Connecting Content and Logical Words

Abstract

Content words (e.g. nouns and adjectives) are generally connected: there are no gaps in their denotations; no noun means ‘table or shoe’ or ‘animal or house’. We explore a formulation of connectedness which is applicable to content and logical words alike, and which compares well with the classic notion of monotonicity for quantifiers. On a first inspection, logical words satisfy this generalized version of the connectedness property at least as well as content words do — that is, both in terms of what may be observed in the lexicons of natural languages (although our investigations remain modest in that respect) and in terms of acquisition biases (with an artificial rule learning experiment). This reduces the putative differences between content and logical words, as well as the associated challenges that these differences would pose, e.g., for learners.

Numerals under negation: Empirical findings

“…Originally connectedness and convexity were hypothesized to be constraints on the meaning of content words such as nouns and adjectives. But recently, Chemla et al (2019) propose that the notion of connectedness can be extended to function words as well, in particular quantifiers, where it can be related to the well-known property of monotonicity (Barwise & Cooper 1981). They demonstrate that in an artificial quantifier learning task, the connectedness of a rule facilitates its acquisition, a finding that makes this a possible candidate for a semantic universal.…”

“…an odd/even number of). With regards to disjunction, Chemla et al (2019) observe that to ensure that convexity is preserved for the disjunction of two quantifiers would require one of them to necessarily be trivial, rendering the entire disjunction useless. Disjunction thus emerges as a natural way of expressing non-convex meanings.…”

Constraints on the lexicons of human languages have cognitive roots present in baboons ( Papio papio )

“…Recently, Chemla et al (4) have generalized the notion of connectedness from the domain of content words (in which the relevant notion of betweenness is often difficult to specify; see ref. 5) to the domain of logical words, specifically, quantifiers (in which a precise, canonical notion of betweenness naturally arises based on the mathematical subset relation between sets).…”

“…6 for a survey). Furthermore, Chemla et al (4) show that humans have corresponding learning biases favoring connected quantifiers, as evidenced by performance on rule learning, or pattern extraction, tasks: It is easier to discover connected rules than nonconnected ones, and easier still to discover monotone ones.…”

“…A natural hypothesis is that the source of the regularity of the world's lexicons, for both content and logical words, is a learning bias for connectedness. Indeed, Chemla et al (4) argue that their experimental results with humans support this Significance Universals in language are hard to come by, yet one candidate is that words across the lexicons of the world's languages are, by and large, connected: When a word applies to two objects, it also applies to any objects "between" those two. A natural hypothesis is that the source of this regularity is a learning bias for connected patterns, a hypothesis supported by recent experimental studies.…”