Kluwer Academic Publishers (2002)
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|
|Categories||categorize this paper)|
|Buy the book||$57.94 used (66% off) $118.00 new (31% off) $131.72 direct from Amazon (23% off) Amazon page|
|Call number||QA9.A638 2002|
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Citations of this work BETA
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Supra-Logic: Using Transfinite Type Theory with Type Variables for Paraconsistency.Jørgen Villadsen - 2005 - Journal of Applied Non-Classical Logics 15 (1):45-58.
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 Metatheory: Scope and Limits.Georg Schiemer, Richard Zach & Erich Reck - 2017 - Synthese 194 (1):33-65.
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