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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.

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