Modal logic
Journal of Logic, Language and Information
Axiomatizing Hybrid Products of Monotone Neighborhood Frames
Electronic Notes in Theoretical Computer Science (ENTCS)
Generalized product of coalgebraic hybrid logics
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
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We consider the non-orthodox proof rules of hybrid logic from the viewpoint of topological semantics. Topological semantics is more general than Kripke semantics. We show that the hybrid proof rule BG is topologically not sound. Indeed, among all topological spaces the BG rule characterizes those that can be represented as a Kripke frame (i.e., the Alexandroff spaces). We also demonstrate that, when the BG rule is dropped and only the Name rule is kept, one can prove a general topological completeness result for hybrid logics axiomatized by pure formulas. Finally, we indicate some limitations of the topological expressive power of pure formulas. All results generalize to neighborhood frames.