S. Abramsky, P.-A. Melli es. Concurrent games and full completeness. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science (LICS '99), IEEE Computer Society Press, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....have di erent denotations. It has turned out very dicult to discover syntax independent constructions of such models and only the recent advances in game semantics seem to have provided a methodology allowing one to try to address the issue. A variety of game models for fragments of linear logic [3, 63, 1, 14, 15, 10, 95, 100] and intuitionistic logic [62, 60, 102, 61] have been proposed, a large majority of which are fully and faithfully complete. These early developments have stimulated progress in other areas and some models based on domain theory [84, 85] and Chuspaces [36] emerged shortly afterwards. However, the ....

.... (respectively faithful) Game semantics has provided the rst fully and faithfully complete models of various fragments of linear logic, notably multiplicative linear logic (MLL) with the MIX rule [3] the rst such result) without the MIX rule [63] and multiplicative additive linear logic (MALL) [10]. The full completeness problem for full linear logic is still open, but there exist game models modelling MELL in a less satisfactory fashion [14, 15] The methodology has also proved successful with regard to intuitionistic logic [102] and second order polymorphism [60, 102] Its most celebrated ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Proceedings, Fourteenth IEEE Symposium on Logic in Computer Science, pages 431-442. IEEE Computer Society Press, 1999. 185

....On the contrary, in the untyped setting, in [DFH99] it has been shown that game models capture only a very limited number of # theories, related to Bohm trees and Levy Longo trees. Wave GoI categories and algebras have been studied very little in the literature, apart from some special models, [BDER97,AM99]. A question which arises naturally is whether wave models allow to capture a richer class of untyped # theories. In this paper, we focus on the basic setting for wave GoI, i.e. Rel , actually on the category Rel # of pointed sets and relations preserving the distinguished point. We show that ....

S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99.

....of low level implementation of this semantics. We extend the introduction of garbage (corresponding to rules in [15] and [6] to the generalized ; connector, and hence to multidimensional garbage. Among the proofs of full abstraction for MALL, we wish to mention the work of Abramsky and Mellis [2], based on concurrent games. We would like to know what, if anything, our constructions have to do with concurrent games. 7 Conclusion and future work This work started with the search for a context semantics for the MultiplicativeAdditive Linear Logic and for a convenient proofnet syntax for ....

....context semantics enjoys some completeness property. The read back algorithm could probably reformulated in the game semantics framework, which might be the starting point to some comparisons between the concrete insight given by the context semantics and some more theoretical games constructions [1, 2]. ....

S. Abramsky and P.-A. Mellis. Concurrent games and full completeness. In LICS'99, pages 431-442. IEEE, July 1999.

....is the investigation of a timeless version of our model in the spirit of the Baillot, Danos, Ehrhard Regnier [6] construction starting from a symmetrized games model of Linear Logic and ending in a polarized variant of relational semantics. The concurrent games of Abramsky Mellies [1] and their polarized version by Mellies could prove useful here, since they are an intermediate step between games and hypercoherences. Current investigation with Ehrhard shows that there are probabilistic coherence spaces that could bridge the gap, at least in the intuitionistic case. 2 ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Proceedings, Fourteenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1999.

.... models to give an interpretation of concurrent features is therefore a natural development, although it requires a substantial change in perspective, as existing models are based on representation of interaction as alternating sequences of tokens (moves) One such construction concurrent games [3] has been used by Abramsky and Mellies to model multiplicative additive linear logic (in which concurrency is implicit rather than otherwise) The concurrent games are based on a true concurrency representation of interaction as information ow, with no notion of moves as discrete pieces of ....

....of the calculus with arithmetic. The extension to model concurrency has two key features; multi threading and synchronous message passing. The interpretation of multiple threads of control requires the most radical extension to previous work in game semantics, which (with the exception of [3]) has built models of sequential languages by representing interaction of strategies as a sequences of moves. We add a new set of concurrency pointers to these sequences, so that they can be seen as representing the interaction of two strategies as a tree of moves. Retaining the sequential ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Proceedings of the 14th annual Symposium on Logic In Computer Science, LICS '99, 1999.

....of. Also there has been research towards nondeterminism [HaMcC99] Very recently there has been developed a new concurrent form of game semantics resolving problems posed by the sequentiality of the traditional ones and giving a full completeness result for multiplicative additive linear logic [AbrMel99, Abr99c]. Also, game semantics has been employed to develop a notion of Process Realizability [Abr99c] Applications of game semantics to reasoning about security issues can be found in [MalHan99] Some of the work currently in progress addresses subtyping, and in another line of research, ....

S. Abramsky, P.-A. Melli es, Concurrent Games and Full Completeness, in: Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE 1999, p. 431-442

....than non well formed nets, these nets should be viewed as syntactic regions of larger well formed nets what (Girard 1987b) calls modules. The partitions in E and F are here to represent the di erent switchings of the environment of the module : Similar de nitions appear in (Loader 1994; Abramsky and Melli es 1999). Observe that there is no empty object = 0; f;g; f;g) in M. Such an object would contradict connectedness: two well formed nets 1 : and 2 : would compose into a non well formed (non connected) net 1 ; 2 . Module. Arrows in M are called modules. Warning The category M we ....

S. Abramsky, P.-A. Mellies, Concurrent games and full completeness. In Proceedings LICS'99, Trento, 1999.

....is the investigation of a timeless version of our model in the spirit of the Baillot, Danos, Ehrhard Regnier [6] construction starting from a symmetrized games model of Linear Logic and ending in a polarized variant of relational semantics. The concurrent games of Abramsky Mellies [1] and their polarized version by Mellies could prove useful here, since they are a sort of intermediate step between games and hypercoherences. Current investigation with Ehrhard shows that there are probabilistic coherence spaces that could bridge the gap, at least in the intuitionistic case. 2 ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Proceedings, Fourteenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1999.

.... 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. These are by no means games that share common characteristics. For example, the games in [Hyland Ong, 1995] are games without any conventions of ....

Abramsky, S. and Mellies, P.-A.: (1998) Concurrent games and full completeness, Preprint, 12 pages.

....Lemma of the earlier work, to show that M is a universal model which induces the Bohm tree theory. To our knowledge, DEAC and M are the first syntax independent universal models. Concurrent games A new concurrent form of game semantics has been introduced by S. Abramsky and P. A. Melli es [1]. It 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 multiplicative additive linear logic has been proved for this semantics. This model could ....

S. Abramsky and P.-A. Melli`es. Concurrent games and full completeness. Accepted for LICS 99.

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S. Abramsky, P.-A. Melli es. Concurrent games and full completeness. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science (LICS '99), IEEE Computer Society Press, 1999.

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S. Abramsky, P.-A. Mellies. Concurrent games and full completeness. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, LICS '99, IEEE Computer Society Press, 1999.

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S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Draft paper, 37 pages, 1998.

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S. Abramsky, P.-A. Melli es. Concurrent games and full completeness. Proceedings of LICS'99.

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S. Abramsky, P.-A. Mellies. Concurrent games and full completeness. In Proceedings LICS'99, Trento, 1999.

....games . In such games there is no longer a global polarization (we can have positions in which both players can move concurrently) although there are still local polarizations (each local decision is made by just one of the players) This idea of concurrent games was used by Abramsky and Melli es [AM99] to give a fully complete model for Linear Logic in its original form (i.e. not hyper sequentialized ) and indeed the correspondence is with proof nets, the parallel syntax for proof theory in Girard s phrase [Gir95a] In this way, the distinction between sequentiality and concurrency is re ....

....= x; d( y) y) d(in i (x) in j (y) in i (x y) in j (x y) Again, this has the same denotation as the proof which introduces the two s in the opposite order. However, it should be noted that in general, strategies must be taken modulo partial equivalence relations as in [AM99] in order to obtain the unicity properties for product and coproduct (i.e. the commutative conversions in sequent calculus terms, or conversions in calculus terminology) Interestingly, partial equivalence relations are also needed in Ludics [Gir01] Now one can check, unfolding the de ....

[Article contains additional citation context not shown here]

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, 431-44, 1999.

....ed by the proof structures arising from the semantic objects. The rst step typically uses uniformity arguments of a fairly general nature, while the second step makes more delicate use of speci c features of the model. The full completeness proof for concurrent games with respect to MALL [AM98, AM99] is of this general form. The connection made is with the proof nets for MALL introduced in [Gir95a] which eliminate additive boxes in favour of boolean weights, which distribute information about causal dependencies around the proof net. An important point is that what seemed to be mere ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Draft paper, 37 pages, 1998.

....games . In such games there is no longer a global polarization (we can have positions in which both players can move concurrently) although there are still local polarizations (each local decision is made by just one of the players) This idea of concurrent games was used by Abramsky and Melli es [AM99] to give a fully complete model for Linear Logic in its original form (i.e. not hyper sequentialized ) and indeed the correspondence is with proof nets, the parallel syntax for proof theory in Girard s phrase [Gir95a] In this way, the distinction between sequentiality and concurrency is re ....

....= x; d( y) y) d(in i (x) in j (y) in i (x y) in j (x y) Again, this has the same denotation as the proof which introduces the two s in the opposite order. However, it should be noted that in general, strategies must be taken modulo partial equivalence relations as in [AM99] in order to obtain the unicity properties for product and coproduct (i.e. the commutative conversions in sequent calculus terms, or conversions in calculus terminology) Interestingly, partial equivalence relations are also needed in Ludics [Gir01] Now one can check, unfolding the de ....

[Article contains additional citation context not shown here]

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, 431-44, 1999.

....satis ed by the proof structures arising from the semantic objects. The rst step typically uses uniformity arguments of a fairly general nature, while the second step makes more delicate use of speci c features of the model. The full completeness proof for concurrent games with respect to MALL [AM98, AM99] is of this general form. The connection made is with the proof nets for MALL introduced in [Gir95a] which eliminate additive boxes in favour of boolean weights, which distribute information about causal dependencies around the proof net. An important point is that what seemed to be mere ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Draft paper, 37 pages, 1998.

....Abr91] Moreover, these models can also yield new mathematical principles for reasoning on syntactical theories (observational equivalences) like for example Scott s Induction Principle. Recently, Game Semantics has been used to define fully complete models for various fragment of Linear Logic ([AJ94a, AM99]) and to give fully abstract models for many programming languages, including PCF [AJM96, HO96, Nic94] richer functional languages # Work supported by TMR Linear FMRX CT98 0170. 1 [AM95, McC96, HY97] and languages with non functional features such as reference types and non local control ....

....realizability, especially in connection with full completeness and full abstraction problems. Realizability can be regarded as a powerful tool for mediating between intensional and extensional aspects of computation, and it has been used for extensionalizing intensional constructions (e.g. in [AM99]) and as a technique for building directly interesting (possibly fully complete fullyabstract) models. Examples of this latter use of realizability are in this paper, and also in [AL99] where a fully abstract PER model for PCF, alternative to the game model of [AJM96] is provided using the ....

S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99 Conf. Proc., 1999.

....Abr91] Moreover, these models can also yield new mathematical principles for reasoning on syntactical theories (observational equivalences) like for example Scott s Induction Principle. Recently, Game Semantics has been used to define fully complete models for various fragment of Linear Logic ([AJ94a, AM99]) and to give fully abstract models for many programming languages, including PCF [AJM96, HO96, Nic94] richer functional languages Work supported by TMR Linear FMRX CT98 0170. 1 [AM95, McC96, HY97] and languages with non functional features such as reference types and non local control ....

....realizability, especially in connection with full completeness and full abstraction problems. Realizability can be regarded as a powerful tool for mediating between intensional and extensional aspects of computation, and it has been used for extensionalizing intensional constructions (e.g. in [AM99]) and as a technique for building directly interesting (possibly fully complete fullyabstract) models. Examples of this latter use of realizability are in this paper, and also in [AL99] where a fully abstract PER model for PCF, alternative to the game model of [AJM96] is provided using the ....

S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99 Conf. Proc., 1999.

....importance of fully (and faithfully) complete, and fully abstract denotational models is that they characterize the space of proofs programs in a compositional, syntax independent way. Recently, Game Semantics has been used to define fully complete models for various fragments of Linear Logic ([AJ94a,AM99]) and to give fully abstract models for many programming languages, including PCF [AJM96,HO96,Nic94] richer functional languages [McC96] and languages with non functional features such as reference types and non local control constructs [AM97,Lai97] Work partially supported by Linear ....

S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99.

....and faithfully complete model for ML polymorphic types of system F. Keywords: ML polymorphic types, linear logic, PER models, Geometry of Interaction, full completeness. Introduction Recently, Game Semantics has been used to define fully complete models for various fragments of Linear Logic ([AJ94a,AM99]) and to give fully abstract models for many programming languages, including PCF [AJM96,HO96,Nic94] richer functional languages [McC96] and languages with non functional features such as reference types and non local control constructs [AM97,Lai97] All these results are crucially based on ....

....realizability, especially in connection with full completeness and full abstraction problems. Realizability can be regarded as a powerful tool for mediating between intensional and extensional aspects of computation, and it has been used for extensionalizing intensional constructions (e.g. in [AM99]) and as a technique for building directly interesting (possibly fully complete fullyabstract) models. Examples of this latter use of realizability appear in this paper, and in [AL99] where a fully abstract PER model for PCF, alternative to the game model of [AJM96] is provided using the ....

S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99.

....much richer system than MLL, as shown by the much more sophisticated and complex notion of proof net it requires [Gir95] Our proof of Full Completeness is correspondingly lengthy and complex. We can only give an outline in this extended abstract; a detailed account is given in a draft full paper [AM98]. However, we believe that our methods and results will extend to the exponentials as well, thus yielding a complete analysis of Linear Logic. Independently, Girard has obtained a form of Full Completeness result using a game semantics [Gir98a,b] His methods, and the details of his results, ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Draft paper, 37 pages, 1998.

....much richer system than MLL, as shown by the much more sophisticated and complex notion of proof net it requires [Gir95] Our proof of Full Completeness is correspondingly lengthy and complex. We can only give an outline in this extended abstract; a detailed account is given in a draft full paper [AM98]. However, we believe that our methods and results will extend to the exponentials as well, thus yielding a complete analysis of Linear Logic. Independently, Girard has obtained a form of Full Completeness result using a game semantics [Gir98a,b] His methods, and the details of his results, ....

S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. Draft paper, 37 pages, 1998.

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S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Proc. of the 14th Int. Symposium on Logic in Computer Science, (Computer Society Press of the IEEE), 1999.

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S. Abramsky and P.-A. Mellies. Concurrent games and full completeness. In Fourteenth Annual IEEE Symposium on Logic in Computer Science, LiCS 1999.

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S. Abramsky, P.-A. Melli es, Concurrent Games and Full Completeness, in: Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE 1999, p. 431-442

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S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99.

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S.Abramsky, P.Mellies. Concurrent Games and Full Completeness, LICS'99, 431-442.

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Samson Abramsky and Paul-Andre Mellies. Concurrent games and full completeness. In Proceedings of the Fourteenth International Symposium on Logic in Computer Science (LICS'99), pages 431--442. IEEE Computer Society Press, 1999.

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