Paraconsistent Dynamic Epistemic Logic: puzzles about inconsistent knowledge and information

• Grant number: 25/01892-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Walter Alexandre Carnielli
• Grantee: Rafael dos Santos Ongaratto
• Supervisor: Hans Van Ditmarsch
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Institut De Recherche En Informatique De Toulouse, France
• Associated to the scholarship: 24/00807-6 - Solving Puzzles and Reframing Paradoxes: an investigation in non-classical logics, BP.DR

Abstract

If we think in terms of truth, paraconsistency rivals classical logic, by introducing a third truth value. However, the brazillian school of paraconsistent logic, conceived in the works of Walter Carnielli and Marcelo Coniglio, has a desideratum of thinking about paraconsistency in terms of information instead of truth, that is, Logics of Formal Inconsistency, the logics developed in this tradition, are supposed to represent preservation of (possibly conflicting) information. In that vein, we propose making paraconsistent puzzles based on an epistemic interpretation of paraconsistency, that is, thinking in terms of information. When applying this to real-world problems, however, limitations begin to appear: paraconsistent logics such as LFI1 are able to represent a static informational state that is impersonal: it doesn't say anything about the knowledge of multiple agents, nor it can represent updates in information. These two features can be successfully incorporated to logic if we consider dynamic epistemic logic, which are logics that deal with update and transformation of the knowledge of multiple agents. Therefore, what we propose is, firstly, to develop paraconsistent dynamic epistemic logics based on LFIs. Our final objective is to produce and solve paraconsistent puzzles based on this dynamic epistemic logic. A paraconsistent version of Public Announcement Logic, the standard dynamic epistemic logic, is also interesting for its own sake: if we are restricted to classical logic, we can only know sets of consistent statements. However, if we are in a paraconsistent logic, there are situations in which a agent may know an inconsistent set of sentences. For example, we can say that we know the naive theory of truth, even though this theory is inconsistent, in some weaker usage of "knowledge". The development of dynamic versions of LFIs also contributes to the epistemic interpretation of paraconsistency.