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This exemplary volume shows how the shared interests of three different research areas can lead to significant and fruitful exchanges: six papers each very accessibly present an exciting contribution to the study and uses of algebras, diagrams, and decisions, ranging from indispensable overview papers about shared formal members to inspirational applications of formal tools to specific problems. Contributors include Pieter Adriaans, Sergei Artemov, Steven Givant, Edward Keenan, Almerindo Ojeda, Patrick Scotto di Luzio, and Edward Stabler.

From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space—the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the Geometry of Meaning provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded.

The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. Language and Grammar examines categorial grammars and type-logical grammars, two linguistic theories that play a significant role in this area of study yet have been overshadowed until recently. The prominent scholars contributing to this volume also explore the impact of the Lambek program on linguistics and logical grammar, producing, ultimately, an exciting and important resource that demonstrates how type-logical grammars are promising future models of reasoning and computation.

Mathematical Structures in Languages introduces a number of mathematical concepts that are of interest to the working linguist. The areas covered include basic set theory and logic, formal languages and automata, trees, partial orders, lattices, Boolean structure,  generalized quantifier theory, and linguistic invariants, the last drawing on Edward L. Keenan and Edward Stabler’s Bare Grammar: A Study of Language Invariants, also published by CSLI Publications. Ideal for advanced undergraduate and graduate students of linguistics, this book contains numerous exercises and will be a valuable resource for courses on mathematical topics in linguistics. The product of many years of teaching, Mathematic Structures in Languages is very much a book to be read and learned from.