We propose a system for the interpretation of anaphoric relationships between unbound pronouns and quantifiers. The main technical contribution of our proposal consists in combining generalized quantifiers ([26], [19], [2]) with dependent types ([23], [29], [20]). Empirically, our system allows a uniform treatment of the major types of unbound anaphora, with the anaphoric (dynamic) effects falling out naturally as a consequence of having generalized quantification on dependent types.
Keywords: scope ambiguity, continuation monad, strength In this paper, we will discuss three semantically distinct scope assignment strategies: traditional movement strategy, polyadic approach, and continuation-based approach. Since generalized quantifiers on a set X are elements of (X ), which is the value of the continuation monad on X , quantifier phrases are interpreted as -computations, in all three approaches. The main goal of this paper is to relate the three strategies to the computational machinery connected to the monad (strength and derived operations). As will be shown, both the polyadic approach and the continuation-based approach make heavy use of monad constructs. In the traditional movement strategy, monad constructs are not used but we still need them to explain how the three strategies are related and what can be expected of them with regard to handling scopal ambiguities in simple sentences. where there is one boy whom all the girls like. As the number of QPs in a sentence increases, the number of distinct readings also increases.
Classical scope-assignment strategies for multi-quantifier sentences involve quantifier phrase (QP)-movement (e.g., [13], [14]). More recent continuation-based approaches provide a compelling alternative, for they interpret QP's in situ -without resorting to Logical Forms or any structures beyond the overt syntax. The continuation-based strategies can be divided into two groups: those that locate the source of scope-ambiguity in the rules of semantic composition (e.g., [1]) and those that attribute it to the lexical entries for the quantifier words (e.g., [9], [2]). In this paper, we focus on the former operation-based approaches and the nature of the semantic operations involved. More specifically, we discuss three such possible operation-based strategies for multi-quantifier sentences, together with their relative merits and costs.
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