# zbMATH — the first resource for mathematics

Characterizing frame definability in team semantics via the universal modality. (English) Zbl 06484974
Paiva, Valeria (ed.) et al., Logic, language, information, and computation. 22nd international workshop, WoLLIC 2015, Bloomington, IN, USA, July 20–23, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-47708-3/pbk; 978-3-662-47709-0/ebook). Lecture Notes in Computer Science 9160, 140-155 (2015).
Summary: Let $$\mathcal{MC}(\square u^+)$$ denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the definability of $$\mathcal{MC}(\square u^+)$$ in the spirit of the well-known Goldblatt-Thomason theorem. We show that an elementary class $${\mathbb {F}}$$ of Kripke frames is definable in $$\mathcal{MC}(\square u^+)$$ if and only if $${\mathbb {F}}$$ is closed under taking generated subframes and bounded morphic images, and reflects ultrafilter extensions and finitely generated subframes. In addition, we initiate the study of modal frame definability in team-based logics. We show that, with respect to frame definability, the logics $$\mathcal{MC}(\square u^+)$$, modal logic with intuitionistic disjunction, and (extended) modal dependence logic all coincide. Thus, we obtain Goldblatt-Thomason-style theorems for each of the logics listed above.
For the entire collection see [Zbl 1319.03010].

##### MSC:
 03B70 Logic in computer science
Full Text: