Inference and Resolution Questions and Answers

Q: What is unification's role in first order resolution?

Resolution requires complementary literals, and in first order logic they may match only after variables are instantiated, which unification computes. Without it a prover would have to enumerate ground instances, which is what the Herbrand approach does far less efficiently. Clause merging is resolution itself, and duplicate removal is factoring. Operating on variables directly, rather than on their instances, is what lifts a propositional method to the first order case.

Q: What is factoring in resolution?

If two literals within one clause can be made identical, the clause may be replaced by its factor, and without this step resolution is not complete. It is easily overlooked because it never arises in the propositional case. Splitting, common factors and subsumption are different operations. A step required only in the lifted version of a rule, and invisible in the propositional one, is exactly the kind of detail that makes a first implementation subtly incomplete.

Q: Why is a resolution search space so large?

The set of clauses grows as resolvents are added, and each new clause may resolve with every existing one, so unrestricted search explodes immediately. That is why strategies restricting which pairs may resolve are essential rather than optional. No new predicates appear, the most general unifier is unique, and conversion happens once. A rule that is complete and unusable without restriction is the normal starting point for practical proof search. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: What is the unit preference strategy?

Resolving with a unit clause always shortens the other clause, so the search moves towards the empty clause rather than away from it. It is a heuristic rather than a restriction and does not affect completeness. Premise preference is input resolution, and the other options describe different rules. Preferring steps that make measurable progress towards the goal is the same principle that orders any search, applied here to clause length. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: What is the set of support strategy?

Requiring that every step touch the negated goal or something derived from it prevents the prover from deriving irrelevant consequences of the premises, and it preserves completeness provided the premises alone are satisfiable. It is the most important of the classical strategies. The other options describe unrelated notions. A restriction that is both a large saving and provably harmless is worth adopting universally, which is what happened. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Why does the set of support strategy preserve completeness?

If the premises are consistent, any contradiction must involve the negated goal, so resolutions among the premises alone can be skipped without losing the proof. That condition must actually hold, and it usually does. Order restriction and universal harmlessness are false. A restriction justified by an argument about where a contradiction must lie is far stronger than one adopted heuristically, and it is worth checking that the argument's premise holds. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: What is subsumption in a resolution prover?

If one clause is an instance of another, or contains all its literals, it adds nothing and may be deleted, which keeps the clause set from growing uncontrollably. Forward and backward subsumption check new clauses against old and old against new respectively. The other options describe different operations. Deleting redundant information aggressively is what keeps a saturating procedure from drowning in its own output.

Q: What is input resolution?

Restricting one parent of every resolution to be an original clause keeps the search linear in shape, and it is complete for Horn clauses though not in general. That partial completeness is exactly why logic programming, which is Horn, can use such a restricted strategy. The other options misread the restriction. A strategy complete for a fragment and incomplete generally is usable precisely where that fragment applies, which must be checked rather than assumed.

Q: Why is input resolution complete for Horn clauses but not in general?

A refutation from Horn clauses can always be arranged so that each step uses an original clause, which is not true when clauses have several positive literals. That structural fact is what logic programming rests on. Horn clauses do contain negative literals, conversion is not the issue, and a Horn set may certainly be unsatisfiable. A completeness result that depends on the shape of the available proofs, rather than on the rule, is worth understanding as such.

Q: What is generalised modus ponens?

Lifting the rule to first order logic requires the antecedent of the implication and the known fact to be unified rather than being identical, which is what forward and backward chaining over definite clauses use. It is sound and complete for definite clauses. The other options describe different extensions. Adding unification to a propositional rule, so that it applies to variables, is the same lifting that produces first order resolution. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

11.

What is unification's role in first order resolution?

A.It converts a first order clause into propositional form
B.It removes duplicate literals from within a clause
C.It makes two literals identical so they can be resolved
D.It merges two clauses into a single longer clause

Answer: C

Resolution requires complementary literals, and in first order logic they may match only after variables are instantiated, which unification computes. Without it a prover would have to enumerate ground instances, which is what the Herbrand approach does far less efficiently. Clause merging is resolution itself, and duplicate removal is factoring. Operating on variables directly, rather than on their instances, is what lifts a propositional method to the first order case.

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12.

What is factoring in resolution?

A.Splitting a clause into two smaller clauses
B.Extracting a common factor from several clauses
C.Removing a clause that is subsumed by another
D.Merging two literals in a clause that unify with each other

Answer: D

If two literals within one clause can be made identical, the clause may be replaced by its factor, and without this step resolution is not complete. It is easily overlooked because it never arises in the propositional case. Splitting, common factors and subsumption are different operations. A step required only in the lifted version of a rule, and invisible in the propositional one, is exactly the kind of detail that makes a first implementation subtly incomplete.

Discuss in Forum

13.

Why is a resolution search space so large?

A.Every pair of clauses may resolve, producing yet more clauses
B.Each resolution step introduces new predicate symbols
C.Unification generates infinitely many substitutions
D.Clauses must be converted to normal form repeatedly

Answer: A

The set of clauses grows as resolvents are added, and each new clause may resolve with every existing one, so unrestricted search explodes immediately. That is why strategies restricting which pairs may resolve are essential rather than optional. No new predicates appear, the most general unifier is unique, and conversion happens once. A rule that is complete and unusable without restriction is the normal starting point for practical proof search. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

14.

What is the unit preference strategy?

A.Resolving only clauses derived in the previous step
B.Resolving with single literal clauses first
C.Preferring clauses that were supplied as premises
D.Choosing the clause with the fewest variables

Answer: B

Resolving with a unit clause always shortens the other clause, so the search moves towards the empty clause rather than away from it. It is a heuristic rather than a restriction and does not affect completeness. Premise preference is input resolution, and the other options describe different rules. Preferring steps that make measurable progress towards the goal is the same principle that orders any search, applied here to clause length. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

15.

What is the set of support strategy?

A.The premises are divided into supporting and unsupported sets
B.Each clause must be resolved with at least one other clause
C.Every resolution must involve a clause descended from the negated goal
D.Only clauses supported by evidence may be used in the proof

Answer: C

Requiring that every step touch the negated goal or something derived from it prevents the prover from deriving irrelevant consequences of the premises, and it preserves completeness provided the premises alone are satisfiable. It is the most important of the classical strategies. The other options describe unrelated notions. A restriction that is both a large saving and provably harmless is worth adopting universally, which is what happened. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

16.

Why does the set of support strategy preserve completeness?

A.Every clause is eventually derived from the goal in any case
B.The strategy restricts only the order in which clauses are used
C.Completeness is preserved by every restriction on resolution
D.The premises alone are satisfiable so no contradiction lies within them

Answer: D

If the premises are consistent, any contradiction must involve the negated goal, so resolutions among the premises alone can be skipped without losing the proof. That condition must actually hold, and it usually does. Order restriction and universal harmlessness are false. A restriction justified by an argument about where a contradiction must lie is far stronger than one adopted heuristically, and it is worth checking that the argument's premise holds. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

17.

What is subsumption in a resolution prover?

A.Discarding a clause implied by a more general one already present
B.Absorbing one knowledge base into a larger one
C.Replacing a clause by the resolvent that produced it
D.Combining several clauses into a single stronger clause

Answer: A

If one clause is an instance of another, or contains all its literals, it adds nothing and may be deleted, which keeps the clause set from growing uncontrollably. Forward and backward subsumption check new clauses against old and old against new respectively. The other options describe different operations. Deleting redundant information aggressively is what keeps a saturating procedure from drowning in its own output.

Discuss in Forum

18.

What is input resolution?

A.Resolution is applied only to the input's own unit clauses
B.Every step must involve one of the original input clauses
C.Only clauses read from the input file may be resolved
D.The input is resolved before any inference begins

Answer: B

Restricting one parent of every resolution to be an original clause keeps the search linear in shape, and it is complete for Horn clauses though not in general. That partial completeness is exactly why logic programming, which is Horn, can use such a restricted strategy. The other options misread the restriction. A strategy complete for a fragment and incomplete generally is usable precisely where that fragment applies, which must be checked rather than assumed.

Discuss in Forum

19.

Why is input resolution complete for Horn clauses but not in general?

A.General clauses cannot be converted into input form
B.Horn clauses are always satisfiable so their refutation is trivial
C.Horn clause refutations always have the required linear shape
D.Horn clauses contain no negative literals to resolve upon

Answer: C

A refutation from Horn clauses can always be arranged so that each step uses an original clause, which is not true when clauses have several positive literals. That structural fact is what logic programming rests on. Horn clauses do contain negative literals, conversion is not the issue, and a Horn set may certainly be unsatisfiable. A completeness result that depends on the shape of the available proofs, rather than on the rule, is worth understanding as such.

Discuss in Forum

20.

What is generalised modus ponens?

A.Modus ponens applied to several implications at once
B.A generalisation of implication to more than two arguments
C.Modus ponens extended to non-monotonic reasoning
D.Modus ponens with unification applied to the premises

Answer: D

Lifting the rule to first order logic requires the antecedent of the implication and the known fact to be unified rather than being identical, which is what forward and backward chaining over definite clauses use. It is sound and complete for definite clauses. The other options describe different extensions. Adding unification to a propositional rule, so that it applies to variables, is the same lifting that produces first order resolution. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

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