A (new) approach based on theory of hyperlattices applied to logical systems and probabilities

• Grant number: 24/18577-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2024
• End date: November 30, 2026
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Kaique Matias de Andrade Roberto
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 20/16353-3 - Rationality, logic, and probability: RatioLog, AP.TEM

Abstract

Algebraic hyperstructures are generalizations of the usual algebraic structures obtained from the generalization of the concept of algebraic operations. In particular, Sette and Morgado presented a generalized and quite intuitive definition of hyperlattice. There are numerous applications of hyperstructures such as semantics for logical systems, automata, cryptography, artificial intelligence, probabilities, and others. Thus, the main proposal of this project is to develop and apply, to logical systems and probabilities, results obtained in a theory of multialgebras based on the study of the definition of reticuloide (hyperlattice) presented by Morgado and studied by Sette.