Paraconsistent set theory

• Grant number: 21/04883-0
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: July 01, 2023
• End date: August 31, 2024
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Aldo Figallo Orellano
• Grantee: Aldo Figallo Orellano
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Carles Noguera Clofent ; Carlos Caleiro ; Guillermo Badia ; Hugo Luiz Mariano ; Itala Maria Loffredo D'Ottaviano ; Lluis Godo ; Martín Figallo ; Petr Cintula ; Umberto Rivieccio
• Associated scholarship(s): 24/00683-5 - Dissemination of advances in paraconsistent logic and its applications, BP.JC; 24/05117-8 - Ehrenfeucht Fraïssé methods in model theory of F-structures, BP.DD; 24/00688-7 - Dissemination of advances in the area of paraconsistency and applications, BP.JC; 23/05914-2 - Paraconsistent set theory, BP.JP

Abstract

This project aims to develop the model theory of the models of Type ZF Paraconsistent Set Theory (PST) based on da Costa Logic Cw. Recently, we present F-structures valued models following the methodology developed for Heyting-valued models; with these models, we are able to prove the axioms of ZF are valid on them. The proof is strongly based on the existence of paraconsistent models ofLeibniz law; also, in this setting, we discuss the difficulty of having algebraic paraconsistent models of the law. As a principal main of this project, we pretend to present paraconsistent models forothers PSTs based on logics that can be expressed as extensions of classical logic of the literature, such us da Costa Cn and several of Logics of Formal Inconsistency that already have semantics by F-structures. Among the main objectives of this project, we plan to present independence proofs for PSTs and display paraconsistent models of ZFC following the methodology developed for Boolean-valued models. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIGALLO, A. V.; FIGALLO-ORELLANO, A.; FIGALLO, M.. Super-Lukasiewicz logics expanded by ⠂. FUZZY SETS AND SYSTEMS, v. 465, p. 26-pg., 2023-05-25. (21/04883-0, 22/03862-2)