Vers une pragmatique théorique basée sur la ludique et les continuations

Symmetric calculi and Ludics for the semantic interpretation

Purpose and topics

In recent years there have been some important new developments in methods of dealing with semantic and pragmatic phenomena in Linguistics, inspired by developments in Logic and Theoretical Computer Science. Among these developments, Continuation Theory, Symmetric calculi and Ludics play an important role. Continuation theory dates back from the early seventies (cf. Reynolds, 93) and was at the heart of Programming Languages like Scheme. More recently, a logical account was given to it, by extending the Curry-Howard homomorphism (Griffin, 1990),. This led to several calculi like such as Parigot’s lambda-mu-calculus, Curien-Herbelin’s lambda-mu-mu-tilde-calculus, Wadler’s dual calculus and so on. These calculi are based on the core idea that programs and contexts are dual entities and this is reflected in the symmetry of the “classical” sequents. These systems were prefigured by the so called Lambek-Grishin calculus (Grishin, 83), a calculus extending the Lambek calculus by taking classical sequents into account.

Classical linear logic (Girard, 87, 95) gives another viewpoint, where the co-product is realized by an authentic parallelisation connective. Linguistic applications have been given since around 2000, particularly by C. Barker (Barker, 2000), Ken Chung-chieh Shan (Chung-chieh Shan, 2002) and P. de Groote (de Groote, 2001) who exploited the advantages of these systems in the task of giving several readings of an ambiguous sentence. De Groote (de Groote, 2007) also shows that we gain a new dynamical logic which enables us to elegantly treat phenomena of discourse like anaphora resolution. M. Moortgat and R. Bernardi (Moortgat \& Bernardi, 2007) use the Lambek-Grishin system as a way to avoid structural modalities by means of the Grishin postulates, which make product and co-product interact. Independently, linear logic was intensively studied in particular by Girard himself who invented “Ludics” as a new conception of logic, where the dualism between syntax and semantics is abolished : the meaning of rules is in the rules themselves. This conception has some similarities with more traditional “Game Semantics” (Lorenz, Lorenzen, Hintikka…) but it is dynamic, in the sense that “strategies” are replaced by interacting processes. Moreover, a new step in abstraction is provided, which consists in stating rule schemata which are only expressed in terms of loci (that we may see as memory cells).

The two approaches in this workshop are connected, basically because of their common root : explorations in the meaning of Logics and in particular reflections on one of the symmetrical systems : linear logic. Linguistic applications of Ludics remain very embryonic, but some authors have already emphasized that it is suitable for giving a framework in which it is possible to study speech acts and dialogue (Livet, 2007, Tronçon, 2006). Other authors have pointed out similarities of the Ludics’ philosophy with Wittgenstein’s views on language games (Pietarinen, 2006). This workshop will provide an opportunity to study these questions. It will accept several kinds of contributions : theoretical works on continuation theory, symmetric calculi and ludics, applied works of these theory concerning linguistic topics (semantics, pragmatics) and philosophical investigations.

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