On the logic and arithmetics of relations

• Grant number: 09/00533-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2009
• End date: March 31, 2013
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Leandro Oliva Suguitani
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In 1975, Alfred Tarski visited Unicamp and delivered two lectures on his axiomatization of relation algebra, which is a product of the relational calculus originaly developed by De Morgan, Peirce and Schroder. In our Master dissertation we transcribed the lectures and revisited some of the problems left by Tarski at that time, tracing a line of the development on their results in the literature. Currently, relational formalisms have been extensively applied in computer science, also being of theoretical interests in logic and mathematics. In this work, we explore the logic and arithmetics of relations, introducing some formal systems which are adequate to investigate the expressive power and proof power that relations may offer. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SUGUITANI, Leandro Oliva. On the logic and arithmetic of relations. 2013. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.