A Quantitative-Informational Approach to Logical Consequence

• Autor(a) principal: Alves, Marcos Antonio [UNESP]
• Data de Publicação: 2015
• Outros Autores: Loffredo D’Ottaviano, Itala M.
• Tipo de documento: Capítulo de livro
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/978-3-319-15368-1_3; http://hdl.handle.net/11449/205139
• topic: Information; Informational logical consequence; Logical consequence; Nonclassical logics; Paraconsistent logic; Probability; Semantics

In this chapter, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon’s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity of information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results; among them certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence.