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A MultipleConclusion MetaLogic
 In Proceedings of 9th Annual IEEE Symposium On Logic In Computer Science
, 1994
"... 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 [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic pro ..."
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Cited by 86 (7 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 [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends the languages λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. As a metalanguage, Forum greatly extends the expressiveness of these other logic programming languages. To illustrate its expressive strength, we specify in Forum a sequent calculus proof system and the operational semantics of a functional programming language that incorporates such nonfunctional features as counters and references. 1
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 ..."
Abstract

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 Proof Theory for Generic Judgments
, 2003
"... this paper, we do this by adding the #quantifier: its role will be to declare variables to be new and of local scope. The syntax of the formula # x.B is like that for the universal and existential quantifiers. Following Church's Simple Theory of Types [Church 1940], formulas are given the type ..."
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Cited by 61 (14 self)
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this paper, we do this by adding the #quantifier: its role will be to declare variables to be new and of local scope. The syntax of the formula # x.B is like that for the universal and existential quantifiers. Following Church's Simple Theory of Types [Church 1940], formulas are given the type o, and for all types # not containing o, # is a constant of type (# o) o. The expression # #x.B is ACM Transactions on Computational Logic, Vol. V, No. N, October 2003. 4 usually abbreviated as simply # x.B or as if the type information is either simple to infer or not important
Concurrency and Communication in Transaction Logic
 IN JOINT INTL. CONFERENCE AND SYMPOSIUM ON LOGIC PROGRAMMING
, 1996
"... In previous work, we developed Transaction Logic (or T R), which deals with state changes in deductive databases. T R provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. T R accounts not only for the updates themselves, bu ..."
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Cited by 58 (15 self)
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In previous work, we developed Transaction Logic (or T R), which deals with state changes in deductive databases. T R provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. T R accounts not only for the updates themselves, but also for important related problems, such as the order of update operations, nondeterminism, and transaction failure and rollback. In the present paper, we propose Concurrent Transaction Logic (or CT R), which extends Transaction Logic with connectives for modeling the concurrent execution of complex processes. Concurrent processes in CT R execute in an interleaved fashion and can communicate and synchronize themselves. Like classical logic, CT R has a "Horn" fragment that has both a procedural and a declarative semantics, in which users can program and execute database transactions. CT R is thus a deductive database language that integrates concurrency, communication, and updates. All th...
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.
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.
Asynchronous Communication Model Based on Linear Logic
 Formal Aspects of Computing
, 1995
"... We propose a new framework called ACL for concurrent computation based on linear logic. ACL is a kind of linear logic programming framework, where its operational semantics is described in terms of proof construction in linear logic. We also give a modeltheoretic semantics as a natural extension of ..."
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Cited by 47 (6 self)
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We propose a new framework called ACL for concurrent computation based on linear logic. ACL is a kind of linear logic programming framework, where its operational semantics is described in terms of proof construction in linear logic. We also give a modeltheoretic semantics as a natural extension of phase semantics, a model of linear logic. Our framework well captures concurrent computation based on asynchronous communication. It will, therefore, provide us with a new insight into other models of concurrent computation from a logical point of view. We also expect ACL to become a formal framework for verification, reasoning, and transformation of concurrent programs by the use of techniques for traditional logic programming. ACL's attractive features for concurrent programming paradigms are also discussed. 1 Introduction For future massively parallel processing environments, concurrent programming languages based on asynchronous communication would become more and more important. Due ...
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...
A Concurrent Logical Framework II: Examples and Applications
, 2002
"... CLF is a new logical framework with 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 ..."
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Cited by 46 (30 self)
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CLF is a new logical framework with 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 #.