Towards a More Robust Theory of Swap Structures

• Grant number: 25/22258-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2026
• End date: December 31, 2026
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Felipe Nunes de Souza Camargo
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Non-Deterministic Matrices are structures that generalize the usual Logical Matrices and allow the application of unique and finite matrices to a much wider class of propositional logics. Still, those matrices do not provide several useful resources for combining logics characterized by them. Beyond that, the several values that they include, manipulated by hyperalgebraic operators, are sometimes hard to interpret and deal with. Swap Structures, on the other hand, represent the values of a Non-Deterministic Matrix as combinations of boolean values. This allows for a straightforward way of combining those logics. They also express the hyperalgebraic operations in a more informative manner with respect to the required interpretation and, in some cases, make them much easier to deal with. However, Swap Structures have still been underexplored and have a narrow range of applications, at least when compared to their potential. The research proposed in this project aims to analyze possible alternatives for expanding the scope of applications of Swap Structures and their combinations by presenting some original contributions and laying the groundwork for future studies. This will be done by the study of the relevant bibliography and discussion with other researchers in the field. The main expected results are the production of a monograph and the sharing of the research through seminars at congresses and research groups. (AU)