A horn clause is ___________ .
2015
A horn clause is ___________ .
- A.
A clause in which no variables occur in the expression
- B.
A clause that has at least one negative literal
- C.
A disjunction of a number of literals
- D.
A clause that has atmost one positive literal
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Correct answer: D
Definition: A Horn clause is a clause that contains at most one positive literal.
Equivalent statements:
As a disjunction: a Horn clause is a disjunction of literals with at most one positive literal.
As an implication: it can be written as the conjunction of the negative literals implying the positive literal (if present).
Common special cases and examples:
Definite clause (exactly one positive literal): example 'p ∨ ¬q ∨ ¬r', which corresponds to 'q ∧ r → p'.
Fact (no negative literals): example 'p' (a Horn clause with one positive literal and no negatives).
Goal or constraint (no positive literal): example '¬p ∨ ¬q' (a purely negative Horn clause).
Why this matters: Horn clauses are important because they permit efficient inference algorithms and form the basis of logic programming languages like Prolog.