Formal approaches to modality
Stefan Kaufmann, Cleo Condoravdi, Valentina Harizanov · 2006
Modal notions are pervasive in the meaning of a wide range of expressions from grammatical categories, such as tenses, to the lexical semantics of particular words, such as modal adverbials (probably, necessarily) and modal auxiliaries (must, may, can). The best known modalities are the alethic 1 modalities necessary and possible. Other modalities include temporal, deontic, epistemic, and doxastic ones, and modalities pertaining to disposition, ability, provability, mood, aspect, and so on. Temporal modalities deal with time. Deontic 2 modalities deal with obligation and permission. Epistemic 3 modalities deal with knowledge, and doxastic 4 modalities deal with belief. Although modals have been thoroughly studied since Aristotle, the formal theory of modality was revolutionized in the 1960’s with the introduction of the possible world semantics by Hintikka and Kripke. In our formal approach to the semantic analysis of modal expressions, we will employ the model-theoretic apparatus of modal logic. In modal logic, modals correspond to sentential operators, whose semantic role is to