 The same basic language as was used for the basic finite probability logic need not change, but the semantics is slightly different: for every state \(w\in W\), the component \(\mathcal{P}_w\) of a modal probabilistic model is replaced by an entire probability space \((\Omega_w,\mathcal{A}_w,\mu_w)\), such that \(\Omega_w\subseteq W\) and \(\mathcal{A}_w\) is a \(\sigma\)-algebra over \(\Omega_w\). The reason we may want entire spaces to differ from one world to another is to reflect uncertainty about what probability space is the right one. For the semantics of probability formulas, \((M,w)\models P(\phi) \ge q\) if and only if \(\mu_w(\{w'\mid (M,w')\models \phi\})\ge q\). Such a definition is not well defined in the event that \(\{w'\mid (M,w')\models \phi\}\not\in \mathcal{A}_w\). Thus constraints are often placed on the models to ensure that such sets are always in the \(\sigma\)-algebras.