• March 23, 2014
• 56 views

Consider the knowledge base

``````false :- a.
false :- b,c.
a :- d.
b :- e.
c :- d,f.
c :- g.
c :- h.
``````

Given that {d,e,f,g,h} is the set of assumables, what is the set of minimal conflicts for the above clauses?

I got

``````{d}
{e,f}
{e,g}
{e,h}
``````

Is that correct? Not 100% sure I understand minimal conflict.

1. A conflict of KB is a set of assumables that, given KB imply false.

But this equal definition may seems more understandable:

A conflict set is a set of assumables that cannot be all true given the observation.

And a minimal conflict is a conflict such that no strict subset is also a conflict.

Accordingly the minimal conflict sets for this KB are exactly:

{d}
{e,f}
{e,g}
{e,h}

To be sure:

• In any of these sets all the assubable(s) cannot be true at the same time.
• None of these sets has a subset which is a conflict too.

To complete the answer, here is the truth table for p → q 2. Previous answer is incorrect as far as I know.

The minimal conflict sets for this KB are exactly:

``````{d}
{e,g}
{e,h}
``````

As for the previous answer e,f,d is a conflict but not minimal because of the d subset being a conflict. e,f is nothing.