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Topological perspective on the hybrid proof rules. (English) Zbl 1278.03051
Blackburn, Patrick (ed.) et al., Proceedings of the international workshop on hybrid logic (HyLo 2006), Seattle, WA, USA, August 11, 2006. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 174, No. 6, 79-94 (2007).
Summary: 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.
For the entire collection see [Zbl 1273.68016].

03B45 Modal logic (including the logic of norms)
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