2 research outputs found
Characterising Modal Definability of Team-Based Logics via the Universal Modality
We study model and frame definability of various modal logics. Let ML(A+)
denote the fragment of modal logic extended with the universal modality in
which the universal modality occurs only positively. We show that a class of
Kripke models is definable in ML(A+) if and only if the class is elementary and
closed under disjoint unions and surjective bisimulations. We also characterise
the definability of ML(A+) in the spirit of the well-known Goldblatt--Thomason
theorem. We show that an elementary class F of Kripke frames is definable in
ML(A+) if and only if F is closed under taking generated subframes and bounded
morphic images, and reflects ultrafilter extensions and finitely generated
subframes. In addition we study frame definability relative to finite
transitive frames and give an analogous characterisation of ML(A+)-definability
relative to finite transitive frames. Finally, we initiate the study of model
and frame definability in team-based logics. We study (extended) modal
dependence logic, (extended) modal inclusion logic, and modal team logic. We
establish strict linear hierarchies with respect to model definability and
frame definability, respectively. We show that, with respect to model and frame
definability, the before mentioned team-based logics, except modal dependence
logic, either coincide with ML(A+) or plain modal logic ML. Thus as a corollary
we obtain model theoretic characterisation of model and frame definability for
the team-based logics.Comment: 30 pages. This is a preprint of a journal article to appear in Annals
of Pure and Applied Logic. The preprint combines and extends two conference
papers arXiv:1502.07884v1 and arXiv:1606.05140. The title of this preprint is
changed to reflect thi
Probabilistic team semantics
Team semantics is a semantical framework for the study of dependence and
independence concepts ubiquitous in many areas such as databases and
statistics. In recent works team semantics has been generalised to accommodate
also multisets and probabilistic dependencies. In this article we study a
variant of probabilistic team semantics and relate this framework to a Tarskian
two-sorted logic. We also show that very simple quantifier-free formulae of our
logic give rise to NP-hard model checking problems