Abstract
The chapter surveys several important theoretical results in first-order logic. In Sect. 12.1 we prove that validity in first-order logic is undecidable, a result first proved by Alonzo Church. Validity is decidable for several classes of formulas defined by syntactic restrictions on their form (Sect. 12.2). Next, we introduce model theory (Sect. 12.3): the fact that a semantic tableau has a countable number of nodes leads to some interesting results. Finally, Sect. 12.4 contains an overview of Gödel’s surprising incompleteness result.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B. Dreben and W.D. Goldfarb. The Decision Problem: Solvable Classes of Quantificational Formulas. Addison-Wesley, Reading, MA, 1979.
J.E. Hopcroft, R. Motwani, and J.D. Ullman. Introduction to Automata Theory, Languages and Computation (Third Edition). Addison-Wesley, 2006.
H.R. Lewis. Unsolvable Classes of Quantificational Formulas. Addison-Wesley, Reading, MA, 1979.
Z. Manna. Mathematical Theory of Computation. McGraw-Hill, New York, NY, 1974. Reprinted by Dover, 2003.
E. Mendelson. Introduction to Mathematical Logic (Fifth Edition). Chapman & Hall/CRC, 2009.
M.L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs, NJ, 1967.
J.D. Monk. Mathematical Logic. Springer, 1976.
R.M. Smullyan. What Is the Name of This Book?—The Riddle of Dracula and Other Logical Puzzles. Prentice-Hall, 1978.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London
About this chapter
Cite this chapter
Ben-Ari, M. (2012). First-Order Logic: Undecidability and Model Theory *. In: Mathematical Logic for Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-4129-7_12
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4129-7_12
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4128-0
Online ISBN: 978-1-4471-4129-7
eBook Packages: Computer ScienceComputer Science (R0)