International audienceWe give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs are at the heart of our analysis: we show that the tq-protocol of normalization for the classical systems LKeta,pol and LKeta,rho,pol perfectly fits normalization of polarized proof-nets. Some more semantical considerations allow us to recover LC as a refinement of multiplicative LKeta,pol
In this paper, we study dialogue as a game, but not only in the sense in which there would exist winning strategies and a priori rules. Dialogue is not governed by game rules like for chess or other games, since even if we start from a priori rules, it is always possible to play with them, provided that some invariant properties are preserved. An important discovery of Ludics is that such properties may be expressed in geometrical terms. The main feature of a dialogue is "convergence". Intuitively, a dialogue "diverges" when it stops prematurely by some disruption, or a violation of the tacit agreed upon conditions of the discourse. It converges when the two speakers go together towards a situation where they agree at least on some points. As we shall see, convergence may be thought of through the geometrical concept of orthogonality. Utterances in a dialogue have as their content, not only the processes (similar to proofs) which lead to them from a monologic view, but also their interactions with other utterances. Finally, any utterance must be seen as co-constructed in an interaction between two processes. That is to say that it not only contains one speaker's intentions but also his or her expectations from the other interlocutor. From our viewpoint, discursive strategies like narration, elaboration, topicalization may derive from such interactions, as well as speech acts like assertion, question and denegation.
-Nous souhaitons dans ce texte illustrer la pertinence d'un nouveau point de vue pour une approche logique des langues naturelles. Parce que l'interaction nous apparaît comme centrale pour aborder les phénomènes langagiers, le cadre ludique, fait justement pour manipuler les concepts primitifs qui la constituent, nous paraît singulièrement approprié. Une telle étude a été initiée dans un projet intitulé « Prélude » 3 dont l'objectif était de transposer des concepts qui ont récemment émergé en logique vers l'étude du langage et d'utiliser les outils novateurs de la ludique dans une perspective de formalisation de divers domaines du langage. À l'occasion de ce projet, plusieurs pistes ont été explorées et balisées : l'étude des dialogues (formalisation, « fallacies », étude de l'argumentation), pragmatique (actes de langage) [Fleury, Tronçon, à paraître ; Livet, à paraître], sémantique (nouvelle approche de la notion de forme logique) [Lecomte, Quatrini, 2009]. Nous présentons dans cet article une approche de la signification des énoncés basée sur les concepts de la Ludique.
International audienceLudics is a rebuilding of Linear Logic from the sole concept of interaction on objects called designs, that abstract proofs. Works have been done these last years to reconsider the formalization of Natural Language: a dialogue may be viewed as an interaction between such abstractions of proofs. We give a few examples taken from dialogue modeling but also from semantics or speech acts to support this approach
Proofs in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We shall follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a dialectical interaction. In this aim, we shall develop many concepts of Ludics like designs (which generalize proofs), cut-nets, orthogonality and behaviours (that is sets of designs which are equal to their bi-orthogonal). Behaviours give statements their interactive meaning. Such a conception may be viewed at the intersection between proof-theoretic and game-theoretical accounts of semantics, but it enlarges them by allowing to deal with possibly infinite processes instead of getting stuck to an atomic level when decomposing a formula.
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