Elementary set theory accustoms the students to mathematical abstractionincludes the standard constructions of relations functions and orderings andleads to a d... » 

Elementary set theory accustoms the students to mathematical abstractionincludes the standard constructions of relations functions and orderings andleads to a discussion of the various orders of infinity. The material on logiccovers not only the standard statement logic and firstorder predicate logicbut includes an introduction to formal systems axiomatization and modeltheory. The section on algebra is presented with an emphasis on lattices aswell as Boolean and Heyting algebras. Background for recent research in naturallanguage semantics includes sections on lambdaabstraction and generalizedquantifiers. Chapters on automata theory and formal languages contain adiscussion of languages between contextfree and contextsensitive and form thebackground for much current work in syntactic theory and computationallinguistics. The many exercises not only reinforce basic skills but offer anentry to linguistic applications of mathematical concepts. For upperlevelundergraduate students and graduate students in theoretical linguisticscomputerscience students with interests in computational linguistics logicprogramming and artificial intelligence mathematicians and logicians withinterests in linguistics and the semantics of natural language. «