| well-formed formula |
Definition. A WELL-FORMED FORMULA (WFF) of
sentential logic is any expression that accords with the following
seven rules: |
| (1) |
A sentence letter standing alone is a wff. |
| atomic sentence |
[Definition. The sentence letters are the ATOMIC SENTENCES of the language of sentential logic.] |
| (2) |
If Φ is a wff, then the expression ~Φ is also a wff. |
| negation |
[Definition. A wff of this form is known as a NEGATION, and ~Φ is known as the NEGATION of Φ.] |
| (3) |
If Φ and Ψ are both wffs, then the expression
(Φ & Ψ) is a wff. |
| conjunction |
[Definition. A wff of this form is known as a CONJUNCTION. Φ and Ψ are known as the left and right CONJUNCTS, respectively.] |
| (4) |
If Φ and Ψ are both wffs, then the expression
(Φ v Ψ) is a wff. |
| disjunction |
[Definition. A wff of this form is known as a DISJUNCTION. Φ and Ψ are the left and right DISJUNCTS, respectively.] |
| (5) |
If Φ and Ψ are both wffs, then the expression
(Φ → Ψ) is a wff. |
conditional,
antecedent,
consequent |
[Definition. A wff of this form is known as a CONDITIONAL. The wff Φ is known as the ANTECEDENT of the conditional. The wff Ψ is known as the CONSEQUENT of the conditional.] |
| (6) |
If Φ and Ψ are both wffs, then the expression (Φ ↔ Ψ) is a wff. |
| biconditional |
[Definition. A wff of this form is known as a BICONDITIONAL. It is also sometimes known as an EQUIVALENCE.] |
| (7) |
Nothing else is a wff. |