Normal Modal Logics Determined by Aligned Clusters
Zofia Kostrzycka,Yutaka Miyazaki +1 more
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TLDR
It is proved that the cardinality of the logics from NExt(KTB) which are determined by linear frames with reflexive and symmetry relation of accessibility is uncountably infinite.Abstract:
We consider the family of logics from NExt(KTB) which are determined by linear frames with reflexive and symmetric relation of accessibility. The condition of linearity in such frames was first defined in the paper [9]. We prove that the cardinality of the logics under consideration is uncountably infinite.read more
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Interpolation in Normal Extensions of the Brouwer Logic
TL;DR: In this article, the Brouwer interpolation property was considered for a special kind of normal extensions of the brouwer logic for deducibility, and the interpolation properties were considered for the special case of the case of a special case.
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On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames
TL;DR: In this article, the authors define Halldén complete modal logics, which are defined semantically and have a nice characterization as they are determined by homogeneous Kripke frames.
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On non‐compact logics in NEXT(KTB)
TL;DR: In this paper, a continuum of logics, extensions of the modal logic T2 = KTB ⊕ □2p □3p are constructed, which are non-compact (relative to Kripke frames) and henceKripke incomplete.