To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Clause (logic)

From Wikipedia, the free encyclopedia

In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause 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 (disjunctive) 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.

See also

References

  1. ^ Chang, Chin-Liang; Richard Char-Tung Lee (1973). Symbolic Logic and Mechanical Theorem Proving. Academic Press. p. 48. ISBN 0-12-170350-9.

External links

This page was last edited on 21 February 2022, at 11:23
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.