A Modal Logic of a Truth Definition for Finite Models^*

Issue title: Bridging Logic, Philosophy, Computer and Cognitive Science: in the Memory of Marcin Mostowski (1955-2017)

Guest editors: Nina Gierasimczuka and Jakub Szymanikb

Article type: Research Article

Authors: Czarnecki, Marek^{c; †} | Zdanowski, Konrad^d

Correspondence: [†] Address for correspondence: Institute of Philosophy, University of Warsaw, Krakowskie Przedmieście 3, 00-047 Warsaw, Poland

Note: [*] This work was supported by the Polish National Science Centre grant number 2013/11/B/HS1/04168.

Abstract: The property of being true in almost all finite, initial segments of the standard model of arithmetic is ∑20 –complete. Thus, it admits a kind of a truth definition. We define such an arithmetical predicate. Then, we define its modal logic SL and prove a completeness theorem with respect to finite models semantics. The proof that SL is the modal logic of the approximate truth definition for finite arithmetical models is based on an extension of SL by a fixed-point construction.

Keywords: finite models, truth definition, modal logic

DOI: 10.3233/FI-2019-1770

Journal: Fundamenta Informaticae, vol. 164, no. 4, pp. 299-325, 2019