Abstract
This chapter extends the machinery of propositional logic to first-order logic (FOL), also called both predicate logic and the first-order predicate calculus. While first-order logic enjoys a degree of expressiveness that makes it suitable for reasoning about computation, it does not admit completely automated reasoning.
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Bibliographic Remarks
A. Church. A note on the Entscheidungsproblem. Journal of Symbolic Logic, 1, 1936.
K. Gödel. Über die Vollständigkeit des Logikkalküls. PhD thesis, University of Vienna, 1929.
K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38:173–198, 1931.
D. Hilbert. Die Grundlagen der Mathematik. Abhandlungen aus dem Seminar der Hamburgischen Universität, 6:65–85, 1928.
J. E. Hopcroft, R. Motwani, and J. D. Ullman. Automata Theory, Languages, and Computation. Addison-Wesley, 3rd edition, 2006.
C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1993.
M. Sipser. Introduction to the Theory of Computation. Course Technology, 1996.
R. M. Smullyan. First-Order Logic. Dover, 1968.
R. Zach. Hilbert’s program. In E. N. Zalta, editor, The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Fall 2003. http://plato.stanford.edu/archives/fall2003/entries/hilbert-program.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). First-Order Logic. In: The Calculus of Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74113-8_2
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DOI: https://doi.org/10.1007/978-3-540-74113-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74112-1
Online ISBN: 978-3-540-74113-8
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