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Formalized Mathematics

(a computer assisted approach)

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Volume 19, Issue 3 (Jan 2011)

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First Order Languages: Further Syntax and Semantics

Marco Caminati
  • Mathematics Department "G. Castelnuovo", Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy
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.

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

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

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

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

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

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

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

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

  • 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.

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

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

  • 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. [Crossref]

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

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

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

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

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

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

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

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

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

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

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

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