Technical Report PHD-2007-13

Title: Types and Meanings in Intensionality, Selection and Quantifier Scope
Authors: Gilad Ben-Avi
Supervisors: Yoad Winter
Abstract: This thesis consists of three independent contributions to the formal semantics of natural languages.

The first contribution, titled "Intensionalization", introduces a procedure that takes a simple version of extensional semantics and generates from it an equivalent possible-world semantics that is suitable for treating intensional phenomena in natural language. This process of intensionalization allows to treat intensional phenomena as stemming exclusively from the lexical meaning of words like "believe", "need" or "fake". We illustrate the proposed intensionalization technique using an extensional toy fragment. This fragment is used to show that independently motivated extensional mechanisms for scope shifting and verb-object composition, once properly intensionalized, are strictly speaking responsible for certain intensional effects, including de dicto/de re ambiguities and coordinations containing intensional transitive verbs. While such extensional intensional relations have often been assumed in the literature, the chapter offers a formal sense for this claim, facilitating the dissociation between extensional semantics and intensional semantics.

The second contribution, titled "Categorial Grammar with Ontology-Refined Types", presents a calculus for type-logical grammars that enables the treatment of semantic selectional restriction like in "John painted the house" vs. the semantically odd sentence "John painted the idea". We use an ontology of a join semi-lattice structure to refine semantic types in the standard associative Lambek calculus with meaning representations. The ontological elements as decoration of types represent relevant semantic properties of natural language expressions. Functional application in the calculus is defined so as to respect these decorations of types. This enables the definition of grammars in which both sentences "John painted the house" and "John painted the idea" are syntactically derivable, but only the former is assigned a meaning representation.

In the third contribution, we characterize the pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1-V-NP2. Simple numerical or set-theoretical considerations that follow from the main result in the chapter are used for characterizing such relations. The variety of examples in which they hold are shown to go far beyond the familiar existential-universal type.

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