A zero-layer based fuzzy probabilistic logic for conditional probability

Authors:
Tommaso Flaminio
Affiliations:
Department of Mathematics and Computer Science, University of Siena, Siena, Italy
Venue:
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2005

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Abstract

This paper is devoted to a logical and algebraic treatment of conditional probability. Unlike the other approaches to this problem (cf [7],[10]) we base our work on the notion of zero-layer (cf [4]). Thus we define the fuzzy modal logic FPk(RŁΔ) with k modalities for non-conditional probably, built up over the many-valued logic RŁΔ (obtained by adding to the Rational Łukasiewicz logic the Baaz connective Δ). The main result of this paper tells us that it is possible to characterize the coherence of an assessment of conditional probability by the consistence of a suitable theory over FPk(RŁΔ).