In this paper we define and axiomatise finitely additive probability measures for events described by formulas in Godel_Delta (G_Delta) 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_Delta as integrals of elements of those algebras (represented canonically as algebras of [0, 1]-valued functions), with respect to Borel probability measures.
Probability Measures in Godel Delta Logic / S. Aguzzoli, M. Bianchi, B. Gerla, D. Valota (LECTURE NOTES IN ARTIFICIAL INTELLIGENCE). - In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty / [a cura di] A. Antonucci, L. Cholvy, O. Papini. - Prima edizione. - [s.l] : Springer International Publishing, 2017. - ISBN 9783319615813. - pp. 353-363 (( convegno ECSQARU tenutosi a Lugano nel 2017 [10.1007/978-3-319-61581-3_32].
Probability Measures in Godel Delta Logic
S. Aguzzoli;M. Bianchi;D. Valota
2017
Abstract
In this paper we define and axiomatise finitely additive probability measures for events described by formulas in Godel_Delta (G_Delta) 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_Delta as 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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