The propositional logic of 'almost always' in tableaux

• Grant number: 12/00284-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2012
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Hércules de Araújo Feitosa
• Grantee: Felipe Augusto Aureliano
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

In his master's degree essay entitled "About quantifiers: a formalization of the quantifier 'almost always' ", Rodrigues (2011) introduces a logic to deal with the concept of 'almost always', as well as done in the Logic of the Ultrafilter. The Logic of the Ultrafilter was develop by Sette, Carnielli and Veloso (1999) in order to capture formally the notions of 'almost always' or 'almost all', through the addition of a generalized quantifier in the classical language of first order. The central aim of this work is to study the propositional logic of 'almost always', introduced by Rodrigues (2011) and denoted by L(<), from the point of view of the modal logic and tableaux. For this we need to understand the methods of the tableaux and also the algebraic approach in which the logic L(<) was presented. Next, we intend to demonstrate the deductive equivalence between the propositional logic of 'almost always' in the axiomatic version in which was introduced and in the version in tableaux that should be presented in this work. (AU)