84 research outputs found
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
Innocent strategies as presheaves and interactive equivalences for CCS
Seeking a general framework for reasoning about and comparing programming
languages, we derive a new view of Milner's CCS. We construct a category E of
plays, and a subcategory V of views. We argue that presheaves on V adequately
represent innocent strategies, in the sense of game semantics. We then equip
innocent strategies with a simple notion of interaction. This results in an
interpretation of CCS.
Based on this, we propose a notion of interactive equivalence for innocent
strategies, which is close in spirit to Beffara's interpretation of testing
equivalences in concurrency theory. In this framework we prove that the
analogues of fair and must testing equivalences coincide, while they differ in
the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014
Inferences and Dialogues in Ludics
International audience– We propose to use Ludics as a unified framework for the analysis of dialogue and as a reasoning system. Not only Ludics gives a denotational semantics for Linear Logic, but it uses interaction as a primitive notion. We first sketch a model for pragmatical and rhetorical aspects of dialogue after a brief review of the way the interactive aspect of dialogue may be represented in Ludics. Then we show how taking into account inferences that occur during a dialogue, with respect to a ISU-like model of dialogue. Through various examples we give an analysis of deductive inferences as well as processes making facts explicit that take place during knowledge updating
Infinitary -Calculi from a Linear Perspective (Long Version)
We introduce a linear infinitary -calculus, called
, in which two exponential modalities are available, the
first one being the usual, finitary one, the other being the only construct
interpreted coinductively. The obtained calculus embeds the infinitary
applicative -calculus and is universal for computations over infinite
strings. What is particularly interesting about , is that
the refinement induced by linear logic allows to restrict both modalities so as
to get calculi which are terminating inductively and productive coinductively.
We exemplify this idea by analysing a fragment of built around
the principles of and . Interestingly, it enjoys
confluence, contrarily to what happens in ordinary infinitary
-calculi
Classical realizability in the CPS target language
AbstractMotivated by considerations about Krivine's classical realizability, we introduce a term calculus for an intuitionistic logic with record types, which we call the CPS target language. We give a reformulation of the constructions of classical realizability in this language, using the categorical techniques of realizability triposes and toposes.We argue that the presentation of classical realizability in the CPS target language simplifies calculations in realizability toposes, in particular it admits a nice presentation of conjunction as intersection type which is inspired by Girard's ludics
Abstract machines for dialogue games
The notion of abstract Boehm tree has arisen as an operationally-oriented distillation of works on game semantics, and has been investigated in two papers. This paper revisits the notion, providing more syntactic support and more examples (like call-by-value evaluation) illustrating the generality of the underlying computing device. Precise correspondences between various formulations of the evaluation mechanism of abstract Boehm trees are established
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