Logical Consequence

boolean-algebra

Definition

Logical Consequence

The logical consequence, denoted as $\models$, is a logical operator in Boolean algebra that is defined as the following.

Let $F_1,\dots ,F_n$ be logical formulas and $I$ be the interpretation, then:

$$F_1,\dots ,F_n{\models }_{I}G:⟺({\text{val}}_I(F_1)=\cdots =1)⟹({\text{val}}_I(G)=1)$$

All logical formulas $F_1,\dots ,F_n$ are true for interpretation $I$ implies that $G$ is true.