Logics of formal inconsistency with replacement: An algebraic and proof-theoretic study

• Grant number: 24/13413-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2025
• End date: October 31, 2027
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Hector Federico Mallea
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The present work focuses on the study and development of logics of formal inconsistency(LFIs) with replacement, primarily from an algebraic perspective, while also addressing issues related to proof theory. It is divided into three main research axes, each one addressingtheoretical and practical aspects of these logics with the aim of advancing in their understanding and potential applications.The first axis focuses on an in-depth study of Boolean algebras with LFI operators (BALFIs), where congruences will be analyzed and characterized, obtaining from this a classification of BALFIs; investigation into a possible topological duality will be conducted,and a combinatorial study of finite BALFIs will be realized. Additionally, their reducts will be compared with those of Boolean algebras, leading to the emergence of new algebraic structures.The second axis deals with the decidability of LFIs with replacement. Here, the decidability problem and the finite model property of LFIs with replacement will be investigated; sequent calculi and natural deduction systems, as well as tableaux systems will be developed, to approach decidability from different perspectives.The third axis focuses on the study of LFIs with an intuitionistic basis, i.e., investigatingLFIs starting from positive intuitionistic logic. The idea is adding replacement to these systems, extending so the scope of LFIs to a broader logical framework.To summarize, this work seeks to advance the understanding and development of LFIswith replacement, addressing algebraic aspects, decidability, and potential applications indifferent contexts. (AU)