Well-formed Formula (Propositional Logic)

logic propositional-logic

Definition

Well-formed Formula (Propositional Logic)

In propositional logic, a well-formed propositional formula is a syntactically correct propositional formula generated by the following rules:

1. Every atom is a propositional formula.
2. and are propositional formulas.
3. If are propositional formulas with , then and are propositional formulas.
4. If is a propositional formula, then is a propositional formula.
5. If and are propositional formulas, then and are propositional formulas.
6. Nothing else is a well-formed propositional formula.

Here, , , , , and are connectives, namely conjunction, disjunction, negation, implication, and equivalence. The symbols and are propositional constants.

Examples

Examples

The following are well-formed propositional formulas:

The following are not well-formed: