This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this notion are shown: for compactness and definability theorems. We also use ultravaluations to check failure of compactness and undefinability.

The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent... knows/beliefs that...’. The second one is to define tableau systemsfor such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker (...) logics in order to avoid the well known problem of logical omniscience. At the same time, we keep the positional counterparts of modal axioms, and. For all of the considered logics we present sound and complete tableau systems. (shrink)

This note provides a review of the book 'On the Sea-Battle Tomorrow That May Not Happen' by Tomasz Jarmużek.