Inference and Resolution Questions and Answers

Q: What is the risk of backward chaining with recursive rules?

A rule stating that ancestor of follows from ancestor of will regenerate the same goal indefinitely unless loop detection or a tabling mechanism is present. Prolog programmers learn to order clauses to avoid it. Rule order is fixed, unbounded derivation is a forward chaining hazard, and proof length is secondary. A failure mode arising from the interaction of a search strategy with a natural way of writing rules is one that a language's users must be taught rather than protected from.

Q: What is tabling in a logic programming system?

Memoising subgoals and their answers both prevents infinite loops on left recursive rules and avoids repeating work, which makes a whole class of natural programs terminate. It is the logic programming analogue of dynamic programming. Storage layout, indexing and presentation are different matters. Adding memoisation to a search that repeats subproblems is a general remedy and it applies here with unusual force.

Q: What is the relationship between backward chaining and search?

Each rule matching a goal gives a branch, and the conditions give the successors, so proving a goal is a search whose nodes are subgoal sets. Prolog searches it depth first. Direct computation and independence are false. Recognising a familiar activity as an instance of search brings the whole vocabulary of completeness, ordering and pruning to bear on it, which is more useful than treating it as a separate topic.

Q: What is a resolution refutation's relationship to backward chaining?

Working backwards from a negated goal, resolving against definite clauses, is exactly what backward chaining does, which is why Prolog is described as a resolution based language. The restriction to definite clauses is what makes the search linear rather than exploding. The other options misstate the relationship. Seeing two apparently different procedures as one restricted to a fragment is what allows results about the general case to be applied to the special one.

Q: What is the cut in Prolog?

The cut commits the search to the choices made so far, which improves efficiency and destroys the declarative reading, since the program's meaning now depends on the search order. Clause removal, depth limits and syntax are different notions. A construct that buys performance by breaking the correspondence between what a program says and what it does is a genuine engineering compromise, and the debate over its use has run for decades. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Q: Why does the cut damage the declarative reading?

With alternatives discarded, whether a goal succeeds depends on which clauses were tried first, so the logical reading no longer predicts the behaviour. Programs using cut must be read procedurally. Negation is a separate feature, some cuts do have logical readings, and no clauses are deleted. A feature whose cost is the loss of the language's principal claim is worth using sparingly and documenting carefully wherever it appears.

Q: What is negation as failure in a logic programming system?

The rule succeeds for not p exactly when the attempt to prove p fails finitely, which implements the closed world assumption operationally. It is sound only when the program is complete about p. The third option overstates it slightly by ignoring the finiteness requirement, and the others misdescribe it. An operational rule standing in for a semantic assumption must be used only where the assumption holds, which is a condition rarely checked in practice. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Why must the failure be finite for negation as failure to be sound?

If the attempt to prove p runs forever, the system has established nothing, and concluding not p would be unjustified. Implementations that time out and report success for the negation are unsound in exactly this way. Memory, goal identity and syntax are not the issue. A soundness condition that depends on the behaviour of a search, rather than on the logic, is easy to violate and hard to notice.

Q: What is the practical summary of inference methods for definite clauses?

Both chaining directions are sound and complete for definite clauses and run in time linear in the knowledge base, which is why this fragment underpins so much practical work. Resolution is also complete but the specialised procedures are far more efficient. The pessimistic options are wrong. A fragment combining adequate expressiveness with linear inference is the sweet spot the whole expressiveness against tractability discussion has been circling. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: What is the overall lesson of the inference topic?

Resolution supplies one rule sufficient for refutation, and the strategies, orderings and redundancy elimination around it are what turn an unusable search into a working tool. Tractable fragments and satisfiability solvers cover much of the rest. Neither pessimism nor unqualified optimism is warranted. That the rule is simple and everything around it is engineering is a fair summary not only of this topic but of much of the field.

71.

What is the risk of backward chaining with recursive rules?

A.The number of facts derived may become unbounded
B.The proof produced may be longer than necessary
C.The search may loop on a goal that reduces to itself
D.The rules may then be applied in an unpredictable order

Answer: C

A rule stating that ancestor of follows from ancestor of will regenerate the same goal indefinitely unless loop detection or a tabling mechanism is present. Prolog programmers learn to order clauses to avoid it. Rule order is fixed, unbounded derivation is a forward chaining hazard, and proof length is secondary. A failure mode arising from the interaction of a search strategy with a natural way of writing rules is one that a language's users must be taught rather than protected from.

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72.

What is tabling in a logic programming system?

A.Storing the facts of the knowledge base in a relational table
B.Arranging the clauses in a table for faster lookup during search
C.Tabulating the results of a query for presentation to the user
D.Recording answered subgoals so they are not recomputed or looped upon

Answer: D

Memoising subgoals and their answers both prevents infinite loops on left recursive rules and avoids repeating work, which makes a whole class of natural programs terminate. It is the logic programming analogue of dynamic programming. Storage layout, indexing and presentation are different matters. Adding memoisation to a search that repeats subproblems is a general remedy and it applies here with unusual force.

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73.

What is the relationship between backward chaining and search?

A.Backward chaining is a search over the space of proof trees
B.Backward chaining avoids search by computing the answer directly
C.Search is used only when backward chaining fails to find a proof
D.Backward chaining and search are entirely unrelated mechanisms

Answer: A

Each rule matching a goal gives a branch, and the conditions give the successors, so proving a goal is a search whose nodes are subgoal sets. Prolog searches it depth first. Direct computation and independence are false. Recognising a familiar activity as an instance of search brings the whole vocabulary of completeness, ordering and pruning to bear on it, which is more useful than treating it as a separate topic.

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74.

What is a resolution refutation's relationship to backward chaining?

A.Resolution is just backward chaining with the goal negated twice
B.Backward chaining is resolution restricted to definite clauses
C.The two are entirely different inference mechanisms
D.Backward chaining is a special case of forward chaining

Answer: B

Working backwards from a negated goal, resolving against definite clauses, is exactly what backward chaining does, which is why Prolog is described as a resolution based language. The restriction to definite clauses is what makes the search linear rather than exploding. The other options misstate the relationship. Seeing two apparently different procedures as one restricted to a fragment is what allows results about the general case to be applied to the special one.

Discuss in Forum

75.

What is the cut in Prolog?

A.A limit on the depth to which the search may proceed
B.A separator between the head and body of a clause
C.A control construct discarding alternative solutions
D.A rule that removes a clause from the knowledge base

Answer: C

The cut commits the search to the choices made so far, which improves efficiency and destroys the declarative reading, since the program's meaning now depends on the search order. Clause removal, depth limits and syntax are different notions. A construct that buys performance by breaking the correspondence between what a program says and what it does is a genuine engineering compromise, and the debate over its use has run for decades. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Discuss in Forum

76.

Why does the cut damage the declarative reading?

A.The cut introduces negation into an otherwise positive program
B.Cuts cannot be given any logical interpretation at all
C.The cut removes clauses that the declarative reading requires
D.The program's meaning becomes dependent on the search order

Answer: D

With alternatives discarded, whether a goal succeeds depends on which clauses were tried first, so the logical reading no longer predicts the behaviour. Programs using cut must be read procedurally. Negation is a separate feature, some cuts do have logical readings, and no clauses are deleted. A feature whose cost is the loss of the language's principal claim is worth using sparingly and documenting carefully wherever it appears.

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77.

What is negation as failure in a logic programming system?

A.Concluding a negated goal when the positive goal fails
B.Reporting failure when a negated goal cannot be proved
C.Treating every unproved goal as false in the knowledge base
D.Negating each clause before adding it to the knowledge base

Answer: A

The rule succeeds for not p exactly when the attempt to prove p fails finitely, which implements the closed world assumption operationally. It is sound only when the program is complete about p. The third option overstates it slightly by ignoring the finiteness requirement, and the others misdescribe it. An operational rule standing in for a semantic assumption must be used only where the assumption holds, which is a condition rarely checked in practice. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

78.

Why must the failure be finite for negation as failure to be sound?

A.Finiteness is required by the syntax of the language
B.An infinite search neither proves nor disproves the goal
C.Infinite failures consume more memory than is available
D.The negation would otherwise be applied to the wrong goal

Answer: B

If the attempt to prove p runs forever, the system has established nothing, and concluding not p would be unjustified. Implementations that time out and report success for the negation are unsound in exactly this way. Memory, goal identity and syntax are not the issue. A soundness condition that depends on the behaviour of a search, rather than on the logic, is easy to violate and hard to notice.

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79.

What is the practical summary of inference methods for definite clauses?

A.No complete procedure exists for definite clauses at all
B.Model checking is the only feasible method for this fragment
C.Forward and backward chaining are sound, complete and linear
D.Only resolution is complete for this fragment of the logic

Answer: C

Both chaining directions are sound and complete for definite clauses and run in time linear in the knowledge base, which is why this fragment underpins so much practical work. Resolution is also complete but the specialised procedures are far more efficient. The pessimistic options are wrong. A fragment combining adequate expressiveness with linear inference is the sweet spot the whole expressiveness against tractability discussion has been circling. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Discuss in Forum

80.

What is the overall lesson of the inference topic?

A.Inference is always intractable and must be avoided in practice
B.Model checking should be preferred to proof in every situation
C.Complete procedures exist for every logic of practical interest
D.A single rule plus strategies makes mechanical proof feasible

Answer: D

Resolution supplies one rule sufficient for refutation, and the strategies, orderings and redundancy elimination around it are what turn an unusable search into a working tool. Tractable fragments and satisfiability solvers cover much of the rest. Neither pessimism nor unqualified optimism is warranted. That the rule is simple and everything around it is engineering is a fair summary not only of this topic but of much of the field.

Discuss in Forum

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