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First-Order Logic: Syntax

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Encyclopedia of Database Systems

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Synonyms

FOL; Predicate calculus; Predicate logic

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...

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Recommended Reading

  1. Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.

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  2. Enderton HB. 1A mathematical introduction to logic. London: Academic; 2000.

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  3. Libkin L. Elements of finite model theory. Berlin: Springer; 2004.

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA

    Val Tannen

Authors
  1. Val Tannen
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Corresponding author

Correspondence to Val Tannen .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, GA, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, ON, Canada

    M. Tamer Özsu

Section Editor information

  1. Dept. of Computer and Inf. Science, Univ. of Pennsylvania, Philadelphia, PA, USA

    Val Tannen

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Tannen, V. (2018). First-Order Logic: Syntax. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_999

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