Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

The topic of temporal meaning in texts has received considerable attention in recent years from scholars in linguistics, logical semantics, cognitive science, and artificial intelligence. Representing Time in Natural Language offers a systematic and detailed account of how we use temporal information contained in a text or in discourse to reason about the flow of time, inferring the order in which events happened when this is not explicitly stated. A new representational system is designed to formalize an appropriately context-dependent notion of situated inference. The Dynamic Aspect Tree, representing temporal dependencies, constitutes a novel and important dynamic temporal logic, one that makes it easy to see "what follows when" from the information given in an ordinary English text.