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Minimal Conflict in Artificial Intelligence

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.

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2

Answers


  1. 0

    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

    enter image description here

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  2. 0

    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.

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