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Can It Be In Horn Form

Posted on 2010-11-10
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Last Modified: 2012-06-27
I'm trying to understand whether R => (E <==> C) can be expressed in Horn form. How do I deal with this?
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Question by:JCW2
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LVL 37

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TommySzalapski earned 500 total points
ID: 34108276
For Horn form I make a truth table with each of the variables and the main clause I'm testing.
For all the Fs in the main clause column all the literals must be F in the same row except for one.
So your equations truth table looks like the following. Can it go into Horn form? Look at the F rows in the last column and tell me.
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Author Comment

by:JCW2
ID: 34115019
By main clause, do you mean R?
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LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 500 total points
ID: 34115139
No. The main clause is R => (E <==> C)
The easiest way to set up the truth table would probably be to put columns for
R, E, C, E<==>C, and R=>(E<==>C)
Then circle all the rows with Fs in the last column. Ignore the E<==>C column when checking for Horn form of course. Just check the literals. I add that column because I don't want to try to do it all in my head.
Generate the truth table and post it so I can help you make sure you are doing it right. I'll be on for a couple hours yet.
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Author Comment

by:JCW2
ID: 34115570
Using E <==> C as the main clause, I don't think I can express my problem in Horn form. Am I correct?
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Author Comment

by:JCW2
ID: 34115580
Disregard the last comment.
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LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 500 total points
ID: 34115614
It is true that E<==>C cannot be expressed in Horn form. So you're probably doing it right.
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Author Comment

by:JCW2
ID: 34115701
From what I can see, the relevant rows are

T T F - F and
T F T - F.

Therefore, we can not express the propositional sentence in Horn form.
Is this correct?
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LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 500 total points
ID: 34115731
100% correct.
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Author Comment

by:JCW2
ID: 34115794
Another thing: is it possible for a sentence to be expressed in Horn form if all literals are F in the proper row?
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LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 500 total points
ID: 34115925
Yes. Sorry. Should have read:

For Horn form I make a truth table with each of the variables and the main clause I'm testing.
For all the Fs in the main clause column all or all but one of the literals must be F in the same row.
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Author Closing Comment

by:JCW2
ID: 34115958
Thank you for your help.
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LVL 37

Expert Comment

by:TommySzalapski
ID: 34115981
A Horn clause has AT MOST one positive literal.
A definite clause has EXACTLY one positive literal.
So the definite clause would not work if the whole row was Ts, but Horn could.
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