Diagramatic Reasoning: contributions to modal logic

• Grant number: 12/09190-4
• Support Opportunities: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): August 01, 2012
• Effective date (End): July 31, 2015
• Field of knowledge: Humanities - Philosophy
• Principal Investigator: Lauro Frederico Barbosa da Silveira
• Grantee: Jorge Luiz Vargas Prudêncio de Barros Pires
• Host Institution: Faculdade de Filosofia e Ciências (FFC). Universidade Estadual Paulista (UNESP). Campus de Marília. Marília , SP, Brazil

Abstract

This project aims to accomplish a study on diagrammatic reasoning as proposed by Charles S. Peirce and its contributions to a modal logic that work effectively for the phenomenological representation of complex reality. The fundamental resources for the construction of a formal system with such features are available in his theory of Existential Graphs, which is divided into Alpha (Logic of Propositions), Beta (Logic of Predicates) and Gamma (Modal Logic). In order to achieve the purpose of this project, some challenges are to be overcome, such as comparing Peirce's Topological Theories to contemporary Topological Theories, specifying the Gama part of the Graphs for the study of Modalities, even in its temporal aspect, studying computability of the Gama part, analyzing the algorithmic complexity of the Graphs for optimal resolution of the logical-topological relations of Modalities, developing a software that allows detailed manipulation of the Graphs in all of their parts, and reproducing and interiorizing into the Graphs all that Peirce and other logicians and scholars have already developed formally, as well as apply this to the relations analysis of real systems, in order to evaluate its representative and operational capacity. Collaborating in the development of such a logical-mathematical system is an urgent task, given the formal qualities and potentialities it presents. Deducing diagrams more in tune with reality will make it possible to assess more appropriately its phenomenological relevance. Should such relevance be confirmed, one will have a tool of immense value for the representation and diagnosis of the state of the environment in its evolutionary potential.