Re: Horn clause question..
- From: Lmbd <lambda.x.fxx.fxx@xxxxxxxxx>
- Date: Mon, 06 Apr 2009 10:03:35 +0200
theunlearnedone wrote:
I was just reading up about horn clause. As per my understanding Horn
clause is a clause with at most one positive literal.No other
conditions are required so I am unable to understand the following
statements associated with Horn clause:
~a1 | ~a2 ... ~ an | b can be written equivalently as
a1 & a2 & ... an -> b
I am unable to reason such an implication. all of a1, ... an and 'b'
can be independent literals so either material or logical implication
can only be incidental, and not a given. What am I not seeing/reading
that will make sense of the implied implication (pun unintended).
In Propositional and Predicate Logic you have the equivalence of A -> B
with ~A | B (either the premise is false or the conclusion needs to be
true). So if you have a conjunction of premises, you can just apply De
Morgan's laws: (A1 & ... & An) -> B is equivalent to ~(A1 & ... & An) |
B is equivalent to ~A1 | ... | ~An | B . For example: A1 = "It's
raining.", A2="I don't have a raincoat." B="I don't leave the house." so
A1 & A2 -> B means "If it's raining and I don't have raincoat, I don't
leave the house". You know only what I will do, if the conditions are
met - otherwise everything is admissible (even that I leave the house
anyway - but you can't expect that).
This left the philosophical point of view a bit on the side - I thought
I'd explain it fastest this way.
hth, Martin
.
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