Can a fact be a definite clause?

Yes. It has exactly one positive literal and no negative literals, corresponding to an empty rule body.

Is every Prolog clause a pure definite clause?

No. Practical Prolog includes additional language features whose behavior extends beyond that simple logical form.

Does failing to prove a head prove its negation?

Not in ordinary classical entailment from definite clauses. Additional assumptions or operational conventions are needed for that interpretation.

AI Glossary / Graphs and symbolic AI / Intermediate

Definite clause

Definition

A definite clause is a logical clause containing exactly one positive literal. It can be written as a rule with a single positive conclusion whose conditions are a conjunction of positive atoms, making it a foundational form for logic programming.

What it means

A literal is an atomic statement or its negation. A clause is a disjunction of literals. For example, not-P or not-Q or R has one positive literal, R, and therefore is definite.

The same statement can be written as: if P and Q, then R. In this rule form, R is the head and P and Q form the body. The body atoms are written positively because moving the negative literals across the implication changes the presentation.

Every definite clause is a Horn clause, but not every Horn clause is definite. Horn clauses permit at most one positive literal, so they also include clauses with none.

How it works

A set of definite clauses describes facts and rules. A fact has a positive head and no conditions. A rule supports its head whenever its body can be established under a consistent substitution for its variables.

Forward reasoning starts with available facts and applies rules to derive additional conclusions. Backward reasoning starts with a goal, matches it to a rule head and tries to establish that rule's body. In first-order logic, variables in a clause are understood as universally quantified.

The logical meaning should be distinguished from an execution strategy. A Prolog program's chosen order of clauses and goals can affect search and termination. Features such as cuts, side effects and negation-as-failure require additional interpretation; they should not be treated as merely the pure definite-clause fragment.

Three practical examples

Relationship reasoning: Rules derive an indirect relationship from simpler recorded links.
Rule-based classification: A system establishes a category when several required properties hold together.
Logic programming: A program uses facts and single-head rules to answer relational queries through matching and proof search.

Think of it this way

Think of a checklist leading to one conclusion: if every required box is checked, the rule supports that conclusion. The analogy highlights conjunction in the body and a single head. It does not imply that checking the conclusion proves each box was checked, because the conclusion could have another explanation.

Worked example

Suppose the facts are Parent(ada,ben) and Parent(ben,cy). Add the rule:

Parent(x,y) and Parent(y,z) implies Grandparent(x,z).

In clause form, it is not-Parent(x,y) or not-Parent(y,z) or Grandparent(x,z). Only Grandparent(x,z) is a positive literal, so this is a definite clause.

Using x = ada, y = ben and z = cy makes both body atoms match the facts. The rule therefore derives Grandparent(ada,cy).

The shared variable y matters: both parent links must involve the same intermediate person. Parent(ada,ben) together with Parent(dan,cy) would not support that conclusion through this rule, because ben and dan are different constants in this example.

Parent(ada,ben) by itself is also a definite clause: it is a fact with one positive literal and an empty body. By contrast, not-P or not-Q has no positive literal. It is Horn but not definite. P or Q has two positive literals and is neither definite nor Horn.

Finally, Grandparent(ada,cy) alone does not let us reverse the rule to infer those particular parent links. The implication supports the head from the body, not an arbitrary reconstruction of its premises.

Illustrative case study

Fictional case: Cedar Relations builds a small rules engine for linking project records. A developer writes a rule intended to connect a project to a department through the project's assigned manager.

During review, the team notices that the two body conditions use different manager variables. The rule can therefore combine a project's manager with an unrelated department manager, producing unintended links.

The team corrects the shared variable and creates examples where names deliberately differ. It also inspects the query execution strategy, because a logically sensible recursive rule can still lead to repeated or nonterminating search in a particular implementation. The case illustrates two separate checks: whether the rule says the right thing and whether the program evaluates it appropriately.

Common misconceptions and mistakes

Definite means certain in an everyday sense. Here it names a syntactic form, not the reliability of the input facts.
Every Horn clause is definite. A Horn clause with no positive literal is a counterexample.
Negative literals in clause notation mean the rule body contains explicit negative tests. The equivalent positive-body implication has a different surface form.
A single rule head guarantees termination. Recursion and search strategy can still lead to nontermination.

Business use

Definite clauses provide a compact, inspectable way to express relationships and derivations. They can help when an application needs explanations that identify which facts and rules support a conclusion.

Review variable sharing, the direction of implications and the meaning of missing facts. Decide whether the application uses pure logical entailment or additional execution conventions. For recursive rules, evaluate search behavior and resource use separately from logical correctness. A rule that is easy to read can still encode the wrong relationship if its variables are connected incorrectly.

Check your understanding

Classify the clause not-A or not-B or C. How would it read as an implication?

Answer: It is definite because C is its only positive literal. It reads: if A and B, then C.

Related terms

Learn next

Write a two-link reachability rule and check that both edges share the same intermediate variable. Translate it into disjunctive clause form. Then compare a fact, a definite rule and a clause with no positive literal.

Literal

Sources

SWI-Prolog's glossary distinguishes clauses, Horn clauses, definite clauses and facts, and explains their rule notation: https://www.swi-prolog.org/pldoc/man?section=glossary

Russell and Norvig provide the broader logical-reasoning context in their textbook materials: https://aima.cs.berkeley.edu/

The family-link derivation and Cedar Relations case are original illustrations. This entry describes the pure logical form and explicitly separates it from additional Prolog execution features.

Previous: Defense in depth (computing) Next: Definite clause grammar