## A zero-layer based fuzzy probabilistic logic for conditional probability.(English)Zbl 1109.03018

Godo, Lluís (ed.), Symbolic and quantitative approaches to reasoning with uncertainty. 8th European conference, ECSQARU 2005, Barcelona, Spain, July 6–8, 2005. Proceedings. Berlin: Springer (ISBN 3-540-27326-3/pbk). Lecture Notes in Computer Science 3571. Lecture Notes in Artificial Intelligence, 714-725 (2005).
Summary: This paper is devoted to a logical and algebraic treatment of conditional probability. Unlike other approaches to this problem, we base our work on the notion of zero-layer. Thus we define the fuzzy modal logic $$FP _{k}(R\text{Ł}_{\Delta})$$ with $$k$$ modalities for non-conditional probability, built up over the many-valued logic $$R \text{Ł}_\Delta$$ (obtained by adding to the Rational Łukasiewicz logic the Baaz connective $$\Delta$$). 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 $$FP_{k}(R\text{Ł}_\Delta)$$.
For the entire collection see [Zbl 1076.68008].

### MSC:

 03B48 Probability and inductive logic 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness 68T37 Reasoning under uncertainty in the context of artificial intelligence
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