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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.
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.
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