Kluwer Academic Publishers (2002)

Abstract
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.
Keywords Logic, Symbolic and mathematical  Type theory
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Call number QA9.A638 2002
ISBN(s) 1402007639   9781402007637
DOI 10.2307/2274454
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What Was the Syntax‐Semantics Debate in the Philosophy of Science About?Sebastian Lutz - 2017 - Philosophy and Phenomenological Research 95 (2):319-352.
Carnap’s Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
Higher Order Modal Logic.Reinhard Muskens - 2006 - In Patrick Blackburn, Johan Van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Elsevier. pp. 621-653.

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