an:05296702
Zbl 1203.68206
Ognjanovi??, Zoran; Ikodinovi??, Neboj??a
A logic with higher order conditional probabilities
EN
Publ. Inst. Math., Nouv. S??r. 82(96), 141-154 (2007).
00222573
2007
j
68T37 68T27 03B48 03B70
probability logic; LCP
Authors' abstract: We investigate a probability logic with conditional probability operators. This logic, denoted LCP, allows making statements such as \(P_{\geq s}\alpha\), \(CP_{\geq s}(\alpha\mid\beta)\), \(CP_{\leq 0}(\alpha\mid\beta)\) with the intended meaning ``the probability of \(\alpha\) is at least \(s\)'', ``the conditional probability of \(\alpha\) given \(\beta\) is at least \(s\)'', ``the conditional probability of \(\alpha\) given \(\beta\) at most \(0\)''. A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: \(P(\alpha\mid\beta)=\frac{P(\alpha\wedge\beta)}{P(\beta)}\), \(P(\beta)>0\), by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. An infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.
Miodrag Ra??kovi?? (Beograd)