Clause (logic)

In logic, a clause is an expression formed from a finite collection of literals (variables 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 or conjunction of literals, depending on the context. Clauses are usually written as follows, where the symbols ${\displaystyle l_{i}}$ are literals:

A clause can be empty (defined from an empty set of literals). The empty clause is denoted by various symbols such as ${\displaystyle \emptyset }$, ${\displaystyle \bot }$, or ${\displaystyle \Box }$. The truth evaluation of an empty clause is always ${\displaystyle false}$.

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