Locativity and Interaction in Logic, Linguistics and Computer Sciences – LOCI

We develop a proof theory methodology which makes the role of interaction to appear (between proofs and counter-proofs). The notion of normalisation of a net of paraproofs provides a model for the study of dialogue.

Argumentation Modelling
analysis of epistemic modalities
lexicon and context
Dialogue Modelling

philosophical researches (Plato's dialogues)

Christophe Fouqueré et Myriam Quatrini,«Un cadre formel issu de la théorie de la démonstration pour la théorie de l'argumentation«, Mathématiques et Sciences humaines, vol. 198, pp. 49-84, 2012,
Christophe Fouqueré et Myriam Quatrini,``Argumentation Modeling in Ludics'' 8th international symposium of Cognition, Logic and Communication, Riga, Latvia 18-20 mai 2012

This project follows a previous one which was funded by ANR (programme BLANC) from 2006 to 2009, PRELUDE : towards theoretical pragmatics based on ludics and the theory of continuations. The PRELUDE program has permitted :
- to make new propositions for the calculus of symbolic representations of discourse, by the use of continuation theories, and particularly of the symmetric calculi invented for dealing with these computer sciences concepts : lambda-mu-calculus, lambda-mu-tilde-mu-calculus of, respectively, M. Parigot and P-Y. Curien and H. Herbelin,
- to explore the possibilities of ludics (a frame invented by J-Y. Girard) to go further by means of tools which allow to represent not only discourse but dialogue, not only according to a static view but also to a dynamic one.
In this new project, we plan both to begin work on extensions of existing concepts of ludics, and conduct research on formal concepts which seem best suited to the representation of processes and their interaction in humanities (language, social, learning practices), including coherence spaces, links to the categories and the place of the first order.
Ludics is in constant development, and new tools such as Terui's computational designs (which extend the possibilities offered by both Girard's designs and the lambda-terms), or the latest version of Girard's Geometry of Interaction allow us to hope to overcome the difficulties encountered to date. Together, the semantic notions emerged in the computer and logical field (coherence semantics, braiding of categorical models with first order, theory of types with records) opens up new opportunities.
In particular, questions put aside like lexical semantics or the possibility to reformulate R. Kempson's dynamic syntax may now be taken into consideration.
We finally look at specific frameworks : the acquisition of sign language introduces a bias that we seek to analyze through in vivo experiments, web communication is a closed frame (data are fully available) where we can more effectively realize the relevance of the approach.
To sum up, we propose to develop, in the line of PRELUDE, new tools and new logical approaches for studying languages and connected domains starting from the very innovative concepts which emerged recently in mathematical logic.
The LOCI project is essentially theoretic but it also opens perspectives for more practical realisations, like programs for detecting and analysing interaction strategies (as they occur in learning of Sign languages for instance), building ontologies for the web (cf. (cf. Abrusci et al. 09), even the elaboration of programming languages for the web (Fouqueré 08). It puts a bridge in between human sciences and some of the sharpest researches in Logic and in Mathematics of nowadays (Geometry of Interaction, von Neumann algebras).