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Axiomatization in the Meaning Sciences

Thomas Icard
Wesley H. Holliday
The Science of Meaning (ed. Ball & Rabern)

Abstract: While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality.