Logic TK: Algebraic Notions from Tarski’s Consequence Operator
Keywords:Tarski space, almost topological space, consequence operator, modal logic, algebraic model.
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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