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43
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 304 (36 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Concurrent Games and Full Completeness
"... A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for ..."
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Cited by 69 (16 self)
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A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for
Proofs nets for unitfree multiplicativeadditive linear logic
 18th IEEE Intl. Symp. Logic in Computer Science (LICS’03
, 2003
"... A cornerstone of the theory of proof nets for unitfree multiplicative linear logic (MLL) is the abstract representation of cutfree proofs modulo inessential commutations of rules. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cutfr ..."
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Cited by 53 (5 self)
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A cornerstone of the theory of proof nets for unitfree multiplicative linear logic (MLL) is the abstract representation of cutfree proofs modulo inessential commutations of rules. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cutfree monomial proof nets can correspond to the same cutfree proof. Thus the problem of finding a satisfactory notion of proof net for unitfree multiplicativeadditive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory. 1
From truth to computability I
 Theoretical Computer Science
"... The recently initiated approach called computability logic is a formal theory of interactive computation. It understands computational problems as games played by a machine against the environment, and uses logical formalism to describe valid principles of computability, with formulas representing c ..."
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Cited by 30 (23 self)
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The recently initiated approach called computability logic is a formal theory of interactive computation. It understands computational problems as games played by a machine against the environment, and uses logical formalism to describe valid principles of computability, with formulas representing computational problems and logical operators standing for operations on computational problems. The concept of computability that lies under this approach is a nontrivial generalization of ChurchTuring computability from simple, twostep (question/answer, input/output) problems to problems of arbitrary degrees of interactivity. Restricting this concept to predicates, which are understood as computational problems of zero degree of interactivity, yields exactly classical truth. This makes computability logic a generalization and refinement of classical logic. The foundational paper “Introduction to computability logic ” [Annals of Pure and Applied Logic 123 (2003), pp. 199] was focused on semantics rather than syntax, and certain axiomatizability assertions in it were only stated as conjectures. The present contribution contains a verification of one of such conjectures: a soundness and completeness proof for the deductive system CL3 which axiomatizes the most basic firstorder fragment of computability logic called the finitedepth, elementarybase fragment.
Definability and full abstraction
 GDP FESTSCHRIFT
"... Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown sin ..."
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Cited by 24 (1 self)
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Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.
Sequentiality vs. Concurrency in Games and Logic
 Math. Structures Comput. Sci
, 2001
"... Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic. ..."
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Cited by 20 (0 self)
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Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
Chu Spaces as a Semantic Bridge Between Linear Logic and Mathematics
 Theoretical Computer Science
, 1998
"... The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soun ..."
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Cited by 16 (2 self)
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The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly interpreting linear logic while fully and concretely embedding a comprehensive range of concrete categories of mathematics. Our main goal is to treat each end of this bridge in expository detail. In addition we introduce the dialectic lambdacalculus, and show that dinaturality semantics is not fully complete for the Chu interpretation of linear logic. 1 Introduction Linear logic was introduced by J.Y. Girard as a "logic behind logic." It separates logical reasoning into a core linear part in which formulas are merely moved around, and an auxiliary nonlinear part in which formulas may be deleted and copied. The core, multiplicative linear logic (MLL), is a substructural logic whose basic connect...
Discreet Games, Light Affine Logic and PTIME Computation
 In Proceedings of CSL2000: Annual Conference of the European Association of Computer Science Logic, Springer LNCS
, 2000
"... This paper introduces a model of IMLAL, the intuitionistic multiplicative ( ; (; x ; ! )fragment of Light Ane Logic, based on games and discreet strategies. We dene a generalized notion of threads, so that a play of a game (of depth k) may be regarded as a number of interwoven threads (of dept ..."
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Cited by 13 (0 self)
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This paper introduces a model of IMLAL, the intuitionistic multiplicative ( ; (; x ; ! )fragment of Light Ane Logic, based on games and discreet strategies. We dene a generalized notion of threads, so that a play of a game (of depth k) may be regarded as a number of interwoven threads (of depths ranging from 1 to k). To constrain the way threads communicate with each other, we organize them into networks at each depth (up to k), in accord with a protocol: A network comprises an Othread (which can only be created by O) and nitely many Pthreads (which can only be created by P).
Syntax vs. semantics: a polarized approach
 THEORETICAL COMPUTER SCIENCE
, 2005
"... We present a notion of sliced proofnets for the polarized fragment of Linear Logic and a corresponding game model. We show that the connection between them is very strong through an equivalence of categories (this contains soundness, full completeness and faithful completeness). ..."
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Cited by 13 (3 self)
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We present a notion of sliced proofnets for the polarized fragment of Linear Logic and a corresponding game model. We show that the connection between them is very strong through an equivalence of categories (this contains soundness, full completeness and faithful completeness).
Category theory for linear logicians
 Linear Logic in Computer Science
, 2004
"... This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categori ..."
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Cited by 13 (2 self)
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This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categories and their relation to intuitionistic logic is followed by a consideration of symmetric monoidal closed, linearly distributive and ∗autonomous categories and their relation to multiplicative linear logic. We examine nonsymmetric monoidal categories, and consider them as models of noncommutative linear logic. We introduce traced monoidal categories, and discuss their relation to the geometry of interaction. The necessary aspects of the theory of monads is introduced in order to describe the categorical modelling of the exponentials. We conclude by briefly describing the notion of full completeness, a strong form of categorical completeness, which originated in the categorical model theory of linear logic. No knowledge of category theory is assumed, but we do assume knowledge of linear logic sequent calculus and the standard models of linear logic, and modest familiarity with typed lambda calculus. 0