Probability logics with vector-valued measures


Probability logic introduced by this paper is based on probability logic $L_{\bbA P}$. Measure ranges in probability models will not be linearly ordered, more precisely, measures will be vector--valued, having ranges $ \mathbb{Q}^{n} \cap { [ 0,1 ]}^{n}$. Axioms and rules of inference are adjusted to determine these types of measures. The completeness theorem for the introduced logic is proved.