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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 ..."
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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.
An Overview of Linear Logic Programming
 in Computational Logic
, 1985
"... Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequen ..."
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Cited by 7 (1 self)
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Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequents and richer dynamics in the rewriting of sequents during proof search, it was inevitable that linear logic would be used to design new and more expressive logic programming languages. We overview how linear logic has been used to design such new languages and describe briefly some applications and implementation issues for them.