Degrees of the Finite Model Property for Superintuitionistic and Modal Logics

ABSTRACT

In this talk, I will introduce a new notion of the degree of the finite model property (the degree of FMP) for superintuitionistic and modal logics. This notion resembles that of the degree of incompleteness of modal logics introduced by Fine (1974). In particular, two logics have the same degree of FMP if the classes of their finite frames coincide. I will show that, in contrast with the famous Blok dichotomy theorem, any countable cardinal, as well as the continuum, can be realized as the degree of FMP for some superintuitionistic and transitive modal logic. This provides a solution of a variant of the long-standing open problem when the degree of incompleteness is replaced by the degree of FMP. This is joint work with Guram Bezhanishvili and Tommaso Moraschini.

SHORT BIO:
(taken from the University of Helsinki)

Nick Bezhanishvili obtained his PhD in 2006 from the ILLC (Institute for Logic, Language and Computation), University of Amsterdam, under the supervision of Professors Dick de Jongh and Yde Venema. He held postdoctoral positions at the University of Leicester (2006–2008), Imperial College London (2008–2012), and Utrecht University (2012–2013). Since 2014, Nick holds an Assistant Professorship at the ILLC. He has more than 70 publications in the top journals, refereed conference proceedings, and book chapters in his area of research, which is centered on applications of algebraic and topological methods in the study of non-classical logics (such as modal and intuitionistic logics). An important feature of this work is the theory of Stone-like dualities, which gives rise to topological and geometric semantics for intuitionistic and modal logics.

Picture: University of Amsterdam