1. Quiz
Propositional Logic

2. 1. Let A,B,C be propositions, i. e
1. Let A,B,C be propositions, i.e. they can take values False (F) or True (T).
a) How many possible worlds are there in this universe of 3 propostions?
b) Define the Knowledge Base:
Convert this KB1 to CNF form (conjunctive normal form).
c) In which worlds is KB1 true? (provide assignments to A,B,C, e.g. [T,T,T]).
d) Consider the query B.
In which worlds is B=T? (again provide assignments).
e) Can we entail B from KB1? Prove your statement or give a counterexample.
f) Consider the Knowledge Base:
Prove that B is entailed by the KB2 using resolution.
g) Is KB2 in Horn form?
all question are worth 2 points

3. How many possible worlds are there in this universe of 3 propostions
 8
b) Define the Knowledge Base:
Convert this KB1 to CNF form (conjunctive normal form). 
c) In which worlds is KB1 true? (provide assignments to A,B,C, e.g. [T,T,T]).
 {[T,T,T],[F,T,T],[F,F,T]}
d) Consider the query B.
In which worlds is B=T? (again provide assignments).
{[T,T,T],[F,T,T],[T,T,F],[F,T,F]}. Also correct if they if they used included KB1=T AND B=T
e) Can we entail B from KB1? Prove your statement or give a counterexample.
No, e.g. [F,F,T] is True in the query but not in the KB
f) Consider the Knowledge Base:
Prove that B is entailed by the KB2 using resolution.
 Add not(B) to the KB. Then A cancels with (not(A) and B) to give B which then
cancels with not(B) to give the empty clause. There are no solutions, hence unsatisfyable,
hence we proved entailment.
Is KB2 in Horn form?
 Yes, all clauses have at most 1 positive literal