Citation
James J. Tyhurst. 1990. “Logical Forms for English Sentences”. Ph.D. dissertation at the University of California, Los Angeles.
References
PDF document: JimTyhurst-1990-Dissertation-Logical_Forms.pdf
Abstract
This dissertation investigates the relationship between syntactic structure and semantic interpretation. The goal of this study is to develop an explicit model of the mapping from surface syntactic forms to a level of Logical Form (LF) and finally to truth values. The mapping from surface structure to LF is done within the framework of the Government and Binding (GB) theory of grammar. A computationally tractable interpretation algorithm is then given for mapping logical forms onto truth values within an extensional model-theory semantics.
The interaction between quantifiers and Boolean operators is used as a diagnostic for the types of structures implicitly required for correct semantic interpretation of English sentences. Most current work on LF assumes that logical forms are ambiguous with regard to quantifier scope. However, two such analyses (May 1985, Aoun and Li 1989) are shown to give incorrect predictions of scope interactions when sentences with more than two quantifiers are considered. An alternative model within the GB framework is proposed in which surface structures are mapped onto unambiguous logical forms. In addition to providing a correct description of complex operator interactions, this approach has the advantage that entailment may be defined at the level of LF.
The algorithm for interpreting logical forms is based on work in generalized quantifiers (Barwise and Cooper 1981, Keenan and Stavi 1986). There are two important results of this algorithm. First, an explicit interpretation is provided for verb phrase (VP) adjunction. Such structures have been assumed in the GB literature, although a method has never been given for interpreting them. Second, the use of generalized quantifiers allows one to provide a uniform interpretation for a wide range of determiners, including those which are not first-order definable (e.g. ‘most’) and those constructed from Boolean combinations of determiners (e.g. ‘some but not all’, ‘at least six but not more than twelve’).
After considering generalized quantifiers, an analysis is given of referentially dependent noun phrases, such as reciprocals (e.g. “each other”, “each other’s children”), which inherently require a higher-order analysis. It is shown that these noun phrases may be grouped into four semantic classes which correlate with differences in syntactic distribution.