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Purpose and topics - Rencontres - Symmetric calculi and Ludics for the semantic interpretation - ANR-PRELUDE
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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