First-Order Logic

Chapter
Part of the Universitext book series (UTX)

Abstract

Mathematics and some other disciplines such as computer science often consider domains of individuals in which certain relations and operations are singled out. When using the language of propositional logic, our ability to talk about the properties of such relations and operations is very limited. Thus, it is necessary to refine our linguistic means of expression, in order to procure new possibilities of description. To this end, one needs not only logical symbols but also variables for the individuals of the domain being considered, as well as a symbol for equality and symbols for the relations and operations in question. First-order logic, sometimes called also predicate logic, is the part of logic that subjects properties of such relations and operations to logical analysis.

Linguistic particles such as “for all” and “there exists” (called quantifiers) play a central role here, whose analysis should be based on a well prepared semantic background. Hence, we first consider mathematical structures and classes of structures. Some of these are relevant both to logic (in particular model theory) and to computer science. Neither the newcomer nor the advanced student needs to read all of 2.1, with its mathematical flavor, at once. The first five pages should suffice. The reader may continue with 2.2 and later return to what is needed.

Keywords

Expense Prefix 

References

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    _________ , Introduction to Logic and to the Methodology of Deductive Sciences, Oxford 1941, 3⟨{ rd}⟩ ed. Oxford Univ. Press 1965 (first edition in Polish, 1936).Google Scholar
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    A. Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica 1 (1936), 261–405 (first edition in Polish, 1933), also in [Ta4, 152-278].Google Scholar
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    D. Hilbert, P. Bernays, Grundlagen der Mathematik, I, II, Berlin 1934, 1939, 2⟨{ nd}⟩ ed. Springer, Vol. I 1968, Vol. II 1970.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikBerlinGermany

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