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About: Neighborhood semantics     Goto   Sponge   NotDistinct   Permalink

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Neighborhood semantics, also known as Scott–Montague semantics, is a formal semantics for modal logics. It is a generalization, developed independently by Dana Scott and Richard Montague, of the more widely known relational semantics for modal logic. Whereas a relational frame consists of a set W of worlds (or states) and an accessibility relation R intended to indicate which worlds are alternatives to (or, accessible from) others, a neighborhood frame still has a set W of worlds, but has instead of an accessibility relation a neighborhood function where is the truth set of A.