“Clause (logic)”的意思、由来-开放百科全书

词条

Clause (logic)

释义

Empty clauses
Implicative form
See also
References
External links

In logic, a clause is an expression formed from a finite collection of literals (atoms or their negations) that is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term). That is, it is a finite disjunction^[1] or conjunction of literals, depending on the context. Clauses are usually written as follows, where the symbols are literals:

Empty clauses

A clause can be empty (defined from an empty set of literals).

The empty clause is denoted by various symbols such as ,

, or . The truth evaluation of an empty disjunctive

clause is always . This is justified by considering that is the neutral element of the monoid .

The truth evaluation of an empty conjunctive clause is always . This is related to the concept of a vacuous truth.

Implicative form

Every nonempty clause is logically equivalent to an implication of a head from a body, where the head is an arbitrary literal of the clause and the body is the conjunction of the negations of the other literals. That is, if a truth assignment causes a clause to be true, and none of the literals of the body satisfy the clause, then the head must also be true.

This equivalence is commonly used in logic programming, where clauses are usually written as an implication in this form. More generally, the head may be a disjunction of literals. If are the literals in the body of a clause and are those of its head, the clause is usually written as follows:

If n = 1 and m = 0, the clause is called a (Prolog) fact.
If n = 1 and m > 0, the clause is called a (Prolog) rule.
If n = 0 and m > 0, the clause is called a (Prolog) query.
If n > 1, the clause is no longer Horn.

References

1. ^{{cite book|last=Chang|first=Chin-Liang|title=Symbolic Logic and Mechanical Theorem Proving|year=1973|publisher=Academic Press|author2=Richard Char-Tung Lee|page=48|ISBN=0-12-170350-9}}

External links

Clause logic related terminology
Clause simultaneously translated in several languages and meanings

3 : Propositional calculus|Predicate logic|Logic programming

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

Empty clauses

Implicative form

See also

References

External links