Question

Suppose that some knowledge base contains various propositional-logic sentences that utilize symbols A, B, C, D (connected with various connectives). There are only two cases when the knowledge base is false: - First case: when A is true, B is false, C is false, D is true. - Second case: when A is false, B is false, C is true, D is false. In all other cases, the knowledge base is true. Write a conjunctive normal form (CNF) for the knowledge base.

Answer 1

Check the explanation

Step-by-step explanation:

The knowledge base is expressed in terms of 4 variables and so the number of models will be 2^4 = 16.

The truth table obtained from the given details is :

A B C D KB ( Knowledge Base )

False False False False True

False False False True True

False False True False False

False False True True True

False True False False True

False True False True True

False True True False True

False True True True True

True False False False True

True False False True False

True False True False True

True False True True True

True True False False True

True True False True True

True True True False True

True True True True True

In conjunctive normal form if a literal X has the value True, then it is represented as X ' and if the value is False, then it is represented as X.

The maxterms for the required conjunctive normal form are ( A v B v ¬ C v D ) , ( ¬ A v B v C ¬ D )

Thus, the required conjunctive normal form for the Knowledge Base is ( A v B v ¬ C v D ) ∧ ( ¬ A v B v C ¬ D ).