Domain of discourse

A domain of discourse is the collection of objects over which variables range in a formal interpretation. It determines what quantified statements can assert.

First-order logic: A formal system with variables, predicates, logical connectives, and quantifiers over objects. Its interpretations specify the domain over which quantified variables range.
Tarski's truth definition: A recursive account of truth in a formal language relative to an interpretation. It evaluates quantified formulas by checking objects in the interpretation's domain.
Empty domain: A domain containing no objects, permitted in some logical systems and excluded in others. Allowing it changes the truth behavior of existential and universal sentences.
Model theory: The mathematical study of formal languages through their interpretations and models. It compares structures with different domains to study the same theory.
Quine's criterion of ontological commitment: A method for identifying a theory's commitments by examining what its bound variables must range over. It makes domain choice central to deciding what a theory says exists.
Variable (mathematics): A symbol that stands for an object or value, often constrained by an expression or quantifier. A domain supplies the possible objects a logical variable can denote.
Variable assignment: A function assigning objects from a structure's domain to variables. It specifies which domain objects free variables denote during evaluation.
Many-sorted logic: A logic with distinct domains for different types of objects and quantifiers. It replaces one undifferentiated range with separate typed domains.
Model (mathematical logic): A structure in which every sentence of a specified theory is true. A model's domain provides the objects that witness or refute its sentences.
Indispensability argument: An argument that commitment to mathematical entities follows from their indispensable role in successful science. It uses quantified scientific theories to debate whether mathematical objects belong in their domains.

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