Lieu: Amphi Inria, Bât B avenue Héloïse à Villeneuve d’Ascq (en attente de confirmation)
Nous avons le plaisir de vous annoncer une séance exceptionnelle du séminaire « Histoire et Philosophie de l’informatique », vendredi 27 octobre à 14h00 à 15h30 Amphi Inria, Bât B avenue Héloïse à Villeneuve d’Ascq (en attente de confirmation). Cette séance est co-organisée avec CRISTaL et INRIA Lille et fait partie du Colloquium Polaris.
Wilfried Sieg (Carnegie Mellon, Etats-Unis), What is the concept of computation?
The Church-Turing Thesis asserts that particular mathematical notions are adequate to represent informal notions of effective calculability or mechanical decidability. I first sketch contexts that called for such adequate mathematical notions, namely, problems in mathematics (e.g., Hilbert’s 10th problem), decision problems in logic (e.g., the Entscheidungsproblem for firs-torder logic), and the precise characterization of formality (for the general formulation of Gödel’s incompleteness theorems). The classical approach to the effective calculability of number theoretic functions led, through Gödel and Church, to a notion of computability in logical calculi and metamathematical absoluteness theorems. The classical approach to the mechanical decidability of problems concerning syntactic configurations led, through Turing and Post, to a notion of computability in formal calculi (canonical systems) and metamathematical representation theorems.
Particular features of formal calculi motivate the formulation of an abstract concept of a computable dynamical system. This concept articulates finiteness and locality conditions that are satisfied by the standard concrete notions of computation. A representation theorem can be established: Turing machines can simulate the computations of any concrete system falling under the abstract concept. I sketch a generalization of this approach to obtain computable parallel dynamical systems. Some applications will conclude my discussion.
Prof Wilfried Sieg is professor at the Carnegie Mellon University
His research in mathematical logic is broadly concerned with the Foundations of Mathematics and focuses in particular on proof theoretic investigations. It is complemented by work in the History of Modern Logic & Mathematics and in the Philosophy of Mathematics. The historical research has led to participation in editorial projects, which have helped to shed a new and distinctive light on the development of logic in the first half of the 20th century; these projects concern Paul Bernays, David Hilbert and Kurt Gödel.
In 1996, he founded the Laboratory for Symbolic & Educational Computing (LSEC) and have been directing it since that time, first with Richard Scheines as co-director and since 2005 with Teddy Seidenfeld as co-director.