Abstract
The research presented in this thesis follows the parsing as deduction approach to lin-
guistics. We use the tools of Categorial Type Logic (CTL) to study the interface of
natural language syntax and semantics. Our aim is to investigate the mathematical
structure of CTL and explore the possibilities it offers for analyzing natural
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language
structures and their interpretation.
The thesis is divided into three parts. Each of them has an introductory chapter.
In Chapter 1, we introduce the background assumptions of the categorial approach in
linguistics, and we sketch the developments that have led to the introduction of CTL.
We discuss the motivation for using logical methods in linguistic analysis. In Chapter 3,
we propose our view on the use of unary modalities as `logical features'. In Chapter 5,
we set up a general notion of grammatical composition taking into account the form
and the meaning dimensions of linguistic expressions. We develop a logical theory of
licensing and antilicensing relations that cross-cuts the form and meaning dimensions.
Throughout the thesis we focus attention on polarity. This term refers both to the
polarity of the logical operators of CTL and to the polarity items one finds in natural
language, which, furthermore, are closely connected to natural reasoning. Therefore,
the title of this thesis Reasoning with Polarity in Categorial Type Logic is intended to
express three meanings.
Firstly, we reason with the polarity of the logical operators of CTL and study their
derivability patterns. In Chapter 2, we explore the algebraic principles that govern
the behavior of the type-forming operations of the Lambek calculus. We extend the
categorial vocabulary with downward entailing unary operations obtaining the full tool-
kit that we use in the rest of the thesis. We employ unary operators to encode and
compute monotonicity information (Chapter 4), to account for the different ways of scope
taking of generalized quantifiers (Chapter 6), and to model licensing and antilicensing
relations (Chapter 7).
Secondly, in Chapter 4, we model natural reasoning inferences drawn from structures
suitable for negative polarity item occurrences. In particular, we describe a system
of inference based on CTL. By decorating functional types with unary operators we
encode the semantic distinction between upward and downward monotone functions.
Moreover, we study the advantages of this encoding by exploring the contribution of
v
monotone functions to the study of natural reasoning and to the analysis of the syntactic
distribution of negative polarity items.
Thirdly, in Chapter 7, we study the distribution of polarity-sensitive expressions. We
show how our theory of licensing and antilicensing relations successfully differentiates
between negative polarity items, which are `attracted' by their triggers, and positive
polarity items, which are `repelled' by them. We investigate these compatibility and
incompatibility relations from a cross-linguistic perspective, and show how we reduce
distributional differences between polarity-sensitive items in Dutch, Greek and Italian
to differences in the lexical type assignments of these languages.
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