Focusing in Asynchronous Games

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear logic, of very different flavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc

К вопросу об асимметрии теоретико-игровой семантике

This article offers an analysis of the key aspects of the game-theoretic semantics, and demonstrates its advantages regarding the presentation of incomplete information and imperfect recall in comparison with Frege — Russell fi rst-order logic. The article offers a review of some limitations of the game-theoretic semantics towards the problem of asymmetry in semantic games. Author provides an overview of the concurrent game-theoretic semantics.В статье обсуждаются ключевые аспекты теоретико-игровой семантики, и демонстрируются ее преимущества в деле анализа игр с несовершенной информацией и несовершенной памятью по сравнению с логикой первого порядка Фреге — Рассела. В статье обсуждаются ограничения теоретико-игровой семантики Я. Хинтикки относительно проблемы асимметрии в семантических играх. Представлен обзор характеристик параллельной теоретико-игровой семантики

The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)

We introduce a geometry of interaction model for Mazza's multiport interaction combinators, a graph-theoretic formalism which is able to faithfully capture concurrent computation as embodied by process algebras like the $\pi$-calculus. The introduced model is based on token machines in which not one but multiple tokens are allowed to traverse the underlying net at the same time. We prove soundness and adequacy of the introduced model. The former is proved as a simulation result between the token machines one obtains along any reduction sequence. The latter is obtained by a fine analysis of convergence, both in nets and in token machines