an:06360934
Zbl 1433.03062
Ili??-Stepi??, Angelina; Ognjanovi??, Zoran; Ikodinovi??, Neboj??a
Conditional \(p\)-adic probability logic
EN
Int. J. Approx. Reasoning 55, No. 9, 1843-1865 (2014).
00337441
2014
j
03B48 03B25 68T27
\(p\)-adic; conditional probability
Summary: In this paper we present the proof-theoretical approach to \(p\)-adic valued conditional probabilistic logics. We introduce two such logics denoted by \(\mathrm{CPL}_{\mathbf{Z}_{\mathbf{p}}}\) and \(\mathrm{CPL}_{\mathbf{Q}_{\mathbf{p}}}^{\mathrm{fin}}\). Each of these logics extends classical propositional logic with a list of binary (conditional probability) operators. Formulas are interpreted in Kripke-like models that are based on \(p\)-adic probability spaces. Axiomatic systems with infinitary rules of inference are given and proved to be sound and strongly complete. The decidability of the satisfiability problem for each logic is proved.