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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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