Introduction to linear logic and ludics, part II

This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently developped in an aim of further unveiling the fundamental interactive nature of computation and logic. We hope to offer a few computer science insights into this new theory

Ludics without Designs I: Triads

In this paper, we introduce the concept of triad. Using this notion, we study, revisit, discover and rediscover some basic properties of ludics from a very general point of view.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441

Ludics and its Applications to natural Language Semantics

Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a dialectical interaction. The conception is at the intersection of a proof-theoretic and a game-theoretic accounts of semantics, but it enlarges them by allowing to deal with possibly infinite processes

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

Ludics, dialogue and inferentialism

In this paper, we try to show that Ludics, a (pre-)logical framework invented by J-Y. Girard, enables us to rethink some of the relationships between Philosophy, Semantics and Pragmatics. In particular, Ludics helps to shed light on the nature of dialogue and to articulate features of Brandom\u27s inferentialism

Interactive observability in Ludics: The geometry of tests

AbstractLudics [J.-Y. Girard, Locus solum, Math. Structures in Comput. Sci. 11 (2001) 301–506] is a recent proposal of analysis of interaction, developed by abstracting away from proof-theory. It provides an elegant, abstract setting in which interaction between agents (proofs/programs/processes) can be studied at a foundational level, together with a notion of equivalence from the point of view of the observer.An agent should be seen as some kind of black box. An interactive observation on an agent is obtained by testing it against other agents.In this paper we explore what can be observed interactively in this setting. In particular, we characterize the objects that can be observed in a single test: the primitive observables of the theory.Our approach builds on an analysis of the geometrical properties of the agents, and highlights a deep interleaving between two partial orders underlying the combinatorial structures: the spatial one and the temporal one

A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments

We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry of interaction which interprets proofs as operators in a von Neumann algebra. The expressivity of the logic soundly interpreted in this model is dependent on properties of a MASA which is a parameter of the interpretation. We also unveil the essential role played by MASAs in previous geometry of interaction constructions