Synonyms
Definition
First-order logic (FOL) is a formalization of the most common kind of mathematical reasoning. It is characterized by the quantification of variables that range over a “universe of discourse” (a set of values). Less complex reasoning is captured by propositional (a.k.a. Boolean or sentential) logic. More complex reasoning is captured by second-order or even higher-order logic.
The syntactic aspects of FOL comprise a vocabulary (a.k.a. language or signature), formulae and, in particular, sentences (a.k.a. assertions), and a proof system (one of many equivalent ones!), structures (a.k.a. models or interpretations), and the satisfaction (a.k.a. truth or validity or “holds in”) relationship between sentences and structures. All are detailed below.
FOL is the source of the relational paradigm that was introduced by E. F. Codd in 1970 and has been dominating database technology for 30+ years.
Key Points
A first-order vocabulary...
Recommended Reading
Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.
Enderton HB. 1A mathematical introduction to logic. London: Academic; 2000.
Libkin L. Elements of finite model theory. Berlin: Springer; 2004.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media LLC
About this entry
Cite this entry
Tannen, V. (2016). First-Order Logic: Syntax. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_999-2
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7993-3_999-2
Received:
Accepted:
Published:
Publisher Name: Springer, New York, NY
Online ISBN: 978-1-4899-7993-3
eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering