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Continuation Semantics for Multi-Quantifier Sentences : Operation-Based Approaches

Grudzińska Justyna, Zawadowski Marek

Fundamenta Informaticae

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2019

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Vol. 164, nr 4

327--344

EN

Classical scope-assignment strategies for multi-quantifier sentences involve quantifier phrase (QP)-movement (e.g., [11], [12]). More recent continuation-based approaches provide a compelling alternative, for they interpret QPs 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., [2], [8]). 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.

2

A proof-theoretic approach to scope ambiguity in compositional vector space models

Wijnholds G. J.

Journal of Language Modelling

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2018

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Vol. 6, No. 2

261--286

EN

We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form Every man loves some woman). Such sentences containing two quantifiers introduce two readings, a direct scope reading and an inverse scope reading. This ambiguity has been treated in a vector space model using bialgebras by Hedges and Sadrzadeh (2016) and Sadrzadeh (2016), though without an explanation of the mechanism by which the ambiguity arises. We combine a polarised focussed sequent calculus for the non-associative Lambek calculus NL, as described in Moortgat and Moot (2011), with the vector-based approach to quantifier scope ambiguity. In particular, we establish a procedure for obtaining a vector space model for quantifier scope ambiguity in a derivational way.

3

Scope ambiguities, monads and strengths

Grudzińska J., Zawadowski M.

Journal of Language Modelling

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2017

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Vol. 5, No. 2

179--227

EN

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 C(X), which is the value of the continuation monad C on X, quantifier phrases are interpreted as C-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 C (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.