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Algorithmic Game Semantics
 In Schichtenberg and Steinbruggen [16
, 2001
"... Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependen ..."
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Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with nonfunctional features such as control operators and locallyscoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computerassisted verification and program analysis. Some promising steps have already been taken in this
Dialectic Semantics for Argumentation Frameworks
 In ICAIL
, 1999
"... We provide a formalism for the study of dialogues, where a dialogue is a twoperson game, initiated by the proponent who defends a proposed thesis. We examine several different winning criteria and several different dialogue types, where a dialogue type is determined by a set of positions, an attack ..."
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Cited by 46 (0 self)
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We provide a formalism for the study of dialogues, where a dialogue is a twoperson game, initiated by the proponent who defends a proposed thesis. We examine several different winning criteria and several different dialogue types, where a dialogue type is determined by a set of positions, an attack relation between positions and a legalmove function. We examine two proof theories, where a proof theory is determined by a dialogue type and a winning criterion. For each of the proof theories we supply a corresponding declarative semantics. 1 Introduction Artificial intelligence has long dealt with the challenge of modeling argumentation ([Tou84], [Fel84], [Vre97]). Abstract argumentation and formal dialectics have been developed in noteworthy works such as [Dun95], [Vre93], [KT96], [PS96], [PS97], [Ver96] and [Lou98a]. These fields are useful for the purpose of decisionmaking and discussion among intelligent agents, such as in [Ree97] and [PJ98]. In addition, they are important in the...
A Semantic analysis of control
, 1998
"... This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that ..."
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Cited by 32 (5 self)
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This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Nonlocal control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for highertype, sequential computation with access to the flow of control. A simple operational semantics for both callbyname and callbyvalue evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.
From intuitionistic logic to GödelDummett logic via parallel dialogue games
 IN PROCEEDINGS OF THE 33RD IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC
, 2003
"... Building on a version of Lorenzen’s dialogue foundation for intuitionistic logic, we show that a suitable game of communicating parallel dialogues is sound and complete for GödelDummett logic G. Among other things, this provides a computational interpretation of Avron’s hypersequent calculus for G ..."
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Cited by 8 (4 self)
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Building on a version of Lorenzen’s dialogue foundation for intuitionistic logic, we show that a suitable game of communicating parallel dialogues is sound and complete for GödelDummett logic G. Among other things, this provides a computational interpretation of Avron’s hypersequent calculus for G.
Symmetry and Interactivity in Programming
 Bulletin of Symbolic Logic
, 2001
"... We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics. ..."
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Cited by 5 (1 self)
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We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics.
Games And Definability For FPC
 Bulletin of Symbolic Logic
, 1997
"... . A new games model of the language FPC, a type theory with products, sums, function spaces and recursive types, is described. A definability result is proved, showing that every finite element of the model is the interpretation of some term of the language. 1. Introduction. The work of Lorenzen [2 ..."
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. A new games model of the language FPC, a type theory with products, sums, function spaces and recursive types, is described. A definability result is proved, showing that every finite element of the model is the interpretation of some term of the language. 1. Introduction. The work of Lorenzen [24, 23] proposed dialogue games as a foundation for intuitionistic logic. The idea is simple: associated to a formula A is a set of moves for two players, each of which is either an attack on Aan attempt to refute its validityor a defence. The players, O who wants to refute A and P who wants to prove A, take turns to make moves according to some rules. The rules determine which player has won when play ends, and the formula A is semantically valid if there is a strategy by which P can always win: a winning strategy. More recently, games of this kind have been applied in computer science to give programming languages a new kind of semantics with a strong intensional flavour. The game in...
Games and WeakHead Reduction for Classical PCF
 Proceedings of TLCA 97, LNCS 1210
, 1997
"... . We present a game model for classical PCF, a finite version of PCF extended by a catch/throw mechanism. This model is build from Edialogues, a kind of twoplayers game defined by Lorenzen. In the Edialogues for classical PCF, the strategies of the first player are isomorphic to the Bohm trees of ..."
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. We present a game model for classical PCF, a finite version of PCF extended by a catch/throw mechanism. This model is build from Edialogues, a kind of twoplayers game defined by Lorenzen. In the Edialogues for classical PCF, the strategies of the first player are isomorphic to the Bohm trees of the language. We define an interaction in Edialogues and show that it models the weakhead reduction in classical PCF. The interaction is a variant of Coquand's debate and the weakhead reduction is a variant of the reduction in Krivine's Abstract Machine. We then extend Edialogues to a kind of games similar to HylandOng's games. Interaction in these games also models weakhead reduction. In the intuitionistic case (i.e. without the catch/throw mechanism), the extended Edialogues are HylandOng's games where the innocence condition on strategies is now a rule. Our model for classical PCF is different from Ong's model of Parigot's lambdamucalculus. His model works by adding new moves t...
A games semantics for reductive logic and proofsearch
 GaLoP 2005: Games for Logic and Programming Languages
, 2005
"... Abstract. Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive l ..."
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Abstract. Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive logic and show how it may be used to model two important examples of control, namely backtracking and uniform proof. 1 Introduction to reductive logic and proofsearch Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive logic and show how it may be used to model two important
Parallel Dialogue Games and Hypersequents for Intermediate Logics
 Proceedings of TABLEAUX 2003, Automated Reasoning with Analytic Tableaux and Related Methods
, 2003
"... Abstract. A parallel version of Lorenzen’s dialogue theoretic foundation for intuitionistic logic is shown to be adequate for a number of important intermediate logics. The soundness and completeness proofs proceed by relating hypersequent derivations to winning strategies for parallel dialogue game ..."
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Abstract. A parallel version of Lorenzen’s dialogue theoretic foundation for intuitionistic logic is shown to be adequate for a number of important intermediate logics. The soundness and completeness proofs proceed by relating hypersequent derivations to winning strategies for parallel dialogue games. This also provides a computational interpretation of hypersequents. 1
Applications of Game Semantics: From Program Analysis to Hardware Synthesis
"... After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. C ..."
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After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. Chronology, methodology, ideology Game Semantics is a denotational semantics in the conventional sense: for any term, it assigns a certain mathematical object as its meaning, which is constructed compositionally from the meanings of its subterms in a way that is independent of the operational semantics of the object language. What makes Game Semantics particular, peculiar maybe, is that the mathematical objects it operates with