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40
Geometry of Interaction and Linear Combinatory Algebras
, 2000
"... this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by S ..."
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Cited by 43 (10 self)
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this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by Stefanescu (Stefanescu 2000).) However, the first author realized, following a stimulating discussion with Gordon Plotkin, that traced monoidal categories provided a common denominator for the axiomatics of both the Girardstyle and AbramskyJagadeesanstyle versions of the Geometry of Interaction, at the basic level of the multiplicatives. This insight was presented in (Abramsky 1996), in which Girardstyle GoI was dubbed "particlestyle", since it concerns information particles or tokens flowing around a network, while the AbramskyJagadeesan style GoI was dubbed "wavestyle", since it concerns the evolution of a global information state or "wave". Formally, this distinction is based on whether the tensor product (i.e. the symmetric monoidal structure) in the underlying category is interpreted as a coproduct (particle style) or as a product (wave style). This computational distinction between coproduct and product interpretations of the same underlying network geometry turned out to have been partially anticipated, in a rather di#erent context, in a pioneering paper by E. S. Bainbridge (Bainbridge 1976), as observed by Dusko Pavlovic. These two forms of interpretation, and ways of combining them, have also been studied recently in (Stefanescu 2000). He uses the terminology "additive" for coproductbased (i.e. our "particlestyle") and "multiplicative" for productbased (i.e. our "wavestyle"); this is not suitable for our purposes, because of the clash with Linear Logic term...
Probabilistic Game Semantics
 Computer Science Society
, 2000
"... A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a ..."
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Cited by 30 (1 self)
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A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.
Angelic semantics of finegrained concurrency
 In Proceedings of FOSSACS ’04, number 2987 in LNCS
, 2004
"... Abstract. We introduce a game model for a procedural programming language extended with primitives for parallel composition and synchronization on binary semaphores. The model uses an interleaved version of HylandOngstyle games, where most of the original combinatorial constraints on positions are ..."
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Cited by 26 (10 self)
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Abstract. We introduce a game model for a procedural programming language extended with primitives for parallel composition and synchronization on binary semaphores. The model uses an interleaved version of HylandOngstyle games, where most of the original combinatorial constraints on positions are replaced with a simple principle naturally related to static process creation. The model is fully abstract for mayequivalence. 1 Introduction The two major paradigms of concurrent programming are messagepassing and sharedvariable. The latter style of programming is closer to the underlying machine model, which makes it both more popular and more "lowlevel " (and more errorprone) than the former. This constitutes very good motivation for the study of such languages. Concurrent sharedvariable programming languages themselves can come in several varieties: Finegrained languages have designated atomic actions which are implemented directly by the hardware on which the program is executed. In contrast, coarsegrained programming languages can specify sequences of actions to appear as indivisible. Languages with static process creation execute statements in parallel and
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.
Sequential algorithms and strongly stable functions
 in the Linear Summer School, Azores
, 2003
"... ..."
Concurrent strategies
 In LICS’11. IEEE Computer Society
, 2011
"... Abstract—A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, en ..."
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Cited by 11 (5 self)
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Abstract—A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate. I.
Asynchronous Games: Innocence without Alternation
 In Proceedings of CONCUR’05, volume 4703 of LNCS
, 2007
"... Abstract. The notion of innocent strategy was introduced by Hyland and Ong in order to capture the interactive behaviour of λterms and PCF programs. An innocent strategy is defined as an alternating strategy with partial memory, in which the strategy plays according to its view. Extending the defin ..."
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Cited by 9 (3 self)
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Abstract. The notion of innocent strategy was introduced by Hyland and Ong in order to capture the interactive behaviour of λterms and PCF programs. An innocent strategy is defined as an alternating strategy with partial memory, in which the strategy plays according to its view. Extending the definition to nonalternating strategies is problematic, because the traditional definition of views is based on the hypothesis that Opponent and Proponent alternate during the interaction. Here, we take advantage of the diagrammatic reformulation of alternating innocence in asynchronous games, in order to provide a tentative definition of innocence in nonalternating games. The task is interesting, and far from easy. It requires the combination of true concurrency and game semantics in a clean and organic way, clarifying the relationship between asynchronous games and concurrent games in the sense of Abramsky and Melliès. It also requires an interactive reformulation of the usual acyclicity criterion of linear logic, as well as a directed variant, as a scheduling criterion. 1
Socially Responsive, Environmentally Friendly Logic
 in Truth and Games: Essays in Honour of Gabriel Sandu, Aho, Tuomo and AhtiVeikko Pietarinen, eds., Acta Philosophica Fennica
, 2006
"... We consider the following questions: What kind of logic has a natural semantics in multiplayer (rather than 2player) games? How can we express branching quantifiers, and other partialinformation constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these ..."
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Cited by 7 (0 self)
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We consider the following questions: What kind of logic has a natural semantics in multiplayer (rather than 2player) games? How can we express branching quantifiers, and other partialinformation constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on KahnPlotkin concrete domains. Partial information constraints are represented as coclosure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and coarities. This enables a fully compositional account of a wide
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 7 (1 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