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Fair Games and Full Completeness for Multiplicative Linear Logic without the MIXRule
, 1993
"... We introduce a new category of finite, fair games, and winning strategies, and use it to provide a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted as games, and proofs as winning strategies. This interpretation provides a categorical model of mll wh ..."
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Cited by 46 (4 self)
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We introduce a new category of finite, fair games, and winning strategies, and use it to provide a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted as games, and proofs as winning strategies. This interpretation provides a categorical model of mll which satisfies the property that every (historyfree, uniformly) winning strategy is the denotation of a unique cutfree proof net. Abramsky and Jagadeesan first proved a result of this kind and they refer to this property as full completeness. Our result differs from theirs in one important aspect: the mixrule, which is not part of Girard's Linear Logic, is invalidated in our model. We achieve this sharper characterization by considering fair games. A finite, fair game is specified by the following data: ffl moves which Player can play, ffl moves which Opponent can play, and ffl a collection of finite sequences of maximal (or terminal) positions of the game which are deemed to be fair. N...
Designs, Disputes And Strategies
, 2002
"... Important progresses in logic are leading to interactive and dynamical models. Geometry of Interaction and Games Semantics are two major examples. Ludics, initiated by Girard, is a further step in this direction. The objects ..."
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Cited by 23 (6 self)
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Important progresses in logic are leading to interactive and dynamical models. Geometry of Interaction and Games Semantics are two major examples. Ludics, initiated by Girard, is a further step in this direction. The objects
Comparing Hierarchies of Types in Models of Linear Logic
, 2003
"... We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distri ..."
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Cited by 6 (3 self)
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We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distributive laws % : ! : ! M G ) G ! N commuting to the promotion rule. The key ingredient of the proof is a notion of backandforth translation between the hierarchies of types induced by M and N. We apply this result to compare (1) the qualitative and the quantitative hierarchies induced by the coherence (or hypercoherence) space model, (2) several paradigms of games semantics: errorfree vs. erroraware, alternated vs. nonalternated, backtracking vs. repetitive, uniform vs. nonuniform.
Innocence in 2Dimensional Games
"... In this note, we reformulate HylandOngNickau pointer game semantics for PCF, as a more concurrent style of games, called 2dimensional games. The main novelty of these games is that they are played on concurrent graphs, instead of trees. This enables to permute moves, and to decompose the inno ..."
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In this note, we reformulate HylandOngNickau pointer game semantics for PCF, as a more concurrent style of games, called 2dimensional games. The main novelty of these games is that they are played on concurrent graphs, instead of trees. This enables to permute moves, and to decompose the innocence constraint on strategies, as local permutation properties.
Innocent Game Semantics via Intersection Type Assignment Systems ∗
"... The aim of this work is to correlate two different approaches to the semantics of programming languages: game semantics and intersection type assignment systems (ITAS). Namely, we present an ITAS that provides the description of the semantic interpretation of a typed lambda calculus in a game model ..."
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The aim of this work is to correlate two different approaches to the semantics of programming languages: game semantics and intersection type assignment systems (ITAS). Namely, we present an ITAS that provides the description of the semantic interpretation of a typed lambda calculus in a game model based on innocent strategies. Compared to the traditional ITAS used to describe the semantic interpretation in domain theoretic models, the ITAS presented in this paper has two main differences: the introduction of a notion of labelling on moves, and the omission of several rules, i.e. the subtyping rules and some structural rules.
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"... Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F: C ⇄ D: G and transformations IdC ..."
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Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F: C ⇄ D: G and transformations IdC ⇒ GF and IdD ⇒ F G, and