|
|
| Line 1: |
Line 1: |
| {{Other uses|Clause (disambiguation)}}
| | The title of the author is Numbers. What I love performing is doing ceramics but I haven't produced a dime with it. In her professional lifestyle she is a payroll clerk but she's always needed her own company. My family lives in Minnesota and my family members loves it.<br><br>My web site: [http://mcb-law.net/candidiasis-tips-you-have-to-remember/ http://mcb-law.net/] |
| {{confusing|date=April 2010}}
| |
| In [[logic]], a '''clause''' is a finite [[Logical disjunction|disjunction]] of
| |
| [[Literal (mathematical logic)|literals]].<ref>{{cite book|last=Chang|first=Chin-Liang|title=Symbolic Logic and Mechanical Theorem Proving|year=1973|publisher=Academic Press|coauthors=Richard Char-Tung Lee|page=48|ISBN=0-12-170350-9}}</ref> Clauses
| |
| are usually written as follows, where the symbols <math>l_i</math> are
| |
| literals:
| |
| | |
| :<math>l_1 \vee \cdots \vee l_n</math>
| |
| | |
| In some cases, clauses are written (or defined) as sets of literals, so that clause above
| |
| would be written as <math>\{l_1, \ldots, l_n\}</math>. That this set is to be
| |
| interpreted as the disjunction of its elements is implied by the
| |
| context. A clause can be empty; in this case, it is an empty set of literals.
| |
| The empty clause is denoted by various symbols such as <math>\empty</math>,
| |
| <math>\bot</math>, or <math>\Box</math>. The truth evaluation of an empty
| |
| clause is always <math>false</math>.
| |
| | |
| In [[first-order logic]], a clause is interpreted as the universal closure of the disjunction of literals.{{Citation needed|date=April 2011}} Formally, a first-order
| |
| ''atom'' is a formula of the kind of <math>P(t_1,\ldots,t_n)</math>, where
| |
| <math>P</math> is a predicate of arity <math>n</math> and each <math>t_i</math>
| |
| is an arbitrary [[First-order logic#Formation rules|term]], possibly containing variables. A first-order ''literal'' is either an atom <math>P(t_1,\ldots,t_n)</math> or a negated atom <math>\neg P(t_1,\ldots,t_n)</math>. If
| |
| <math>L_1,\ldots,L_m</math> are literals, and <math>x_1,\ldots,x_k</math> are
| |
| their (free) variables, then <math>L_1,\ldots,L_m</math> is a clause, implicitly read as the closed first-order formula <math>\forall x_1,\ldots,x_k .
| |
| L_1,\ldots,L_m</math>.
| |
| The usual definition of satisfiability assumes free variables to be existentially quantified, so the omission of a quantifier is to be taken as a convention and not as a consequence of how the semantics deal with free variables.
| |
| | |
| In [[logic programming]], clauses are usually written as the implication of a
| |
| head from a body. In the simplest case, the body is a conjunction of literals
| |
| while the head is a single literal. More generally, the head may be a
| |
| disjunction of literals. If <math>b_1,\ldots,b_m</math> are the literals in the
| |
| body of a clause and <math>h_1,\ldots,h_n</math> are those of its head, the clause
| |
| is usually written as follows:
| |
| | |
| :<math>h_1,\ldots,h_n \leftarrow b_1,\ldots,b_m</math>
| |
| | |
| * If m=0 and n=1, the clause is called a ([[Prolog]]) fact.
| |
| * If m>0 and n=1, the clause is called a (Prolog) rule.
| |
| * If m>0 and n=0, the clause is called a (Prolog) query.
| |
| * If n>1, the clause is no longer [[Horn clause|Horn]].
| |
| | |
| ==See also==
| |
| * [[Conjunctive normal form]]
| |
| * [[Disjunctive normal form]]
| |
| * [[Horn clause]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.articleworld.org/index.php/Clause_%28logic%29 Clause logic related terminology]
| |
| * [http://www.free-dictionary-translation.com/Clause.html Clause simultaneously translated in several languages and meanings]
| |
| | |
| [[Category:Propositional calculus]]
| |
| [[Category:Predicate logic]]
| |
| [[Category:Logic programming]]
| |
The title of the author is Numbers. What I love performing is doing ceramics but I haven't produced a dime with it. In her professional lifestyle she is a payroll clerk but she's always needed her own company. My family lives in Minnesota and my family members loves it.
My web site: http://mcb-law.net/