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12 relations: Clause (logic), Function (mathematics), Ground expression, Herbrand structure, Herbrand's theorem, Interpretation (logic), Interpretation (model theory), Jacques Herbrand, Logical constant, Mathematical logic, Satisfiability, Syntax.
Clause (logic)
In logic, a clause is an expression formed from a finite collection of literals (atoms or their negations) that is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Ground expression
In mathematical logic, a ground term of a formal system is a term that does not contain any free variables.
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Herbrand structure
In first-order logic, a Herbrand structure S is a structure over a vocabulary σ, that is defined solely by the syntactical properties of σ.
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Herbrand's theorem
Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930).
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Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language.
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Interpretation (model theory)
In model theory, interpretation of a structure M in another structure N (typically of a different signature) is a technical notion that approximates the idea of representing M inside N. For example every reduct or definitional expansion of a structure N has an interpretation in N. Many model-theoretic properties are preserved under interpretability.
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Jacques Herbrand
Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician.
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Logical constant
In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics.
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Syntax
In linguistics, syntax is the set of rules, principles, and processes that govern the structure of sentences in a given language, usually including word order.
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