Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

First-Order Logic: Syntax

  • Val TannenEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_999


FOL; Predicate calculus; Predicate logic


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...

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Recommended Reading

  1. 1.
    Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
  2. 2.
    Enderton HB. 1A mathematical introduction to logic. London: Academic; 2000.Google Scholar
  3. 3.
    Libkin L. Elements of finite model theory. Berlin: Springer; 2004.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Section editors and affiliations

  • Val Tannen
    • 1
  1. 1.Dept. of Computer and Inf. ScienceUniv. of PennsylvaniaPhiladelphiaUSA