"In case you are considering to adopt this book for courses with
over 50 students, please contact ""[email protected]"" for
more information. "
This introduction to mathematical logic starts with propositional
calculus and first-order logic. Topics covered include syntax,
semantics, soundness, completeness, independence, normal forms,
vertical paths through negation normal formulas, compactness,
Smullyan's Unifying Principle, natural deduction, cut-elimination,
semantic tableaux, Skolemization, Herbrand's Theorem, unification,
duality, interpolation, and definability.
The last three chapters of the book provide an introduction to
type theory (higher-order logic). It is shown how various
mathematical concepts can be formalized in this very expressive
formal language. This expressive notation facilitates proofs of the
classical incompleteness and undecidability theorems which are very
elegant and easy to understand. The discussion of semantics makes
clear the important distinction between standard and nonstandard
models which is so important in understanding puzzling phenomena
such as the incompleteness theorems and Skolem's Paradox about
countable models of set theory.
Some of the numerous exercises require giving formal proofs. A
computer program called ETPS which is available from the web
facilitates doing and checking such exercises.
"Audience: " This volume will be of interest to mathematicians,
computer scientists, and philosophers in universities, as well as
to computer scientists in industry who wish to use higher-order
logic for hardware and software specification and verification.
"
General
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