Tableaux method and the relevance logic

• Grant number: 16/07446-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2016
• End date: April 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Luiz Henrique da Cruz Silvestrini
• Grantee: Luis Felipe Salvador Boato
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

In this work, we intend to present a non-classical paraconsistent logic through an alternative to the axiomatic deductive method (Hilbert). In this case, we are emphasizing the tableaux deductive method. We develop a tableaux analytical system for the Relevance Logic RM introduced in 1975 by Anderson and Belnap from the axiomatic system presented by Middelburg in 2011, that is, for the Hilbert-style deductive system RM3. We show the equivalence between the relevance logic in an axiomatic version and in tableaux systems. From this equivalence, we also proved the soundness and completeness properties in this new deductive method. (AU)