Abstract
In this paper we define and axiomatise finitely additive probability measures for events described by formulas in GödelΔ(GΔ) propositional logic. In particular we show that our axioms fully characterise finitely additive probabilitymeasures over the free finitely generated algebras in the variety constituting the algebraic semantics of GΔas integrals of elements of those algebras (represented canonically as algebras of [0, 1]-valued functions), with respect to Borel probability measures.
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Aguzzoli, S., Bianchi, M., Gerla, B., & Valota, D. (2017). Probability measures in GödelΔ logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10369 LNAI, pp. 353–363). Springer Verlag. https://doi.org/10.1007/978-3-319-61581-3_32
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