Conditional p-adic probability logic

•We presented two p-adic valued conditional probabilistic logics.•Formulas are interpreted in Kripke-like models.•Axiomatic systems are given and proved to be sound and strongly complete.•The decidability of the satisfiability problem for each logic is proved.

In this paper we present the proof-theoretical approach to p  -adic valued conditional probabilistic logics. We introduce two such logics denoted by CPLZpCPLZp and CPLQpfin. 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.