Vagueness in Predicates and Objects
This addresses foundational issues in semantics and logic for researchers in linguistics and philosophy, but it appears incremental as it builds on classical semantics without claiming broad SOTA impact.
The paper tackles the problem of modeling reference, predication, and quantification in classical semantics, which assumes precise predicates and objects, by generalizing it to account for variability due to vagueness, context, and diversity. It presents Variable Reference Semantics, a framework that accommodates multiple modes of variability for both predicates and objects, without specifying concrete numerical results.
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.