Logic TK: Algebraic Notions from Tarski’s Consequence Operator

Hércules A. Feitosa; Mauri C. do Nascimento; Maria Claudia C. Grácio

doi:10.5007/1808-1711.2010v14n1p47

Logic TK: Algebraic Notions from Tarski’s Consequence Operator

Authors

Hércules A. Feitosa São Pauko State University – UNESP/FC
Mauri C. do Nascimento São Pauko State University - UNESP/FC
Maria Claudia C. Grácio São Pauko State University - UNESP/FC

DOI:

https://doi.org/10.5007/1808-1711.2010v14n1p47

Keywords:

Tarski space, almost topological space, consequence operator, modal logic, algebraic model.

Abstract

Tarski presented his definition of consequence operator to explain the most important notions which any logical consequence concept must contemplate. A Tarski space is a pair constituted by a nonempty set and a consequence operator. This structure characterizes an almost topological space. This paper presents an algebraic view of the Tarski spaces and introduces a modal propositional logic which has as a model exactly the closed sets of a Tarski space.