Cognitive Semantics and Quantities

At the heart of the multi-faceted enterprise of formal semantics lies a simple yet powerful conception of meaning based on truth conditions: one understands a sentence if one knows under which circumstances the sentence is true. This notion has been extremely fruitful, resulting in a wealth of theoretical insights and practical applications. But to what extent can it also account for human linguistic behavior? The past decade has seen increasing interaction between cognitive science and formal semantics and the emergence of the new field of experimental semantics. One of its main challenges is the traditional normative take on meaning, which makes semantic theories hard to compare with experimental data. This project aims to advance experimental semantics by building computational cognitive models of meaning.

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 we learn the meaning of quantifiers? how do we decide the truth values of quantifier sentences? why do we have specific quantifiers and not others? Etc.

The project's results fall naturally into two different, however related, research lines. The first line is mostly concerned with how people represent quantifier meanings. The project's second focus is why people only represent a small subset of all logically possible quantifiers.

1. Formal semantics, the theory of linguistic meaning founded on logic, has been a success story leading to much progress in linguistics, philosophy, and related disciplines. The intense interaction between formal semantics and cognitive science has recently led to the creation of a new field of experimental semantics1. With the move of formal semantics from the proverbial armchair to the lab, it has become apparent that the traditional conception of meaning, formulated in terms of logical truth conditions, may be too rigid to account for the wealth of actual data. One pressing issue is the relation between meaning and other aspects of cognition, e.g. available cognitive strategies. We have shown that the methodology and concepts taken from experimental psychology of individual differences and decision-making prove useful in answering such questions. To integrate individual differences in meaning representations, we have proposed a new theory of semantic representations and implemented it in several cognitive computational models that can explain a wealth of psycholinguistics data.

Figure 1: Ramotowska and colleagues, using various technics of computational cognitive modeling, have demonstrated in many experiments that individual differences exist in how people represent quantifier meaning. The figure shows that various participants (grey lines) assign various thresholds for different quantifier concepts. While some participants think that, for instance, "most" means "more than 50%", others would assign it a higher threshold of around 60%. Such findings go against rigid definitions of meaning found in logical semantics, e.g. identifying meanings of "most" and "more than half."

2. There are roughly 7000 languages spoken in the world. At first glance, the world's natural languages exhibit tremendous differences. After all, learning a second language as an adult is not an easy task. Yet, linguistics teaches us that languages also share tremendous amounts of structure. Thus arises one of the central questions in linguistic theory: What is the range of variation in human languages? That is: which out of all of the logically possible languages that humans could speak do they, in fact, speak? A limitation on the range of possible variations will be a property that all (or at least almost all) languages share. Such a property will be a linguistic universal. Universals have been discovered at all levels of linguistic analysis: phonology, morphology, syntax, and semantics. For example, all languages have consonants and vowels, nouns and verbs, etc. Whenever a universal is attested, it is natural to ask for an explanation of its source. Why does the universal hold? Many theorists search for cognitive explanations of universals. Such an explanation would locate the existence of universal in a feature of the human mind with which language must interface. Our group has developed computational explanations of the constraint cross-linguistic variation in terms of learnability, evolution, complexity, and communicative efficiency.

Figure 2: Semantic universals are properties of meaning shared by the world's languages. Steinert-Threlkeld & Szymanik explained the presence of such universals by measuring simplicity in terms of ease of learning. They showed that expressions satisfying universals are simpler than those that do not. They measured the ease of learning using machine learning tools and analyzed universals in function words (quantifiers) and content words (color terms). The results prove that semantic universals across both function and content words reflect simplicity as measured by ease of learning. The figure shows that a neural network learning a new artificial color categorization struggles more when color categories are less convex (not geometrically well-behaved). Convexity has been proposed as a universal constraint on color (and not only) meaning across languages.

We have proved that the formal semantics, computational linguistics, and cognitive science methods can be fruitfully combined to understand how linguistic meaning is represented and provide a cognitive computational explanation for the universal properties across languages.

Periodic Reporting for period 4 - CoSaQ (Cognitive Semantics and Quantities)

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