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 Schütze 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 Schütze,
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