipleConclusion MetaLogic
 In Proceedings of 9th Annual IEEE Symposium On Logic In Computer Science
, 1994
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic pro ..."
Abstract

Cited by 86 (7 self)
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The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends the languages λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. As a metalanguage, Forum greatly extends the expressiveness of these other logic programming languages. To illustrate its expressive strength, we specify in Forum a sequent calculus proof system and the operational semantics of a functional programming language that incorporates such nonfunctional features as counters and references. 1
Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder program ..."
Abstract

Cited by 85 (11 self)
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The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.
GoalDirected Proof Search in MultipleConclusioned Intuitionistic Logic
 In Proceedings of the First International Conference on Computational Logic, volume LNAI 1861
, 2000
"... . A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multip ..."
Abstract

Cited by 1 (0 self)
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. A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multipleconclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goaldirected proofs for a multipleconclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both singleconclusioned and multipleconclusioned systems (although the latter are less well known). In this paper we show that the language obtained for the multipleconclusioned system differs from that for the singleconclusioned case, show how hereditary Harrop formulae can be recovered, and investigate contractionfree fragments of the logic. 1 Introduction Logic programming is based upon the observation that if ...
On GoalDirected Proofs in MultipleConclusioned Intuitionistic Logic
"... A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multiple ..."
Abstract
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A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multipleconclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goaldirected proofs for a multipleconclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both singleconclusioned and multipleconclusioned systems (although the latter are less well known than the former). In this paper we show that the language obtained for the multipleconclusioned system differs from that for the singleconclusioned case, and discuss the consequences of this result. Keywords: Multipleconclusioned intuitionistic logic, goaldirected proofs, logic programming languages, hereditary Harrop formu...