Interpretation

Definition

Interpretation

In logic, an interpretation provides the “meaning” of the non-logical symbols in a formal language. Its definition depends on the level of the logic:

Propositional Logic

Definition

Interpretation (Propositional Logic)

In propositional logic, an interpretation is a truth assignment (sometimes ) that maps each atom to a truth value, where is the set of atoms.

The assignment extends to formulas compositionally: the value of a complex formula is determined by the values of its subformulas.

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First-Order Logic

Definition

Interpretation (First-Order Logic)

For a language and a non-empty set serving as the universe, an interpretation assigns meanings to the non-logical symbols:

Together, and form the structure . Variables receive values separately through a variable assignment .

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