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31
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 262 (33 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
, 1998
"... 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 MultiplicativeAdditive Linear Logic is ..."
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Cited by 49 (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 MultiplicativeAdditive Linear Logic is proved for this semantics. 1 Introduction This paper contains two main contributions: ffl the introduction of a new form of game semantics, which we call concurrent games. ffl a proof of full completeness of this semantics for MultiplicativeAdditive Linear Logic. We explain the significance of each of these in turn. Concurrent games Traditional forms of game semantics which have appeared in logic and computer science have been sequential in format: a play of the game is formalized as a sequence of moves. The key feature of this sequential format is the existence of a global schedule (or polarization) : in each (finite) position, it is (exactly) one player's turn to move 1 . This seq...
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 39 (4 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
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 17 (2 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.
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 14 (14 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.
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 13 (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 soundly interp ..."
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Cited by 12 (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...
Exhausting Strategies, Joker Games and Full Completeness for IMLL with Unit
 In Proc. 8th Conf. CTCS'99. ENTCS 29
, 1999
"... We present a game description of free symmetric monoidal closed categories, which can also be viewed as a fully complete model for the Intuitionistic Multiplicative Linear Logic with the tensor unit. We model the unit by a distinguished onemove game called Joker. Special rules apply to the joker mo ..."
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Cited by 11 (6 self)
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We present a game description of free symmetric monoidal closed categories, which can also be viewed as a fully complete model for the Intuitionistic Multiplicative Linear Logic with the tensor unit. We model the unit by a distinguished onemove game called Joker. Special rules apply to the joker move. Proofs are modelled by what we call conditionally exhausting strategies, which are deterministic and total only at positions where no joker move exists in the immediate neighbourhood, and satisfy a kind of reachability condition called Pexhaustion. We use the model to give an analysis of a counting problem in free autonomous categories which generalises the Triple Unit Problem. 1 Introduction We aim to construct a fully complete game model for IMLL with unit, the intuitionistic multiplicative (\Omega ; (;?)fragment of Linear Logic (we write ? for the tensor unit). The notion of full completeness [2] is best formulated in terms of a categorical model of the logic, in which formulas (or...
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 8 (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).
Games in the Semantics of Programming Languages
 Dept. of Philosophy, University of Amsterdam
, 1997
"... ion for PCF Motivated by the full completeness results, it became of compelling interest to reexamine perhaps the bestknown "open problem" in the semantics of programming languages, namely the "Full Abstraction problem for PCF", using the new tools provided by game semantics. 2 PCF is a highero ..."
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Cited by 8 (1 self)
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ion for PCF Motivated by the full completeness results, it became of compelling interest to reexamine perhaps the bestknown "open problem" in the semantics of programming languages, namely the "Full Abstraction problem for PCF", using the new tools provided by game semantics. 2 PCF is a higherorder functional programming language; modulo issues of the parameterpassing strategies, it forms a fragment of any programming language with higherorder procedures (which includes any reasonably expressive objectoriented language). The aspect of the Full Abstraction problem I personally found most interesting was: to construct a syntaxindependent model in which every element is the denotation of some program (note the analogy with full completeness, whose definition had in turn been motivated in part by this aspect of full abstraction). This is not how the problem was originally formulated, but by "general abstract nonsense", given such a model one can always quotient it to get a fully ab...