Rationality, logic, and probability: RatioLog

• Grant number: 20/16353-3
• Support Opportunities: Research Projects - Thematic Grants
• Start date: February 01, 2023
• End date: January 31, 2028
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Marcelo Esteban Coniglio
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais:( Atuais ): Walter Alexandre Carnielli
• Pesquisadores principais:( Anteriores ): Marcelo Esteban Coniglio
• Associated researchers: Abilio Azambuja Rodrigues Filho ; Carlile Campos Lavor ; Fábio Maia Bertato ; Francesc Esteva ; Henrique Antunes Almeida ; Juan Carlos Agudelo Agudelo ; Juliana Bueno ; Julio Michael Stern ; Lluis Godo ; Mariana Matulovic da Silva Rodrigueiro ; Newton Marques Peron ; Rodolfo Cristian Ertola Biraben ; Tommaso Flaminio
• Associated scholarship(s): 24/18577-7 - A (new) approach based on theory of hyperlattices applied to logical systems and probabilities, BP.PD; 24/07687-6 - Non-Conventional Probability Theories, their importance and applications, BE.PQ

Abstract

The present research project consists of three large interrelated spheres, called `tasks'. These three tasks will support the main issues to be addressed, related to the notions of consistency, contradiction and evidence, which, together with their probabilistic interpretations, aim at reaching a more solid position on the general philosophy of paraconsistency, its understanding, its impact and its importance in the philosophy of science and in the philosophy of mathematics. Task I: Evidence, Probability and Logic intends to investigate probabilistic and possibilistic semantics, emphasizing some specially designed new logical systems, including the generalization of such ideas towards plausibility measures (\cite{fried-halpner:1995}) and (\cite{halpern:2001}). Task II: Non-Deterministic Methods: Hyperalgebraic Structures, Modalities, and Extensions of Probabilities aims to develop and apply results obtained from a multialgebra theory to specific logical systems and to the theory of probabilities;Task III: Contradictions, Evidence and Truth: Towards a Global Philosophy of Paraconsistency seeks to investigate technical and philosophical aspects of an epistemic approach to paraconsistency. The three tasks will support the general objectives of the present project, which are the study of the various aspects of formal rationality, logic and probability with special emphasis on new methods of algebra, semantics and probability theory, involving expansions of standard logic systems to non-classical logics. (AU)