Topics in modal quantification theory

Author(s)

Felipe de Souza Salvatore

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH/SBD)
• Defense date: 2015-08-21

Examining board members

Rodrigo Bacellar da Costa e Silva; Marcelo Finger; David Gilbert; Edelcio Gonçalves de Souza

• Advisor: Rodrigo Bacellar da Costa e Silva

Abstract

The modal logic S5 gives us a simple technical tool to analyze some main notions from philosophy (e.g. metaphysical necessity and epistemological concepts such as knowledge and belief). Although S5 can be axiomatized by some simple rules, this logic shows some puzzling properties. For example, an interpolation result holds for the propositional version, but this same result fails when we add first-order quantifiers to this logic. In this dissertation, we study the failure of the Definability and Interpolation Theorems for first-order S5. At the same time, we combine the results of justification logic and we investigate the quantified justification counterpart of S5 (first-order JT45). In this way we explore the relationship between justification logic and modal logic to see if justification logic can contribute to the literature concerning the restoration of the Interpolation Theorem. (AU)

• FAPESP's process: 12/24619-7 - Topics in Modal Quantification Theory
• Grantee: Felipe de Souza Salvatore
• Support Opportunities: Scholarships in Brazil - Master