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.

Check the explanation

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 ).