Somewhat frequent
0/14
Logical Reasoning
Syllabus domain six: entailment, inference rules, CNF, and resolution - symbolic AI at Round 1 depth.
Syllabus domain six: entailment, inference rules, CNF, and resolution - symbolic AI at Round 1 depth.
10 multiple choice at 2 marks and 2 fill-in-the-blank at 5, marked exactly as Round 1 marks them. Each answer is explained as soon as you check it. The clock is shown, not enforced.
Logical reasoning is domain six of the syllabus. It is symbolic rather than statistical, and you can improve quickly by working through the same inference steps until they feel routine.
means every model of the knowledge base is also a model of . The identity that underpins every proof by refutation:
Related vocabulary that appears as straight definition questions: a sentence is valid if true in every model, satisfiable if true in at least one, and unsatisfiable if true in none.
Also standard: and-elimination, or-introduction, and the resolution rule below.
A rule is sound if everything it derives is entailed, and a procedure is complete if it can derive everything entailed. Being able to state both precisely is worth easy marks.
Two invalid patterns that appear as multiple-choice distractors:
Both look like the valid rules above and are not. If a question offers all four, it is testing exactly this.
Resolution needs conjunctive normal form - a conjunction of disjunctions of literals. In order:
Step 3 is where errors concentrate. Practise until it is mechanical.
To prove : convert to CNF and resolve until you derive the empty clause, which signals a contradiction and therefore proves the entailment.
Quantifiers extend propositional logic. The two points most likely to be asked: quantifier order changes meaning, and negation flips a quantifier while moving inward -
Proof by refutation rests on the entailment/unsatisfiability equivalence. Modus tollens is valid; affirming the consequent and denying the antecedent are not.
Follow the CNF steps in order - negation-pushing is the error-prone one. Deriving the empty clause completes a resolution proof.
From and you may infer…
Modus ponens: the implication and its premise yield the conclusion .
Select an answer
Resolve with . What clause do you get?
and cancel. The remainder is .
Select an answer