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Provability in Intuitionistic Linear Logic from a New Interpretation on Petri nets (Extended Abstract)
 Electronic Notes in Theoretical Computer Science
, 1998
"... Linear logic is a logic of actions which seems well suited to various computer science applications. From its intrinsic ability to reflect computational resources, it is possible to refine different programming paradigms like formulaeastypes (proofsas programs) or formulaeasstates (proofsasco ..."
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Cited by 10 (5 self)
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Linear logic is a logic of actions which seems well suited to various computer science applications. From its intrinsic ability to reflect computational resources, it is possible to refine different programming paradigms like formulaeastypes (proofsas programs) or formulaeasstates (proofsascomputations) with a finer control on resource management. In the latter case, the correspondence between Intuitionistic Linear Logic (ILL) and Petri nets illustrates the interest of efficient proof search methods for proving specifications or properties of distributed systems. In contrast to existing methods, for instance based on canonical proofs, we propose here to revisit the semantics of ILL and its interpretation on Petri nets to provide new proof techniques for proving or disproving properties. From the relationships between the notions of ordered monoid and of quantale we define a new interpretation of ILL on Petri nets that is complete and verifies the property of finite models. Possi...
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.
FormulaeasResources Management for an Intuitionistic Theorem Prover
 In 5th Workshop on Logic, Language, Information and Computation, WoLLIC'98, Sao Paulo
, 1998
"... This paper outlines new concepts for an alternative implementation of the intuitionistic contractionfree LJT system (and consequently proof search) in imperative programming languages with a good and efficient management of formulae (as resources). Logic programming languages provide natural suppor ..."
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Cited by 2 (2 self)
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This paper outlines new concepts for an alternative implementation of the intuitionistic contractionfree LJT system (and consequently proof search) in imperative programming languages with a good and efficient management of formulae (as resources). Logic programming languages provide natural support to implement automated proof search, without necessity to have explicit knowledge about the form and the number of formulae arising in LJT proofs. By the introduction of a new notion of subformula (and of subformula property) for the LJT system, we obtain interesting and usable results about the possible management of formulae in a proof. A derived structure (a direct acyclic graph), including sharing of subformulae, is proposed to deal with formulae during the proof search and the application of logical rules. The corresponding proof search method is independent of the possible strategies. Therefore we can obtain an eOEcient implementation of LJT in imperative programming language...
Proofs, concurrent objects and computations in a FILL framework
 In Workshop on Objectbased Parallel and Distributed Computation, OBPDC'95
, 1995
"... There are several major approaches to model concurrent computations using logic. In this context, one aim can be to achieve different forms of programming as logic, objectoriented or concurrent ones in a same logical language. Linear logic seems to be wellsuited to describe computations that are c ..."
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Cited by 1 (1 self)
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There are several major approaches to model concurrent computations using logic. In this context, one aim can be to achieve different forms of programming as logic, objectoriented or concurrent ones in a same logical language. Linear logic seems to be wellsuited to describe computations that are concurrent and based on state transitions. In this paper, we propose and analyze a framework based on Full Intuitionistic Linear Logic (FILL), logical fragment with potentialities for nondeterminisms management, as foundation of concurrent objectoriented programming, following the two paradigms proofsearch as computation and proofs as computations.
Specification of Term Rewriting in Linear Logic
, 1998
"... We present an axiomatization of term rewriting systems in Forum, a presentation of linear logic in terms of uniform proofs, which allows us to relate provability and derivability in a natural way. The resulting theory can be used to prove properties of the original system. Vice versa the structure o ..."
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Cited by 1 (1 self)
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We present an axiomatization of term rewriting systems in Forum, a presentation of linear logic in terms of uniform proofs, which allows us to relate provability and derivability in a natural way. The resulting theory can be used to prove properties of the original system. Vice versa the structure of the formulas used in the encoding suggests us a possible operational interpretation of Forum. The considered fragment turns out to be an extension of previously proposed multiconclusion logics.