The tableaux method applied to a quasi-modulated logic for the quantifier "few"

• Grant number: 12/10272-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2012
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Luiz Henrique da Cruz Silvestrini
• Grantee: Helen Gomes da Silva
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The use of alternative deductive methods to the axiomatic method has been of great interest to the Proof Theory and the Theory of Computation, the latter being characterized, for example, by searching for suitable methods for implementation on computers. Among these methods, we emphasize the method of analytic tableaux introduced by Smullyan in 1968. The logical systems in tableaux have been extensively explored in the literature, especially for the modulated logics, which are obtained from first order classical logic with the addition of a generalized quantifier in its language, governed by a specific set of axioms. These generalized quantifiers are called modulated quantifiers and capture notions of 'many', 'most' and 'almost everywhere', for example. In 2011, Oliveira introduced the logic of the few, inspired by a dualization to a modulated logic that formalizes the quantifier 'many' of natural language. thus, in this research project, we propose to compare the axiomatic method to the method of analytic tableaux and we put forward a non-classical first order logic, namely the logic of the few, in a system of analytic tableaux. (AU)