Zeroth-order logic

Zeroth-order logic is first-order logic without variables or quantifiers. Some authors use the phrase "zeroth-order logic" as a synonym for the propositional calculus,[1] but an alternative definition extends propositional logic by adding constants, operations, and relations on non-Boolean values.[2] Every zeroth-order language in this broader sense is complete and compact.[2]


  1. Andrews, Peter B. (2002), An introduction to mathematical logic and type theory: to truth through proof, Applied Logic Series, 27 (Second ed.), Kluwer Academic Publishers, Dordrecht, p. 201, doi:10.1007/978-94-015-9934-4, ISBN 1-4020-0763-9, MR 1932484.
  2. Tao, Terence (2010), "1.4.2 Zeroth-order logic", An epsilon of room, II, American Mathematical Society, Providence, RI, pp. 27–31, doi:10.1090/gsm/117, ISBN 978-0-8218-5280-4, MR 2780010.
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