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Logic TK: Algebraic Notions from Tarski’s Consequence Operator

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Author(s): Hércules A. Feitosa | Mauri C. do Nascimento | Maria Claudia C. Grácio

Journal: Principia : an International Journal of Epistemology
ISSN 1414-4247

Volume: 14;
Issue: 1;
Start page: 47;
Date: 2010;
Original page

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.
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