For example, the Horn clause written above behaves as the procedure:

Horn clause programs can only represent state change by the change in arguments to predicates.

A form of logical sentences commonly found in logic programming, but not exclusively, is the Horn clause.

These three kinds of Horn clauses are illustrated in the following propositional example:

Stratification is not only useful for guaranteeing unique interpretation of Horn clause theories.

Horn-satisfiability: given a set of Horn clauses, is there a variable assignment which satisfies them?

It is described by some as a controversial control facility because it was added for efficiency reasons only and isn't a Horn clause.

Horn clauses play a basic role in constructive logic and computational logic.

Quasiidentities are special type of Horn clauses.

It is a refinement of resolution, which is both sound and refutation complete for Horn clauses.

Guarded Horn clause languages: are they deductive and Logical?

However, he is best known for his contributions to the development of logic programming, starting with the procedural interpretation of Horn clauses.

Prolog also uses Horn clauses.

Despite its simplicity compared with classical logic, this combination of Horn clauses and negation as failure has proved to be surprisingly expressive.

Pure Prolog is restricted to Horn clauses.

In mathematical logic, a Horn clause is a clause (a disjunction of literals) with at most one positive literal.

Satisfiability of first-order Horn clauses is undecidable.

A Horn formula is a propositional formula formed by conjunction of Horn clauses.

These properties of Horn clauses can lead to greater efficiencies in proving a theorem (represented as the negation of a goal clause).

Horn clauses are also the basis of logic programming, where it is common to write definite clauses in the form of an implication:

He also developed the minimal model and the fixpoint semantics of Horn clauses with Maarten van Emden.

It also became clear that such clauses could be restricted to definite clauses or Horn clauses, where , , .

Pure Prolog was originally restricted to the use of a resolution theorem prover with Horn clauses of the form:

Prolog uses a subset of logic (Horn clauses, closely related to "rules" and "production rules") that permit tractable computation.

Pure Prolog is based on a subset of first-order predicate logic, Horn clauses, which is Turing-complete.