The importance of being discrete

The paper discusses discrete frames as an attractive semantics for modal logic. We study questions of completeness, persistence and definability. We prove that notions of completeness, strong completeness and strong global completeness coincide for discrete frames; moreover, they turn out to be equivalent to conservativity of minimal hybrid extensions. This characterization allows us to identify an incomplete normal modal logic with a complete minimal hybrid extension. The paper also provides some criteria of di-persistence and a GoldblattThomason theorem for discrete frames.

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