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This book is a direct continuation of (Kornai, 2019), but unlike its predecessor, it is nolonger a textbook. The earlier volume, henceforth abbreviated S19, mostly covered materialthat 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 textbookdistinguishes itself from other books on semantics by its interdisciplinarity: it presentsthe perspectives of linguistics, computer science, philosophy and cognitive science. Iexpect big changes in the field in coming years, so that a broad coverage of foundationsis the right approach to equipping students with the knowledge they need to tacklesemantics 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 ordinaryEuclidean space. S19:2.7 discusses some of the mathematical underpinnings. Thismaterial 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 (ourreferences will be to this new version). But for now, vectorial semantics has relativelyfew contact points with mainstream linguistic semantics, so little that the most comprehensive(five volumes) contemporary summary, Gutzmann et al. (2021), has not devoteda single chapter to the subject. Sixty years ago, McCarthy (1963) urged:Mathematical linguists are making a serious mistake in their concentration onsyntax and, even more specially, on the grammar of natural languages. It is evenmore important to develop a mathematical understanding and a formalization ofthe kinds of information conveyed in natural language
