In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution.

Literals can be divided into two types:

• A positive literal).

• A negative literal).

The polarity of a literal is positive or negative depending on whether it is a positive or negative literal.

In logics with double negation elimination) the complementary literal or complement.. Double negation elimination occurs in classical logics but not in intuitionistic logic.

In the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula.

In Boolean functions appears twice) these qualify as two separate occurrences.

Examples

In propositional calculus a literal is simply a propositional variable or its negation.

In predicate calculus a literal is an atomic formula or its negation, where an atomic formula is a predicate symbol applied to some terms with the terms recursively defined starting from constant symbols, variable symbols, and function is a negative literal with the constant symbol 2, the variable symbols x, y, the function symbols f, g, and the predicate symbol Q.

References

Notes