Abstract
This fundamental theorem shows the equivalence of two at first sight different properties of a set of clauses S:
-
satisfiability, or the existence of a model of S;
-
coherence (= irrefutability = consistency), i.e., the impossibility of obtaining the empty clause when applying DPP to a finite subset of S/H S .
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
Notes
- 1.
Recall the failed attempt of Saccheri to prove the incompatibility of the postulates of Euclid with the negation of the Fifth Postulate: page after page, he was in fact describing a model of non-Euclidean geometry.
- 2.
Dante Alighieri, The Inferno, translation by Robert Hollander.
- 3.
L. Tolstoy, The Death of Ivan Ilych, translation by Louise and Aylmer Maude.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Italia
About this chapter
Cite this chapter
Mundici, D. (2012). Gödel’s Completeness Theorem for the Logic of Clauses. In: Logic: A Brief Course. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-2361-1_14
Download citation
DOI: https://doi.org/10.1007/978-88-470-2361-1_14
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2360-4
Online ISBN: 978-88-470-2361-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)