Proof strategies in linear logic

Tammet, Tanel

doi:10.1007/bf00885763

Cited by 42 publications

(24 citation statements)

References 6 publications

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“…Context splitting can be performed as efficiently as in resource management systems [5]. There is, however, no need for transformations in negational normal form or for following the connectives during proof search (an advantage also over Tammet's proof search strategies [26]). Prefix-Unification appears to be as efficient as the acyclicity test implicitly contained in [7] but yields informations which make the conversion into sequent proofs more efficient.…”

Section: Resultsmentioning

confidence: 99%

“…This phenomenon is called permutability of rules and has been investigated for linear logic in [1,10,26]. As solutions to fix an order for such rules the focusing principle [1], normal proofs [10], and proof search strategies [26] have been proposed. Though being improvements compared to simple sequent calculus proof search all these proposals suffer from that they are still connective oriented.…”

Section: A Matrix Characterization Of Logical Validity In Mllmentioning

confidence: 99%

“…The former cover all of linear logic but are not useful for efficient proof search because of the many redundancies contained in them. Attempts to remove permutabilities from sequent proofs [1,10] and to add proof strategies [26] have provided some improvements but the main difficulties still remain. Proof nets, on the other hand, are applicable only to a small fragment of the logic.…”

Section: Introductionmentioning

confidence: 99%

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Connection-based proof construction in linear logic

Kreitz

Mantel

Otten

et al. 1997

Automated Deduction—CADE-14

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Abstract. We present a matrix characterization of logical validity in the multiplicative fragment of linear logic. On this basis we develop a matrix-based proof search procedure for this fragment and a procedure which translates the machine-found proofs back into the usual sequent calculus for linear logic. Both procedures are straightforward extensions of methods which originally were developed for a uniform treatment of classical, intuitionistic and modal logics. They can be extended to further fragments of linear logic once a matrix characterization has been found.

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Section: Resultsmentioning

confidence: 99%

Section: A Matrix Characterization Of Logical Validity In Mllmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Connection-based proof construction in linear logic

Kreitz

Mantel

Otten

et al. 1997

Automated Deduction—CADE-14

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“…There is also work on the inverse method in intuitionistic logic [18] and linear logic [17] which have resulted in inverse method provers for full first-order intuitionistic and linear logics. Most of the improved strategies and optimizations used in these works (some described in the previous section) would most probably be applicable to inverse method theorem proving in BI.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

The Inverse Method for the Logic of Bunched Implications

Donnelly

Gibson

Krishnaswami

et al. 2005

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. The inverse method, due to Maslov, is a forward theorem proving method for cut-free sequent calculi that relies on the subformula property. The Logic of Bunched Implications (BI), due to Pym and O'Hearn, is a logic which freely combines the familiar connectives of intuitionistic logic with multiplicative linear conjunction and its adjoint implication. We present the first formulation of an inverse method for propositional BI without units. We adapt the sequent calculus for BI into a forward calculus. The soundness and completeness of the calculus are proved, and a canonical form for bunches is given.

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“…We do not treat other sources of non-determinism, which can be handled according to standard techniques in a logic programming framework [Pfe92], or that we might want to keep open in a theorem prover and in the implementation of a concurrent linear logic programming language such as ACL [KY93]. Similarly, we do not consider orthogonal issues in linear proof search, such as the permutability of inference rules, which have been treated exhaustively elsewhere [GP94,Min93,Tam94]. We will focus our attention on the language Lolli [Hod94,HM94], that we used to test the techniques described below [CHMP].…”

Section: Introductionmentioning

confidence: 99%

Efficient resource management for linear logic proof search

Cervesato

Hodas

Pfenning

1996

Extensions of Logic Programming

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The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf ). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in non-trivial applications. This paper studies this problem in the case of Lolli [HM94], though its results have application to other systems. We first give a prooftheoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the nondeterminism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system.

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Proof strategies in linear logic

Cited by 42 publications

References 6 publications

Connection-based proof construction in linear logic

Connection-based proof construction in linear logic

The Inverse Method for the Logic of Bunched Implications

Efficient resource management for linear logic proof search

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