Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 19, Issue 3 (Jan 2011)

Issues

First Order Languages: Further Syntax and Semantics

Marco Caminati
  • Mathematics Department "G. Castelnuovo", Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-04-26 | DOI: https://doi.org/10.2478/v10037-011-0027-0

First Order Languages: Further Syntax and Semantics

Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced. Depth of a formula. Definition of satisfaction and entailment (aka entailment or logical implication) relations, see [18] III.3.2 and III.4.1 respectively.

  • Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Google Scholar

  • Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.Google Scholar

  • Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Google Scholar

  • Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992.Google Scholar

  • Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Google Scholar

  • Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Google Scholar

  • Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Google Scholar

  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.Google Scholar

  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Google Scholar

  • Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • Marco B. Caminati. Preliminaries to classical first order model theory. Formalized Mathematics, 19(3):155-167, 2011, doi: 10.2478/v10037-011-0025-2.CrossrefGoogle Scholar

  • Marco B. Caminati. Definition of first order language with arbitrary alphabet. Syntax of terms, atomic formulas and their subterms. Formalized Mathematics, 19(3):169-178, 2011, doi: 10.2478/v10037-011-0026-1.CrossrefGoogle Scholar

  • M. B. Caminati. Basic first-order model theory in Mizar. Journal of Formalized Reasoning, 3(1):49-77, 2010.Google Scholar

  • Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Google Scholar

  • H. D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical logic. Springer, 1994.Google Scholar

  • Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.Google Scholar

  • Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.Google Scholar

  • Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.Google Scholar

  • Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Google Scholar

  • Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Google Scholar

  • Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Google Scholar

  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • Edmund Woronowicz. Many-argument relations. Formalized Mathematics, 1(4):733-737, 1990.Google Scholar

  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

About the article


Published Online: 2012-04-26

Published in Print: 2011-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-011-0027-0.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Marco Caminati
Formalized Mathematics, 2011, Volume 19, Number 3

Comments (0)

Please log in or register to comment.
Log in