Classical semantics assumes that one can model reference, predication and quantification with respect to a fixed domain of precise referent objects. Non-logical terms and quantification are then interpreted directly in terms of elements and subsets of this domain. We explore ways to generalise this classical picture of precise predicates and objects to account for variability of meaning due to factors such as vagueness, context and diversity of definitions or opinions. Both names and predicative expressions can be given either multiple semantic referents or be associated with semantic referents that incorporate some model of variability. We present a semantic framework, Variable Reference Semantics, that can accommodate several modes of variability in relation to both predicates and objects.
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