Well-formed Formula

logic

Definition

Well-formed Formula

A well formed formula is a formula that is syntactically correct according to the formation rules of a formal language.

A string that does not obey the formation rules is not a formula at all.

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.

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First-Order Logic

A well formed formula is built from terms, predicates, logical connectives, and quantifiers.

Examples

• is a well formed formula.
• is a well formed formula.
• is not a well formed formula.