Resource modalities in tensor logic

PA Melliès, N Tabareau - Annals of Pure and Applied Logic, 2010 - Elsevier
The description of resources in game semantics has never achieved the simplicity and
precision of linear logic, because of the misleading conception that linear logic is more …

Asynchronous games 4: A fully complete model of propositional linear logic

PA Mellies - 20th Annual IEEE Symposium on Logic in …, 2005 - ieeexplore.ieee.org
We construct a denotational model of propositional linear logic based on asynchronous
games and winning uniform innocent strategies. Every formula A is interpreted as an …

Asynchronous games 2: The true concurrency of innocence

PA Melliès - Theoretical Computer Science, 2006 - Elsevier
In game semantics, the higher-order value passing mechanisms of the λ-calculus are
decomposed as sequences of atomic actions exchanged by a Player and its Opponent …

On traced monoidal closed categories

M Hasegawa - Mathematical Structures in Computer Science, 2009 - cambridge.org
The structure theorem of Joyal, Street and Verity says that every traced monoidal category
arises as a monoidal full subcategory of the tortile monoidal category Int. In this paper we …

Asynchronous games 2: the true concurrency of innocence

PA Mellies - International Conference on Concurrency Theory, 2004 - Springer
In game semantics, one expresses the higher-order value passing mechanisms of the λ-
calculus as sequences of atomic actions exchanged by a Player and its Opponent in the …

An explicit formula for the free exponential modality of linear logic

PA Melliès, N Tabareau, C Tasson - International Colloquium on …, 2009 - Springer
The exponential modality of linear logic associates a commutative comonoid! A to every
formula A in order to duplicate it. Here, we explain how to compute the free commutative …

Asynchronous template games and the gray tensor product of 2-categories

PA Melliès - 2021 36th Annual ACM/IEEE Symposium on Logic …, 2021 - ieeexplore.ieee.org
In his recent and exploratory work on template games and linear logic, Melliès defines
sequential and concurrent games as categories with positions as objects and trajectories as …

Models of a non-associative composition

G Munch-Maccagnoni - … of Software Science and Computation Structures …, 2014 - Springer
We characterise the polarised evaluation order through a categorical structure where the
hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as …

An explicit formula for the free exponential modality of linear logic

PA Melliès, N Tabareau, C Tasson - Mathematical Structures in …, 2018 - cambridge.org
The exponential modality of linear logic associates to every formula A a commutative
comonoid! A which can be duplicated in the course of reasoning. Here, we explain how to …

Dialogue categories and chiralities

PA Melliès - Publications of the Research Institute for Mathematical …, 2016 - ems.press
In this paper, we consider a two-sided notion of dialogue category which we call dialogue
chirality and which we formulate as an adjunction between a monoidal category A of proofs …