Model (Logic)

logic

Definition

Model

A model is a semantic object under which a formula is true.

In propositional logic, a model is a variable assignment that maps propositional variables to truth values.

In first-order logic, a model is an interpretation $I$ together with a variable assignment $\sigma$ such that

$$I,\sigma \models F$$

The formula is true under that interpretation and assignment.

Set of Models

For a formula $F$, the set of its models is

$$\mathcal{M}(F)=\{M\mid M\models F\}$$

This set is used to compare logical strength and entailment.