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242
Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder program ..."
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Cited by 85 (11 self)
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The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
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Cited by 73 (25 self)
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The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
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 69 (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.
Cutelimination for a logic with definitions and induction
 Theoretical Computer Science
, 1997
"... In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The l ..."
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Cited by 61 (19 self)
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In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The literature contains many approaches to formally adding these reasoning principles with logic specifications. We choose an approach based on the sequent calculus and design an intuitionistic logic F Oλ ∆IN that includes natural number induction and a notion of definition. We have detailed elsewhere that this logic has a number of applications. In this paper we prove the cutelimination theorem for F Oλ ∆IN, adapting a technique due to Tait and MartinLöf. This cutelimination proof is technically interesting and significantly extends previous results of this kind. 1
Noncommutativity and MELL in the Calculus of Structures
 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible in ..."
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Cited by 58 (22 self)
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We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible in the sequent calculus. Then we show that multiplicative exponential linear logic benefits from its presentation in the calculus of structures, especially because we can replace the ordinary, global promotion rule by a local version. These formal systems, for which we prove cut elimination, outline a range of techniques and properties that were not previously available. Contrarily to what happens in the sequent calculus, the cut elimination proof is modular.
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 Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
A Judgmental Analysis of Linear Logic
, 2003
"... We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, ext ..."
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Cited by 49 (27 self)
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We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our system, employing a form of doublenegation translation.
The Uniform Prooftheoretic Foundation of Linear Logic Programming (Extended Abstract)
 Proceedings of the International Logic Programming Symposium
, 1991
"... ) James Harland Department of Computer Science University of Melbourne Parkville, 3052 Australia jah@cs.mu.oz.au David Pym Department of Computer Science University of Edinburgh Edinburgh EH9 3JZ Scotland, U.K. dpym@lfcs.ed.ac.uk Abstract We present a prooftheoretic analysis of a natu ..."
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Cited by 46 (7 self)
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) James Harland Department of Computer Science University of Melbourne Parkville, 3052 Australia jah@cs.mu.oz.au David Pym Department of Computer Science University of Edinburgh Edinburgh EH9 3JZ Scotland, U.K. dpym@lfcs.ed.ac.uk Abstract We present a prooftheoretic analysis of a natural notion of logic programming for Girard's linear logic. This analysis enables us to identify a suitable notion of uniform proof. This in turn enables us to identify choices of classes of definite and goal formulae for which uniform proofs are complete and so to obtain the appropriate formulation of resolution proof for such choices. Resolution proofs in linear logic are somewhat difficult to define. This difficulty arises from the need to decompose definite formulae into a form suitable for the use of the linear resolution rule, a rule which requires the selected clause to be deleted after use, and from the presence of the modality ! (of course). We consider a translation  resembling ...
ACL  A Concurrent Linear Logic Programming Paradigm
 Proceedings of the 1993 International Logic Programming Symposium
, 1993
"... We propose a novel concurrent programming framework called ACL. ACL is a variant of linear logic programming, where computation is described in terms of bottomup proof search of some formula in linear logic. The whole linear sequent calculus is too nondeterministic to be interpreted as an operatio ..."
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Cited by 46 (4 self)
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We propose a novel concurrent programming framework called ACL. ACL is a variant of linear logic programming, where computation is described in terms of bottomup proof search of some formula in linear logic. The whole linear sequent calculus is too nondeterministic to be interpreted as an operational semantics for a realistic programming language. We restrict formulas and accordingly refine inference rules for those formulas, hence overcoming this problem. Don't care interpretation of nondeterminism in the resulting system yields a very clean and powerful concurrent programming paradigm based on messagepassing style communication. It is remarkable that each ACL inference rule has an exact correspondence to some operation in concurrent computation and that nondeterminism in proof search just corresponds to an inherent nondeterminism in concurrent computation, namely, nondeterminism on message arrival order. We demonstrate the power of our ACL framework by showing several programm...