A. IlićStepić, Z. Ognjanović, N. Ikodinovć, A. PerovićA $p$adic probability logicAbstract
We present some logics for reasoning about $p$adic probability. These logics enriches propositional calculus with the operators: $K_{r,\rho}\alpha$,
$CK_{r,\rho}\alpha,\beta$ and
$D_{\rho}\alpha,\beta$
with the intended meaning: ``the probability of $\alpha$
belongs to the padic ball with the center $r$ and the radius $\rho$", "the conditional probability of $\alpha$ given $\beta$ is in the padic ball
with the center $r$ and the radius $\rho$" and
"the $p$adic distance
between the probabilities of $\alpha$ and $\beta$ is less than or equal to $\rho$", respectively.
We give a sound and complete infinitary axiomatic system for our logics and the decidability of
the satisfiability problem for each logic is proved. One of the possible applications of these logic is presented here.
