Geodesic
A Propositional p-adic Probability Logic
Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 75 .

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We present the $p$-adic probability logic $LpPP$ based on the paper \cite{5} of A. Khrennikov et al. The logical language contains formulas such as $P_{=s}(\alpha)$ with the intended meaning ``the probability of $\alpha$ is equal to $s$", where $\alpha$ is a propositional formula. We introduce a class of Kripke-like models that combine properties of the usual Kripke models and finitely additive $p$-adic probabilities. We propose an infinitary axiom system and prove that it is sound and strongly complete with respect to the considered class of models. In the paper the terms finitary and infinitary concern the meta language only, i.e., the logical language is countable, formulas are finite, while only proofs are allowed to be infinite. We analyze decidability of $LpPP$ and provide a procedure which decides satisfiability of a given probability formula.
Classification : 03B48 03B42 03B45 
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     author = {Milo\v{s} Milo\v{s}evi\'c},
     title = {A {Propositional} p-adic {Probability} {Logic}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {75 },
     publisher = {mathdoc},
     volume = {_N_S_87},
     number = {101},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a4/}
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Miloš Milošević. A Propositional p-adic Probability Logic. Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 75 . http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a4/