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My web site - http://www.hostgator1centcoupon.info/ In logic, a clause is a finite disjunction of literals. Clauses are usually written as follows, where the symbols $l_{i}$ are literals:

$l_{1}\vee \cdots \vee l_{n}$

In some cases, clauses are written (or defined) as sets of literals, so that clause above would be written as $\{l_{1},\ldots ,l_{n}\}$. 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 $\emptyset$, $\bot$, or $\Box$. The truth evaluation of an empty clause is always $false$.

In first-order logic, a clause is interpreted as the universal closure of the disjunction of literals.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. Formally, a first-order atom is a formula of the kind of $P(t_{1},\ldots ,t_{n})$, where $P$ is a predicate of arity $n$ and each $t_{i}$ is an arbitrary term, possibly containing variables. A first-order literal is either an atom $P(t_{1},\ldots ,t_{n})$ or a negated atom $\neg P(t_{1},\ldots ,t_{n})$. If $L_{1},\ldots ,L_{m}$ are literals, and $x_{1},\ldots ,x_{k}$ are their (free) variables, then $L_{1},\ldots ,L_{m}$ is a clause, implicitly read as the closed first-order formula $\forall x_{1},\ldots ,x_{k}.L_{1},\ldots ,L_{m}$. 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 $b_{1},\ldots ,b_{m}$ are the literals in the body of a clause and $h_{1},\ldots ,h_{n}$ are those of its head, the clause is usually written as follows:

$h_{1},\ldots ,h_{n}\leftarrow b_{1},\ldots ,b_{m}$

• 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.

See also

• Conjunctive normal form
• Disjunctive normal form
• Horn clause

References

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External links

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