Mathematical Literal

A Mathematical Literal is an atomic formula ([math]\displaystyle{ P }[/math]) or a negated atomic formula ([math]\displaystyle{ \neg P }[/math]).

• See: Conjunctive Normal Form, Mathematical Logic, Negation, Propositional Logic, Resolution (Logic).

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Literal_(mathematical_logic) Retrieved:2017-11-12.
  • In mathematical logic, a literal is an atomic formula (atom) 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 is just an atom.
    • A negative literal is the negation of an atom.
  • For a literal [math]\displaystyle{ l }[/math], the complementary literal is a literal corresponding to the negation of [math]\displaystyle{ l }[/math] ,

    we can write [math]\displaystyle{ \bar{l} }[/math] to denote the complementary literal of [math]\displaystyle{ l }[/math] . More precisely, if [math]\displaystyle{ l\equiv x }[/math] then [math]\displaystyle{ \bar{l} }[/math] is [math]\displaystyle{ \lnot x }[/math] and if [math]\displaystyle{ l\equiv \lnot x }[/math] then [math]\displaystyle{ \bar{l} }[/math] is [math]\displaystyle{ x }[/math] .

    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.

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