In 1992, Moss and Parikh introduced Toplogic an epistemic modal logic whose semanticas are based on subsets. Since then, research on this logic and it many extensions has been going strong. I will survey most of these results in the first part of this talk. On the second part, I will present how topologic can form a basis for the formalization of belief change operators, such as update, conditionals and contraction. Arbitrary nestings and iterations of such operators are easily automatized which is not the case in other studies of belief change in object language.

There will be a meeting of this seminar on October 18 from 2 to 4 PM in room 4419.  Haim Gaifman (Columbia) and Rohit Parikh (CUNY) will speak.  Details will be announced next week.

This is a meeting of a joint CUNY-Columbia research group on Logic, Probability and Games.

Description: This workshop is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The workshop is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the workshop and distinguished guest speakers and are held alternatively at Columbia University and CUNY Graduate Center.

Schroedinger’s and Turing’s analyses of life phenomena have a twofold aspects. They both follow, first, a “coding paradigm”, of embryogenesis or of human computations and deductions respectively, and then move towards a more “dynamicist” approach. Schroedinger, in the second part of his 1944 book, hints to biological organization as negentropy – a variant of Gibbs dynamical analysis of energy – that we revitalized as anti-entropy, see references. Turing, after stressing that “the nervous system is surely not a Discrete State machine” (1950), invents the mathematics for an action/reaction/diffusion process, a “continuous system” (1952), where chemical matter (an hardware with no software) organizes itself along morphogenesis.
We will hint to the paths for thought opened by Turing’s dynamics as continuous deformations at the core of Turing’s pioneering paper of 1952, where symmetry breakings are a key component of the bio-chemical processes.

References
Schrödinger, E. What Is Life?, Cambridge University Press, 1944.
Alan M. Turing, “On Computable Numbers with an Application to the Entscheidungsproblem”, Proc. London Math. Soc. 42, 230-265, 1936.
Alan M. Turing, “The Chemical Basis of Morphogenesis”, Philo. Trans. Royal Soc., B237, 37-72, 1952.
Francis Bailly, Giuseppe Longo. Mathematics and Natural Sciences : the Physical Singularity of Life, Imperial College Press, London, 2011.
Giuseppe Longo, Maël Montévil, Perspectives on Organisms: Biological Time, Symmetries and Singularities, Springer, 2013.

Papers in http://www.di.ens.fr/users/longo:
Giuseppe Longo, “From exact sciences to life phenomena: following Schrödinger and Turing on Programs, Life and Causality”. Information and Computation, 207, 5: 543-670, 2009.
Francis Bailly, Giuseppe Longo. Biological Organization and Anti-Entropy. In J. Biological Systems, Vol. 17, No. 1, pp. 63-96, 2009.
Giuseppe Longo. Incomputability in Physics and Biology. Invited Lecture, Proceedings of Computability in Europe, Azores, Pt, June 30 – July 4, LNCS 6158, Springer, 2010.
Longo G., P. A. Miquel, C. Sonnenschein, A. Soto. Is Information a proper observable for biological organization? Progress in Biophysics and Molecular Biology, Vol. 109, Issue 3, pp. 108-114, August 2012.