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Some considerations on the logics $$P_ FD$$. A logic combining modality and probability. (English) Zbl 0885.03022
The logic $$P_FD$$, introduced by M. Fattorosi-Barnaba and G. Amati [Stud. Log. 46, 383-393 (1987; Zbl 0645.03016)], based on the propositional language enriched with a family of modal (probability) operators enabling to express the statement that “the probability of a formula is greater than $$r(\in[0,1])$$”, presents an extension of classical propositional calculus by axioms concerning those probability operators. In this paper, a Kripke-type semantics for $$P_FD$$ is developed, including the completeness result, followed by the finite model property and decidability of $$P_FD$$ by using the filtration technique. At the end of the paper some interesting conclusions and alternatives for further research are considered.

##### MSC:
 03B48 Probability and inductive logic 03C80 Logic with extra quantifiers and operators 03B45 Modal logic (including the logic of norms)
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