Definition:Statement Form

Definition

A statement form is a compound statement which is expressed in terms of statement variables along with the logical connectives which join them.

A statement form can be considered as being a statement in its own right.

There are various names for this concept, for example:

• statement scheme or schema;
• symbolic sentence;
• logical form.

Formal Definition

A statement form is an expression containing statement variables and logical connectives, formed using the following rules:

• Any statement variable is a statement form.

• If $A$ and $B$ are statement forms, then:
  • If $\intercal$ is a unary logical connective, then $\left({\intercal A}\right)$ is a statement form.
  • If $\intercal$ is a binary logical connective, then $\left({A \intercal B}\right)$ is a statement form.

Sources

• Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning (1964): $\text{I}: \S 1$
• Alan G. Hamilton: Logic for Mathematicians (1978): $\S 1.1, \ \S 1.2$: Definition $1.2$
• E.J. Lemmon: Beginning Logic (1965): $\S 1.1$
• D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.3$