The field of vector semantics refers to the study of representing and understanding the meaning of words and phrases using mathematical vectors

This book is a direct continuation of (Kornai, 2019), but unlike its predecessor, it is no

longer a textbook. The earlier volume, henceforth abbreviated S19, mostly covered material

that is well known in the field, whereas the current volume is a research monograph,

dominated by the author's own research centering on the 4lang system.

S19 attempted to cater to students of four disciplines, linguistics; computer science;

cognitive science; and philosophy. As Hinrich Schze wrote at the time: "This textbook

distinguishes itself from other books on semantics by its interdisciplinarity: it presents

the perspectives of linguistics, computer science, philosophy and cognitive science. I

expect big changes in the field in coming years, so that a broad coverage of foundations

is the right approach to equipping students with the knowledge they need to tackle

semantics now and in the future."

The big changes were actually already under way, in no small part due to Schze,

1993, who took the fundamental step in modeling word meaning by vectors in ordinary

Euclidean space. S19:2.7 discusses some of the mathematical underpinnings. This

material is now standard, so much so that the main natural language processing (NLP)

textbook, Jurafsky and Martin (2022) is already incorporating it in its new edition (our

references will be to this new version). But for now, vectorial semantics has relatively

few contact points with mainstream linguistic semantics, so little that the most comprehensive

(five volumes) contemporary summary, Gutzmann et al. (2021), has not devoted

a single chapter to the subject. Sixty years ago, McCarthy (1963) urged:

Mathematical linguists are making a serious mistake in their concentration on

syntax and, even more specially, on the grammar of natural languages. It is even

more important to develop a mathematical understanding and a formalization of

the kinds of information conveyed in natural language