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Efficient resource management for linear logic proof search
 Proceedings of the 5th International Workshop on Extensions of Logic Programming
, 1996
"... 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 li ..."
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Cited by 54 (11 self)
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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 nontrivial 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. 1
A Resolution Theorem Prover for Intuitionistic Logic
 Proceedings of CADE13
, 1996
"... We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method is show ..."
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Cited by 42 (4 self)
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We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method is shown to be a decision procedure for a new syntactically described decidable class of intuitionistic logic. We compare the search strategies suitable for the resolution method with strategies suitable for the tableau method. The performance of our prover is compared with the performance of a tableau prover for intuitionistic logic presented in [17].
Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 38 (11 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
linTAP: A Tableau Prover for Linear Logic
 International Conference TABLEAUX’99
, 1999
"... linTAP is a tableau prover for the multiplicative and exponential fragment M?LL of Girards linear logic. It proves the validity of a given formula by constructing an analytic tableau and ensures the linear validity using prex unication. We present the tableau calculus used by linTAP, an algorithm fo ..."
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Cited by 16 (5 self)
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linTAP is a tableau prover for the multiplicative and exponential fragment M?LL of Girards linear logic. It proves the validity of a given formula by constructing an analytic tableau and ensures the linear validity using prex unication. We present the tableau calculus used by linTAP, an algorithm for prex unication in linear logic, the linTAP implementation, and some experimental results obtained with linTAP. 1
ConnectionBased Proof Construction in Linear Logic
 14 th Conference on Automated Deduction, Lecture Notes in Artificial Intelligence 1249
, 1997
"... Abstract. We present a matrix characterization of logical validity in the multiplicative fragment of linear logic. On this basis we develop a matrixbased proof search procedure for this fragment and a procedure which translates the machinefound proofs back into the usual sequent calculus for linea ..."
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Cited by 13 (7 self)
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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 matrixbased proof search procedure for this fragment and a procedure which translates the machinefound 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. 1
Connection Methods in Linear Logic and Proof Nets Construction
 Theoretical Computer Science
, 1999
"... Linear logic (LL) is the logical foundation of some typetheoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proofsearch in different logics. A ..."
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Cited by 12 (2 self)
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Linear logic (LL) is the logical foundation of some typetheoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proofsearch in different logics. Aiming at using proof nets as a tool for automated deduction in linear logic, we define a connectionbased characterization of provability in Multiplicative Linear Logic (MLL). We show that an algorithm for proof net construction can be seen as a proofsearch connection method. This central result is illustrated with a specific algorithm that is able to construct, for a provable MLL sequent, a set of connections, a proof net and a sequent proof. From these results we expect to extend to other LL fragments, we analyse what happens with the additive connectives of LL by tackling the additive fragment in a similar way.
The Inverse Method
, 2001
"... this paper every formula is equivalent to a formula in negation normal form ..."
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Cited by 12 (1 self)
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this paper every formula is equivalent to a formula in negation normal form
Mutable Object State for ObjectOriented Logic Programming: A Survey
, 1993
"... One of the most difficult problems on the way to an integration of ObjectOriented and Logic Programming is the modeling of changeable object state (i.e. object dynamics) in a particular logic in order not to forfeit the declarative nature of LP. Classical logic is largely unsuitable for such a task ..."
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Cited by 11 (2 self)
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One of the most difficult problems on the way to an integration of ObjectOriented and Logic Programming is the modeling of changeable object state (i.e. object dynamics) in a particular logic in order not to forfeit the declarative nature of LP. Classical logic is largely unsuitable for such a task, because it adopts a general (both temporally and spatially), Platonic notion of validity, whereas object state changes over time and is local to an object. This paper presents the problem and surveys the stateoftheart approaches to its solution, as well as some emerging, promising new approaches. The paper tries to relate the different approaches, to evaluate their merits and deficiencies and to identify promising directions for development. Keywords: ObjectOriented Logic Programming, mutable object state, survey. 1 The Problem: Dynamics of Objects From the research literature on integration of ObjectOriented Programming (OOP) and Logic Programming (LP) one gets the impression that ...
A focusing inverse method theorem prover for firstorder linear logic
 In Proceedings of CADE20
, 2005
"... Abstract. We present the theory and implementation of a theorem prover forfirstorder intuitionistic linear logic based on the inverse method. The central prooftheoretic insights underlying the prover concern resource management andfocused derivations, both of which are traditionally understood in ..."
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Cited by 8 (6 self)
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Abstract. We present the theory and implementation of a theorem prover forfirstorder intuitionistic linear logic based on the inverse method. The central prooftheoretic insights underlying the prover concern resource management andfocused derivations, both of which are traditionally understood in the domain of backward reasoning systems such as logic programming. We illustrate how resource management, focusing, and other intrinsic properties of linear connectives affect the basic forward operations of rule application, contraction, and forwardsubsumption. We also present some preliminary experimental results obtained with our implementation.
The inverse method for the logic of bunched implications
 In Proceedings of LPAR 2004, volume 3452 of LNAI
, 2005
"... Abstract. The inverse method, due to Maslov, is a forward theorem proving method for cutfree 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 ..."
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Cited by 6 (1 self)
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Abstract. The inverse method, due to Maslov, is a forward theorem proving method for cutfree 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. 1