A. Abramsky. Semantics of interaction: an introduction to Game Semantics, pages 1--31. Cambridge Press, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....game theory [45] in that payo s for winning or losing a game are not considered, and because there is no use of uncertainty measures, such as probabilities, to model the possible moves of opponents. They also di er from the abstract games recently used as a semantics for interactive computation [1], in the tradition of Jaako Hintikka s game theoretic semantics [25] since these abstract games do not share the rich rule structure of dialogue games, and are not intended to have themselves a semantic interpretation involving the beliefs or actions of multiple agents. The main application of ....

S. Abramsky. Semantics of interaction: an introduction to game semantics. In A. M. Pitts and P. Dybjer, editors, Semantics and Logics of Computation, pages 1-31. Cambridge University Press, Cambridge, UK, 1997.

....in which the term is used. This is a key point at which games models differ from other process models: the distinction between the actions of the system and those of its environment is made explicit from the very beginning. For a fuller discussion of the ramifications of this distinction, see [1]) In the games we shall consider, O always moves first the environment sets the system going and thereafter the two players make moves alternately. What these moves are, and when they may be played, are determined by the rules of each particular game. Since in a programming language a type ....

....are just sets of data values, such as IN and bool. For each such data type, we will have types exp[D] and var[D] of expressions which can produce values of type D, and variables which can store values of type D respectively. We will also have a data type com of commands; this will really be exp[1], where 1 is a one element set, but it will be convenient to distinguish this special case. Thus our syntax of basic types is B : exp[D] j com j var[D] The general class of types we shall consider will contain first order procedures as well as basic types. The syntax is T : B j B T : ....

S. Abramsky. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, pages 1--32. Cambridge Univ. Press, 1997.

....winning or losing a game are not considered, and because there is no use of uncertainty measures, such as probabilities, to model the possible moves of opponents. They also differ from the abstract games recently developed as a semantics for programming languages in theoretical computer science [1], since these latter games do not typically share the rich rule structure of dialogue games, and are not intended to be implemented as interaction protocols. In the multi agent systems arena, dialogue games have been proposed as the basis for protocols for several types of agent interactions, ....

S. Abramsky. Semantics of interaction: an introduction to game semantics. In A. M. Pitts and P. Dybjer, editors, Semantics and Logics of Computation, pages 1-31. Cambridge University Press, Cambridge, UK, 1997.

....(IMAL2) We extend Lamarche s essential nets to the second order ane setting and use them to show that the model is fully and faithfully complete. Keywords: Full Completeness, Game Semantics, Linear Logic, Polymorphism. 1 Introduction This paper is about a second order extension of AJM games [2, 1], which we call evolving games. A play begins with O making an opening move, and the two players alternate thereafter. An evolving game has two kinds of tokens: ground and second order. Ground tokens are standard; they are playable at once (if reachable) Second order tokens are (descriptions of) ....

....that each regular strategy determines a correct essential net for the associated end sequent. Faithful completeness is proved with respect to a notion of equivalence of such nets. Evolving Games and Essential Nets for Ane Polymorphism 3 The only game model for IMAL2 in the literature is given in [1]. Recently Abramsky and Lenisa [3] have constructed a linear combinatory algebra of partial involutions on the natural numbers, arising from Geometry of Interaction constructions; they show that a fully and faithfully complete model for ML polymorphic types of system F can be obtained in this way. ....

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Abramsky, S.: Semantics of Interaction: an introduction to Game Semantics. Semantics and Logics of Computation. Cambridge Univ. Press, 1-32

....yet another way in Section 5. 7 Categories of games Simple games. Let Gam be the category whose objects are games in which Opponent starts and whose maps are (partial deterministic) strategies for Player in the linear function space. This simple category is described in detail in [35] see also [2]. Gam is an ane model for intuitionistic linear logic. Multiplicative structure. The tensor product A B is the game obtained by playing A and B in parallel; the linear function space B C is the game obtained by playing the cogame B (interchanging Opponent and Player) in parallel with C. ....

S. Abramsky. Semantics of interaction: an introduction to game semantics. In Pitts and Dybjer [47], pages 1-31.

....between two agents, a speaker and a hearer, in which the speaker identi es an object using a name, and the hearer eventually agrees on the name as appropriate for the object identi ed. 1 A game theoretic approach in computation is widely used e.g. in game semantics (see for instance introductory [Abr97, AM98] and program synthesis (see [NYY92] for background and references) More recently, games have been used in modeling pushdown processes and automata, in particular to study the complexity of the model checking problem [Wal01] A game is of coordination (also pure coordination ) if ....

S. Abramsky. Semantics of Interaction: an introduction to Game Semantics. In P. Dybjer and A. Pitts, editors, Proceedings of the

....(IMAL2) We extend Lamarche s essential nets to the second order ane setting and use them to show that the model is fully and faithfully complete. Keywords: Full Completeness, Game Semantics, Linear Logic, Polymorphism. 1 Introduction This paper is about a second order extension of AJM games [2, 1], which we call evolving games. A play begins with O making an opening move, and the two players alternate thereafter. An evolving game has two kinds of tokens: ground and second order. Ground tokens are standard; they are playable at once (if reachable) Second order tokens are (descriptions of) ....

....that each regular strategy determines a correct essential net for the associated end sequent. Faithful completeness is proved with respect to a notion of equivalence of such nets. Evolving Games and Essential Nets for Ane Polymorphism 3 The only game model for IMAL2 in the literature is given in [1]. Recently Abramsky and Lenisa [3] have constructed a linear combinatory algebra of partial involutions on the natural numbers, arising from Geometry of Interaction constructions; they show that a fully and faithfully complete model for ML polymorphic types of system F can be obtained in this way. ....

[Article contains additional citation context not shown here]

S. Abramsky. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, pages 1-32. Cambridge Univ. Press, 1997.

....on lax functors B C resulting in lax functors B cChu C cChu that preserve dualization are the isomorphisms. 5 Chu cells in rel : a connection with games Interactions and games have been studied to nd models for certain fragments of linear logic. Rather than the usual trees (cf. e.g. 6] [1], 2] 10] and [11] here we wish to use bipartite labeled state transition systems (LSTSs) of the form R : x y u v r0 r1 a b with two state sets r 0 (for Opponent) and r 1 (for Player) and two labeling relations r 0 r 1 0 a and r 1 r 0 1 b to be interpreted as moves. In fact, ....

Abramsky, S. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, A. M. Pitts and P. Dybjer, Eds., Publications of the Newton Institute. Cambridge University Press, Cambridge, 1997, ch. 1, pp. 1-31.

....the two category structures do not satisfy the middle interchange law. 0 Introduction In order to model certain fragments of linear logic, games based on alternating trees have been introduced as objects of symmetric monoidal closed categories with certain strategies as morphisms, cf. e.g. 3] [1], 2] 4] 5] In [6] we showed these games can also be viewed as 1 cells in a 2 category gam with sets as objects and inclusions as 2 cells. The 1 cell composition in gam was inspired by the relation product and appeared to be in some sense orthogonal to the composition of strategies. Here ....

Abramsky, S. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, A. M. Pitts and P. Dybjer, Eds., Publications of the Newton Institute. Cambridge University Press, Cambridge, 1997, ch. 1, pp. 1--31.

....a and b . Neither beginning state nor nal state of a move have to be determined. Once we x an initial state, we can think of these graphs as games. Recent e orts in nding models for certain fragments of linear logic have focused on (deterministic) games where states were implicit, cf. e.g. [1], 12] or [15] Our theory applies to pfn as category of sets and partial functions, monoidal closed with respect to . Viewing pfn as sub bicategory of rel necessitates a generalization with all dimensions raised by 1. Acknowledgements I am grateful to Jir Ad amek, Victor Pollara and Werner ....

Abramsky, S. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, A. M. Pitts and P. Dybjer, Eds., Publications of the Newton Institute. Cambridge University Press, Cambridge, 1997, ch. 1, pp. 1-31.

....internal language for autonomous categories (see [9] for details) so that the classifying category of IMLL is the autonomous category freely generated from (the discrete graph whose vertices are) the atomic types. The two person games (between P and O) we play are similar to those introduced in [1] though they are finite (no infinite plays) In Section 3, we present a new fully complete model G e for IMLL without unit. Proofs are characterised by what we call exhausting strategies which are history free (in the standard sense) and satisfy a kind of reachability condition called ....

S. Abramsky. Semantics of interaction: an introduction to game semantics. In Semantics and Logics of Computation, pages 1--32. Cambridge Univ. Press, 1997.

....other s failures, divergence, and success. Later it was found that bisimulation precisely expresses the equivalence of choice of two person games. Two person games are a general paradigm for sequential interaction where the player and opponent model alternate moves of the system and environment [Ab]. Systems may exhibit equivalence of choice when they are not structure equivalent and bisimulation is therefore coarser, less expressive, than structure equivalence, though stronger than language equivalence. The grammars G3: S aX aY bZ, X e, Y e, Z e, and G4: S aX bY bZ, X e, Y ....

Samson Abramsky, Semantics of Interaction: An Introduction to Game Semantics, in Semantics of Logics and Computation, Cambridge University press, 1997.

.... case of pure higher order functions (Plotkin 1977) let al..one for the combination of functions with local state (Meyer and Sieber 1988) or with features involving non deterministic interaction (where even mere compositionality is a challenge) Recent developments involving mathematical games (Abramsky 1997; Hyland 1997) promise to solve many of these problems. As with the classical Scott Plotkin denotational models based upon order theoretic structure, a considerable mathematical investment is required to understand and apply such models. The challenge of higher order languages for operational ....

Abramsky, S. (1997). Semantics of interaction: an introduction to game semantics. In A. M. Pitts and P. Dybjer (Eds.), Semantics and Logics of Computation, Publications of the Newton Institute, pp. 1--31. Cambridge University Press.

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A. Abramsky. Semantics of interaction: an introduction to Game Semantics, pages 1--31. Cambridge Press, 1999.

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S. Abramsky, Semantics of interaction: an introduction to game semantics, in: A. Pitts and P. Dybjer (eds.), Semantics and logics of computation (Cambridge, 1995), Cambridge 1997, p. 1--31

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A. Abramsky. Semantics of interaction: an introduction to Game Semantics, pages 1-31. Cambridge Press, 1999.

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