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A Uniform ProofTheoretic Investigation Of Linear Logic Programming
, 1994
"... In this paper we consider the problem of identifying logic programming languages for linear logic. Our analysis builds on a notion of goaldirected provability, characterized by the socalled uniform proofs, previously introduced for minimal and intuitionistic logic. A class of uniform proofs in lin ..."
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Cited by 71 (21 self)
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In this paper we consider the problem of identifying logic programming languages for linear logic. Our analysis builds on a notion of goaldirected provability, characterized by the socalled uniform proofs, previously introduced for minimal and intuitionistic logic. A class of uniform proofs in linear logic is identified by an analysis of the permutability of inferences in the linear sequent calculus. We show that this class of proofs is complete (for logical consequence) for a certain (quite large) fragment of linear logic, which thus forms a logic programming language. We obtain a notion of resolution proof, in which only one left rule, of clausedirected resolution, is required. We also consider a translation, resembling those of Girard, of the hereditary Harrop fragment of intuitionistic logic into our framework. We show that goaldirected provability is preserved under this translation.
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 42 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
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 ..."
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Cited by 26 (12 self)
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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.
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 prov ..."
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Cited by 25 (2 self)
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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 ..."
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Cited by 20 (11 self)
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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.
Implementation and Development Issues for the Linear Logic Programming Language Lygon
 IN AUSTRALASIAN COMPUTER SCIENCE CONFERENCE
, 1995
"... We describe and discuss the implementation of a new logic programming language called Lygon. This language is based on linear logic, a logic designed with bounded resources in mind. Linear logic may be thought of as a generalisation of classical logic, and as a result Lygon contains various features ..."
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Cited by 11 (6 self)
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We describe and discuss the implementation of a new logic programming language called Lygon. This language is based on linear logic, a logic designed with bounded resources in mind. Linear logic may be thought of as a generalisation of classical logic, and as a result Lygon contains various features which do not exist in (pure) Prolog, whilst maintaining all the features of (pure) Prolog. In this paper we describe the implementation of this language, which posed a variety of programming challenges. The operational model for the language is based on the notion of goaldirected provability, a notion which has been much studied in the literature. However, there is a significant amount of nondeterminism in this notion of proof. Hence the task of developing a systematic and deterministic manner in which to search for proofs requires some intricate and novel implementation techniques. We describe and discuss our particular solution, as well as the features of the language and its applicatio...
Proof search for programming in Intuitionistic Linear Logic (Extended Abstract)
 CADE12 Workshop on Proof Search in TypeTheoretic Languages
, 1994
"... Introduction Linear logic (denoted LL) [6] is a powerful and expressive logic with connections to a variety of topics in computer science as logic programming, concurrency or functional programming. From the logical side, LL combines the constructive content of Intuitionistic Logic with the symmetr ..."
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Cited by 8 (3 self)
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Introduction Linear logic (denoted LL) [6] is a powerful and expressive logic with connections to a variety of topics in computer science as logic programming, concurrency or functional programming. From the logical side, LL combines the constructive content of Intuitionistic Logic with the symmetries of Classical Logic and from the computation side, it offers a control on resource management and evaluation order. Concerning functional programming, applications of LL to computation can be seen through the CurryHoward isomorphism in which propositions are interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) [3, 12] and full LL [1] with proposals of linear lambda calculi having important properties as subjectreduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (that are proved equivalent), we can investi
A Note on the Implementation and Applications of Linear Logic Programming Languages
 Proceedings of the Seventeenth Annual Computer Science Conference 647658
, 1994
"... Traditional logic programming languages, such as Prolog, have their origins in classical logic. Recently it has been shown how logic programming languages can be based on linear logic, a logic designed with bounded resources in mind. In this paper we discuss the implementation issues for the linear ..."
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Cited by 7 (6 self)
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Traditional logic programming languages, such as Prolog, have their origins in classical logic. Recently it has been shown how logic programming languages can be based on linear logic, a logic designed with bounded resources in mind. In this paper we discuss the implementation issues for the linear logic programming language Lygon, and describe some of the novel features of the language. These include global variables, a notion of state, mutual exclusion operators and constructs for the manipulation of clauses. We also show how a bin packing problem can be solved simply and elegantly in Lygon. 1 Introduction In recent work [6, 4, 5, 11], the present authors have shown, via an analysis of those fragments of Girard's linear logic [3] for which a certain notion of goaldirected provability completely characterizes logical consequence, how certain fragments of linear logic provide an appropriate logical (prooftheoretic) foundation for logic programming languages. 1 In this paper, we i...
A Survey of Linear Logic Programming
 Computational Logic
, 1995
"... Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic ..."
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Cited by 4 (0 self)
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Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic to design new logic programming languages was inevitable given that it allows for more dynamics in the way sequents change during the search for a proof and since it can account for logic programming in these other logics. We overview how linear logic has been used to design new logic programming languages and describe some applications and implementation issues for such languages. ยง1. Introduction. It is now common place to recognize the important role of logic in the foundations of computer science in general and programming languages more specifically. For this reason, when a major new advance is made in our understanding of logic, we can expect to see that advance ripple into other areas of computer science. Such rippling has been observed during the years
A Linear Logic Specification for Chimera
, 1997
"... . Forum [36], a powerful logic formalism based on Higher Order Linear Logic, is particularly suited to specify and reason about complex programs and systems. Ehhf [12], a subset of Forum, models many interesting logic programming extensions towards O.O. and concurrent systems and can be viewed as ..."
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Cited by 3 (3 self)
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. Forum [36], a powerful logic formalism based on Higher Order Linear Logic, is particularly suited to specify and reason about complex programs and systems. Ehhf [12], a subset of Forum, models many interesting logic programming extensions towards O.O. and concurrent systems and can be viewed as a very high level logic programming specification language. The paper presents some results in this direction, namely the specification in Ehhf of Chimera, an Active, ObjectOriented and Deductive Database System. Keywords: Linear Logic, ObjectOriented and Deductive Databases. 1 Introduction Proof theory and automated deduction have provided relevant contributions to computer science, in particular in the fields of highlevel programming languages and formal verification of software. Many different logics have been proposed and used for these purposes. We will work with Linear logic [22] with the aim to use it as a theoretical foundation for modern and powerful specification language...