Probability Measures in Gödel\(_\varDelta \) Logic
In this paper we define and axiomatise finitely additive probability measures for events described by formulas in Gödel\(_\varDelta \) (G\(_\varDelta \)) propositional logic. In particular we show that our axioms fully characterise finitely additive probability measures over the free finitely generated algebras in the variety constituting the algebraic semantics of G\(_\varDelta \) as integrals of elements of those algebras (represented canonically as algebras of [0, 1]-valued functions), with respect to Borel probability measures.
KeywordsProbability measures in non-classical logics Gödel propositional logic Gödel\(_\varDelta \) propositional logic Free algebras
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