Typed Dynamic Logic for Compositional Grammar

The history of formal semantics started with Montague (1970a, 1973). It is claimed therein that syntax and semantics of English can be formulated as a theory of a formal language in which syntax and model-theoretic semantics have a clear correspondence with each other. One of the key concepts of Montague grammar is compositionality, which states that the meaning of a sentence can be calculated by Intensional Logic (IL) from the meanings of its parts, in other words, from those of words. However, as the study of formal semantics has matured, many phenomena which IL cannot properly describe have been found, such as generalized quantifiers, plurality, and discourse structure. Formal semantics in the 1980s have given expanded theories of IL to deal with them. However, it seemed to be difficult to give a compositional theory which explains the phenomena of E-type anaphora, which was given in Evans (1977, 1980), although non-compositional theories such as DRT in Kamp (1981) and Kamp and Reyle (1993) can deal with them. Groenendijk and Stokhof (1991) presented Dynamic Predicate Logic (DPL) that can handle E-type anaphora in singular forms in a compositional way. However, the original E-type paradigms in Evans (1980) are more complex phenomena which contain a plural pronoun that refers to a generalized quantifier as its antecedent. Under those circumstances, this thesis suggests a new logical language, Typed Dynamic Logic (TDL) as the semantic theory. TDL is based on typed lambda calculus, and defines contexts as sets of assignment functions, and propositions as functions from contexts to contexts. The idea unites Predicate Logic for Plurals in van den Berg (1990) and the socalled functional style of DPL, and serves as both a theory of plurality and a theory of E-type anaphora without raising its order twice. Moreover, we claim that cumulative readings and E-type readings are the default readings for quantifiers and anaphora, by introducing a mechanism of delayed quantification. We demonstrate that distributive readings and bound variable readings are derived from them by means of the distributor. This thesis also presents linear derivation as a new syntactic theory, based on the type checking of TDL. Grammaticality of a sentence is defined by the concept of derivation from a linear structure of phonemes (or characters) to a linear structure of lambda terms, which is mediated by functional applications within the linear structures. Moreover, we define the lexicon also as a collection of derivation rules, which gives a compositional solution without relying on type flexibility or Quantifier Raising, to a problem of generalized quantifiers in non-subject position, which has been long problematic to the theory of types. Furthermore, we propose a mechanism of case assignment by postulating empty prepositions. This thesis thus presents a new framework of the theory of grammar as a combination of the syntactic theory based on linear derivation, and the semantic theory based on TDL. This gives compositional explanations to many phenomena that have been regarded as evidence of the existence of a syntactic component in the language faculty independent of semantic one.