Results 1 
8 of
8
On Proof Normalization in Linear Logic
 Theoretical Computer Science
, 1994
"... We present a prooftheoretic foundation for automated deduction in linear logic. At first, we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a ..."
Abstract

Cited by 26 (12 self)
 Add to MetaCart
We present a prooftheoretic foundation for automated deduction in linear logic. At first, we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a proof. Then we discuss the naturallyarising question of the redundancy reduction and investigate the possibilities of proof normalization which depend on the proof search strategy and the fragment we consider. Thus, we can define the concept of normal proof that might be the basis of works about automatic proof construction and design of logic programming languages based on linear logic. 1 Introduction Linear logic is a powerful and expressive logic with connections to a variety of topics in computer science. We are mainly interested by the significance it may have in different domains as logic programming or program synthesis through theorem proving. As a matter of fact, classical linear ...
Proof Strategies in Linear Logic
 JOURNAL OF AUTOMATED REASONING
, 1994
"... Linear logic, introduced by J.Y.Girard, is a refinement of classical logic providing means for controlling the allocation of "resources". It has aroused considerable interest both from proof theorists and computer scientists. In this paper we investigate methods for automated theorem proving in pro ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
Linear logic, introduced by J.Y.Girard, is a refinement of classical logic providing means for controlling the allocation of "resources". It has aroused considerable interest both from proof theorists and computer scientists. In this paper we investigate methods for automated theorem proving in propositional linear logic. Both the "bottomup" and "topdown" (resolution) proof strategies are analyzed  various modifications of sequent rules and efficient search strategies are presented along with the experiments performed with the implemented theorem provers.
Foundations of Proof Search Strategies Design in Linear Logic
 In Symposium on Logical Foundations of Computer Science
, 1994
"... In this paper, we investigate automated proof construction in classical linear logic (CLL) by giving logical foundations for the design of proof search strategies. We propose common theoretical foundations for topdown, bottomup and mixed proof search procedures with a systematic formalization of s ..."
Abstract

Cited by 20 (11 self)
 Add to MetaCart
In this paper, we investigate automated proof construction in classical linear logic (CLL) by giving logical foundations for the design of proof search strategies. We propose common theoretical foundations for topdown, bottomup and mixed proof search procedures with a systematic formalization of strategies construction using the notions of immediate or chaining composition or decomposition, deduced from permutability properties and inference movements in a proof. Thus, we have logical bases for the design of proof strategies in CLL fragments and then we can propose sketches for their design.
Abstract Interpretation of Linear Logic Programming
 IN PROC. OF ILPS'93
, 1993
"... Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear Lo ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear Logic. A proof normalization procedure, called "focusing", has been proposed to make the problem of proof search tractable. Correspondingly, there is a normalization procedure mapping formulae of Linear Logic into a syntactic fragment of that logic, called LinLog, and in which the focusing normalization for proofs can be most conveniently expressed. In this paper, we propose to push this compilation/normalization process further, by applying abstract interpretation and partial evaluation techniques to (focused) proofs in LinLog. These techniques provide information concerning the evolution of the computational resources (formulae) during the execution (proof construction). The practical outcome that we expect from this theoretical effort is the definition of a general tool for statically analyzing and reasoning about the runtime behavior of programs in frameworks where computations can be accounted for in terms of proof search in Linear Logic.
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 ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
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.
A Procedure for Automatic Proof Nets Construction
, 1992
"... In this paper, we consider the multiplicative fragment of linear logic (MLL) from an automated deduction point of view. Before to use this new logic to make logic programming or to program with proofs, a better comprehension of the proof construction process in this framework is necessary. We propos ..."
Abstract

Cited by 11 (8 self)
 Add to MetaCart
In this paper, we consider the multiplicative fragment of linear logic (MLL) from an automated deduction point of view. Before to use this new logic to make logic programming or to program with proofs, a better comprehension of the proof construction process in this framework is necessary. We propose a new algorithm to construct automatically a proof net for a given sequent in MLL and its proofs of termination, correctness and completeness. It can be seen as an implementation oriented way to consider automated deduction in linear logic.
Canonical Proofs for Linear Logic Programming Frameworks
 ProofTheoretical Extensions of Logic Programming 210, PostConference Workshop for ICLP'94, Santa Margherita Ligure
, 1994
"... We discuss here the prooftheoretic foundations for theorem proving and logic programming in linear logic, mainly studying how to define canonical proofs (that are complete) for efficient proof search in fragments of linear logic. We analyze the conception of such proof forms, for frameworks based o ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We discuss here the prooftheoretic foundations for theorem proving and logic programming in linear logic, mainly studying how to define canonical proofs (that are complete) for efficient proof search in fragments of linear logic. We analyze the conception of such proof forms, for frameworks based on proofconstruction as computation, emphasizing the relationship between the logical fragment and its proof search strategies. This point is essential for the definition and implementation of logic programming languages within linear logic.
Linear Logic with Isabelle: pruning the proof search tree
, 1995
"... This paper introduces a general backward proof search strategy for multiplicative additive linear logic. This strategy, which is based on Isabelle's basic tactics and tacticals, has been implemented and appears to be rather eOEcient. Its eOEciency derives from several heuristics that we introduce in ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This paper introduces a general backward proof search strategy for multiplicative additive linear logic. This strategy, which is based on Isabelle's basic tactics and tacticals, has been implemented and appears to be rather eOEcient. Its eOEciency derives from several heuristics that we introduce in the paper. We prove that these heuristics preserve completeness.