An Introduction To Mathematical Logic And Type Theory: To Truth Through Proof (computer Science And Applied Mathematics)
by Peter B. Andrews /
1986 / English / DjVu
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over 50 students, please contact
In case you are considering to adopt this book for courses with
over 50 students, please [email protected]
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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.
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:
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.
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.