# First Order Languages: Further Syntax and Semantics

Formalized Mathematics (2011)

- Volume: 19, Issue: 3, page 179-192
- ISSN: 1426-2630

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topMarco Caminati. "First Order Languages: Further Syntax and Semantics." Formalized Mathematics 19.3 (2011): 179-192. <http://eudml.org/doc/268157>.

@article{MarcoCaminati2011,

abstract = {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.},

author = {Marco Caminati},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {179-192},

title = {First Order Languages: Further Syntax and Semantics},

url = {http://eudml.org/doc/268157},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Marco Caminati

TI - First Order Languages: Further Syntax and Semantics

JO - Formalized Mathematics

PY - 2011

VL - 19

IS - 3

SP - 179

EP - 192

AB - 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.

LA - eng

UR - http://eudml.org/doc/268157

ER -

## References

top- Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- 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. Zbl06213858
- Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- 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.
- Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- 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] Zbl1276.03030
- 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] Zbl1276.03031
- M. B. Caminati. Basic first-order model theory in Mizar. Journal of Formalized Reasoning, 3(1):49-77, 2010. Zbl1211.03024
- Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- H. D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical logic. Springer, 1994.
- Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
- 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.
- 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.
- Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- 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.

## Citations in EuDML Documents

top- Marco Caminati, Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms
- Karol Pąk, Flexary Operations
- Karol Pąk, Euler’s Partition Theorem
- Marco Caminati, Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem
- Marco Caminati, Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages

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