Knowra Interpretation (logic) Interpretation (logic) An interpretation assigns a domain and meanings to the nonlogical symbols of a formal language. It determines how formulas express properties and relations over that domain.
First-order logic : A formal system with variables, predicates, functions, quantifiers, and rules for expressing claims about objects. Its symbols and formulas are the standard setting in which interpretations are defined.
Term (logic) : A formal expression denoting an object, built from variables, constants, and function symbols. An interpretation evaluates terms to domain elements before evaluating formulas.
Model theory : The branch of mathematical logic that studies structures satisfying formal languages and theories. It investigates which interpretations make sets of sentences true.
Formal proof : A finite sequence of statements derived from axioms by specified inference rules. Interpretation is semantic; proof is syntactic, though soundness links the two.
Domain of discourse : The collection of objects over which variables in a logical language range. An interpretation must specify which objects its variables range over.
Satisfaction relation : A semantic relation stating that a structure and variable assignment make a formula true. It formalizes how an interpretation evaluates formulas, including those with free variables.
Model (mathematical logic) : A structure in which every sentence of a specified theory is true. An interpretation becomes a model of a theory when it satisfies all its axioms.
Syntax (logic) : The formal rules governing expressions and derivations in a logical language, independent of their meanings. Syntax forms expressions; interpretation supplies their semantic assignments.
Nonlogical symbol : A symbol, such as a predicate or function symbol, whose meaning is not fixed by logical rules alone. Interpretations assign meanings to these symbols while leaving logical symbols fixed.
Variable assignment : A mapping from variables to objects in a structure's domain. Assignments supply values for free variables during formula evaluation.
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