<logic> The assignment of objects from the domain to the constants of a formal language, truth-values to the proposition symbols, truth-functions to the connectives, other functions to the function symbols, and extensions to the predicates (when these extensions consist of subsets of the domain). These assignments are made by the human logician and are not native to the symbols of the formal language. These assignments can be captured by a function f so that (for example) for a constant, f(c) = object d from domain D; for a proposition, f(p) = true; for a truth-function, f( =>) = material implication; for a function, f(g) = squaring the successor; or for a predicate, f(P) = the set of purple things. In propositional logic, an interpretation is just such a function; in predicate logic, it is some set (the domain) together with such a function defined for members of that domain.
Cardinality of an interpretation
The cardinality of the domain of the interpretation. See domain, model, model theory
An interpretation for systems with identity in which the relation of identity is assigned to the symbol "=" or some other 2-adic predicate. See first-order theory with identity, model, normal, predicate logic with identity
[Glossary of First-Order Logic]
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