Search

In this study, we investigate the mental representation of non-numerical quantifiers ("some", "many", "all", etc.) by comparing their use in abstract and in grounded perceptual contexts. Using an approach similar to that used in the number domain, we test whether (and to what extent) such representation is constrained by the way we perceive the world through our senses. In two experiments, subjects either judged the similarity of quantifier pairs (presented as written words) or chose among a predetermined list of quantifiers the one that best described a visual image depicting a variable number of target and non-target items. The results were rather consistent across experiments, and indicated that quantifiers are mentally organized on an ordered but non-linear compressed scale where the quantifiers that imply small quantities appear more precisely differentiated across each other compared to those implying large quantities. This fits nicely with the idea that we construct our representations of such symbols mainly by mapping them to the representations of quantities that we derive from perception., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Logical negation is a challenge for distributional semantics, because predicates and their negations tend to occur in very similar contexts, and consequently their distributional vectors are very similar. Indeed, it is not even clear what properties a "negated" distributional vector should possess. However, when linguistic negation is considered in its actual discourse usage, it often performs a role that is quite different from straightforward logical negation. If someone states, in the middle of a conversation, that "This is not a dog," the negation strongly suggests a restricted set of alternative predicates that might hold true of the object being talked about. In particular, other canids and middle-sized mammals are plausible alternatives, birds are less likely, skyscrapers and other large buildings virtually impossible. Conversational negation acts like a graded similarity function, of the sort that distributional semantics might be good at capturing. In this article, we introduce a large data set of alternative plausibility ratings for conversationally negated nominal predicates, and we show that simple similarity in distributional semantic space provides an excellent fit to subject data. On the one hand, this fills a gap in the literature on conversational negation, proposing distributional semantics as the right tool to make explicit predictions about potential alternatives of negated predicates. On the other hand, the results suggest that negation, when addressed from a broader pragmatic perspective, far from being a nuisance, is an ideal application domain for distributional semantic methods. [ABSTRACT FROM AUTHOR]

Abstract: Categorial grammars in the tradition of Lambek are asymmetric: sequent statements are of the form , where the succedent is a single formula A, the antecedent a structured configuration of formulas . The absence of structural context in the succedent makes the analysis of a number of phenomena in natural language semantics problematic. A case in point is scope construal: the different possibilities to build an interpretation for sentences containing generalized quantifiers and related expressions. In this paper, we explore a symmetric version of categorial grammar, based on work by Grishin . In addition to the Lambek product, left and right division, we consider a dual family of type-forming operations: coproduct, left and right difference. Communication between the two families is established by means of structure-preserving distributivity principles. We call the resulting system LG. We present a Curry-Howard interpretation for LG derivations, based on Curien and Herbelin’s lambda mu comu calculus. We discuss continuation-passing-style (CPS) translations mapping LG derivations to proofs/terms of Intuitionistic Multiplicative Linear Logic — the categorial system LP which serves as the logic for natural language meaning assembly. We show how LG, thus interpreted, associates sentences with quantifier phrases with the appropriate range of meanings, thus overcoming the expressive limitations of asymmetric categorial grammars in this area. [Copyright &y& Elsevier]

In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discourse level comes into play for our treatment of questions. Our formalisation uses a type logic sensitive to both the syntactic and semantic properties of natural language. We will show how an account of the linguistic data follows naturally from the logical relations inherent in the type logic. [ABSTRACT FROM PUBLISHER]