Literal (mathematical logic) について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Boolean literal ：ウィキペディア英語版

Literal (mathematical logic)
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

l

, the complementary literal is a literal corresponding to the negation of

l

,
we can write

\bar

to denote the complementary literal of

l

. More precisely, if

l\equiv x

then

\bar

\lnot x

and if

l\equiv \lnot x

then

\bar

x

.
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.
== 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,

P(t_1,\ldots,t_n)

with the terms recursively defined starting from constant symbols, variable symbols, and function symbols. For example,

\neg Q(f(g(x), y, 2), x)

is a negative literal with the constant symbol 2, the variable symbols ''x'', ''y'', the function symbols ''f'', ''g'', and the predicate symbol ''Q''.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
■ウィキペディアで「Literal (mathematical logic)」の詳細全文を読む

スポンサードリンク

翻訳と辞書 : 翻訳のためのインターネットリソース