Читать книгу Formal Semantics in Modern Type Theories - Stergios Chatzikyriakidis - Страница 10

Since its development in the late 1960s and early 1970s, Montague semantics (Montague 1974) has been the dominant approach to formal semantics. There are several textbooks about Montague semantics including, for example, that by Dowty et al. (1981). As explained above, Montague has introduced an intermediate language, called Intensional Logic (IL), for his model-theoretic semantics. For instance, to interpret the sentence in (1.1), we could first give its interpretation (1.2) in IL, where the semantics of John is an entity j and the semantic interpretation talk of the verb “talk” is a predicate over entities of the world, which can be applied to j to form the interpretation (1.2):

(1.1) John talks.

(1.2) talk(j)

This then gives the set-theoretical interpretation of (1.1), i.e. the interpretation of (1.2) in set theory (according to, for example, Henkin’s model interpretation), which says that the set-theoretic interpretation of j is a member of the set that interprets the predicate talk.

In what follows, we shall first describe simple type theory⁶ and then how it is used in Montague semantics.