A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183--220, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....data specialization. 1 Introduction This paper describes an attempt to mix parallelism and partial evaluation. This is motivated by the increasing interest for parallelism based on linear logic [Gir87] The geometry of interaction [Lam90, GAL92, Abr90] interaction nets [Laf90] games semantics [Bla, LS91] are promising theories for understanding concurrency and relation between processes. We have already worked on partial evaluation of interaction nets [Bec92] However, here, we are interesting to know if classical partial evaluation (i.e. based on binding time analysis [J#r92, Con88, JSS89] is ....

A. Blass. A game semantics for linear logic.

....and our output U; V is the result of the game, won by U when the result is 1. Therefore the problem of closing the system is closely related to the search for a complete game semantics for linear logic: the connection between linear logic and game semantics was initiated by Blass, see [B92]) 1.8 Notes on the style Geometry of interaction is most naturally handled by means of C algebras ; this yields surely more elegant proofs, but it obscures the concrete interpretation. So we prefer to follow a down to earth description of the interpretation. An unexpected feature will help us ....

Blass, A. : A game semantics for linear logic, Annals Pure Appl. Logic 56, pp. 183-220, 1992.

....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, ....

Blass, A. A game semantics for linear logic. Ann. Pure Appl. Logic 56 (1992), 183-220.

....But 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. ....

Blass, A. A game semantics for linear logic. Ann. Pure Appl. Logic 56 (1992), 183--220.

....of strategy, cannot be functorial on gam . Nevertheless, the composition of games may be viewed as orthogonal to the familiar composition of strategies in a common framework. 0 Introduction People who study games from a mathematical perspective (e.g. Blass, Abramsky, Hyland, Ong et al. cf. [3] [1] 2] 6] and [5] tend to think of games as certain kinds of trees. In fact, they construct categories with games as objects and strategies as morphisms. In contrast to that approach, here we wish to derive games as the natural choice of morphisms in a certain bicategory with sets as ....

....start with moves in O with strictly alternating strings in (O P ) that start with moves in O . Hence, without loss of generality, we may restrict our attention to strictly alternating sequences of moves from O and P , starting with moves in O , which is precisely what is done in [3], 1] and [5] while in [2] only strict alternation is required. When interested in actual sequences of moves from these sets, we just re interpret our interaction pattern over O and P . Since the non empty down sets that consist of strictly alternating strings over O P form a ....

Blass, A. A game semantics for linear logic. Ann. Pure Appl. Logic 56 (1992), 183--220.

....moves, the categorical description of the structure that leads to the monoidal closed category is even more satisfying. In particular, we then obtain an explicit involution. 0 Introduction People who study games from a mathematical perspective (e.g. Blass, Abramsky, Hyland, Ong et al. cf. [3] [1] 2] 6] and [5] tend to think of games as certain kinds of trees. In fact, they construct categories with games as objects and strategies as morphisms. In contrast to that approach, here we wish to derive games as the natural choice of morphisms in a certain bicategory with sets as ....

....a strictly alternating sequence of moves in O P . But this unique interpretation is the key to a major simplification in the whole set up: without loss of generality we can restrict our attention to strictly alternating sequences of moves from O and P , which is precisely what is done in [3], 1] and [5] but not in [2] When interested in actual sequences of moves from these sets, we just re interpret our interaction pattern over O and P . The study of tensor products in Section 6, however, makes it desirable to have a distinguished move with the meaning I pass available ....

Blass, A. A game semantics for linear logic. Ann. Pure Appl. Logic 56 (1992), 183--220.

.... bases [Jackson, 1987] Recent advances in applying games in computer science include game semantics and full completeness results [Hyland Ong, 1995] game and interaction categories in category theory [Abramsky et al. 1996] and game semantics for fragments of linear logic, such as ane logic [Blass, 1992] and semantics and full completeness for multiplicative [Abramsky Jagadeesan, 1994] and multiplicative additive fragment [Abramsky Melli es, 1998] just to mention a few. One of the goals in this enterprise is to give a precise mathematical analysis of a wide range of programming languages. ....

Blass, A.: (1992) A game semantics for linear logic, Annals of Pure and Applied Logic 56, 183-220.

....v. Therefore winning strategies (i.e. strategies such that the player who follows them is always able to play a move, when on turn) naturally induce total functionals. We base our treatment on [11] Admittedly formalizations based on the categorical semantics of linear logic, as it is the case of [6, 2, 3, 1, 9], have the advantage of being compositional with respect to the type structure, which is not the case of the present one. However the actual description of strategies seems more direct in a formulation which does not make use of the decomposition of the function space bifunctor into linear ....

A. Blass, "A game semantics for linear logic", Annals of Pure and Applied Logic 56, 183-220.

....typing can be regarded as a combination of linear typing (dealing with unique objects) and traditional typing (for non unique objects) connected by a subtyping mechanism. In fact, the part handling uniqueness allows discarding of objects, so it corresponds more closely to affine logic, see Blass (1992). A logical categorical proposal for a related combination appears in Benton (1994) The present paper describes the uniqueness type system in natural deduction style, using an inductive syntax for graph expressions. The emphasis on graph denotations contrasts the original presentation, which ....

....into two layers: a resource conscious part in which occurrences are limited, and a conventional part with no reference restrictions. In fact, the former layer (of unique types, indicated by ffl ) admits discarding input but excludes copying. Therefore it corresponds to affine logic (see Blass (1992)) in which weakening is present but no contraction. The latter layer (of Theta types) corresponds to ordinary (intuitionistic) logic with the same strength as conventional typing. Erik Barendsen and Sjaak Smetsers 14 The two layers are connected: it is possible to move from the ffl layer to the ....

Blass, A. (1992). A game semantics for linear logic, Annals of Pure and Applied Logic 56, pp. 183--220.

....to formalize this distinction, it is natural to consider two party protocols, where one party is carrying out the action represented by a formula while the other makes the external choices required for . There are several ways to think about this and correspondingly several terminologies. In [4], I described a viewpoint oriented toward proving propositions. The two participants in a protocol (or dialog or game) were a proponent and an opponent; the former seeks to establish the truth of the formula under consideration, the latter to establish its falsity, and the heart of the semantics ....

....to establish its falsity, and the heart of the semantics consists of rules for the debate between these two. The idea of using two party dialogs to explain the meanings of logical connectives goes back to Lorenzen [22] and the particular operations on games, which interpret the connectives in [4], go back to [3] In [5] I described a very similar semantics based on a type theoretic viewpoint. The intuition here is that a formula A represents a server capable of providing, to some user, elements of type A.IfAis of the form A 1 A 2 then before the server can provide an appropriate ....

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Andreas Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56:183--220, 1992.

....server is expected to provide an element but cannot. Notice that, by requiring that no infinite sequence have all initial segments in H, we have chosen to consider only protocols that always end after finitely many steps. The theory could be expanded to allow or even require infinite runs (cf. [2]) but nothing of this sort seems to be implicit in the formalism or the underlying intuitions of linear logic. But see the discussion of A below. As suggested by the title of this paper, the protocols considered here can be viewed as games (or debates or dialogs) between the client and the ....

....but nothing of this sort seems to be implicit in the formalism or the underlying intuitions of linear logic. But see the discussion of A below. As suggested by the title of this paper, the protocols considered here can be viewed as games (or debates or dialogs) between the client and the server [1, 2, 10, 11]. In this connection, the server is usually called the proponent or player, and the client is called the opponent. The protocol specifies who is to move (see Note 2) and what moves are legal at any point during a play of the game. Our protocols, unlike some versions of games [1, 2] but like the ....

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A. Blass, A game semantics for linear logic, Ann. Pure Appl. Logic 56 (1992), 183--220.

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183--220, 1992.

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183{ 220, 1992. 14

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(13) :183--220, 1992.

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183--220, 1992.

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(13) :183--220, 1992.

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A. Blass, A game semantics for linear logic, Ann. Pure Appl. Logic 56 (1-3) (1992) 183-220.

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A. Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183{ 220, 1992.

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