Non-deterministic semantics for modal logics

• Grant number: 22/16816-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2023
• Status: Discontinued
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Mahan Vaz Silva
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The project aims to develop non-deterministic semantics for modal logics, expanding the recently developed swap structures by Coniglio , inspired by the works of Kearns, Ivlev and Avron and Lev . We want to work with logics that are able to adequately deal with situations presented by Belnap and Dunn , where we can have evidences for the falsity and truth of a certain statement and want to assign a truth-value for such statement based upon the evidences we have. This motivation is also supported by scenarios where paradoxes are taken into account as testing grounds for these logics. Our final goal is threefolded: to develop non-deterministic semantics and to combine modal operators using Nmatrices and swap structures, aiming to draw answers to paradoxes; to develop swap structure semantics for Ivlev-like modal logics, and to combine these semantics with Kripke models; to apply and implement algorithms to deal with inconsistent data bases, based upon decision methods developed for the logics and semantics proposed.