Periodic Reporting for period 3 - CoSaQ (Cognitive Semantics and Quantities)
Reporting period: 2020-02-01 to 2021-07-31
Numerical information plays a central role in communication. We talk about the number of students in a class or the proportion of votes for a particular political party. In this project, we will focus on the linguistic expressions concerning quantities, known as quantifiers. Recent progress in the study of computational constraints on quantifier processing in natural language has laid the groundwork for extending semantic theory with cognitive aspects. In parallel, cognitive science has furthered the study of non-linguistic quantity representations. The project integrates formal models of quantifier semantics with cognitive representations to answer a number of questions in linguistics and cognitive science, e.g. how do learn the meaning of quantifiers? how do we decide the truth-values of quantifier sentences? etc.
One of the domains we have focused on is color terms. We know that languages differ significantly in what colors they lexicalize. In other words, different languages categorize the color spectrum in different ways. But all languages’ color terms form ’curving-out’, convex, regions of color space. A color category is convex if and only if we select two points within C and draw a line in between them, then all the points on the line will also belong to C. In this sense, nC and nC+ are not convex. Quite opposite, they are concave, see Figure 1a. In order to test the hypothesis that convex color systems are easier to learn than non-convex ones, we generated a large number of artificial color systems within the psychophysiological model of human color perception. The color systems varied in the extent to which they satisfied convexity (intuitively nC is more convex than nC+)1. To measure how learnable each color system is, we trained an artificial computational model, a neural network to learn each system. The accuracy of the neural network learning to name colors was positively correlated with the degree of convexity, see Fig. 2. Therefore, learnability explains convexity universal.
We see similar results in different domains, e.g. modal verbs and quantifiers. The resulting package can be impressionistically described as follows, see Fig. 3, one can imagine a kind of heat map overlaid on the space of possible meanings, with redder shades meaning easier to learn and bluer shades meaning harder to learn. In other words, the claim is, that language learners are attracted to warmer regions on the map. The computational simulations are an argument that individual minds may be better at acquiring meanings satisfying certain universal constraints (attracted to hot regions).