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From: aaron@grad2.cis.upenn.edu (Aaron Watters)
Newsgroups: comp.databases
Subject: Re: errors and 4 valued logic
Keywords: logic, truth values
Message-ID: <32358@netnews.upenn.edu>
Date: 6 Nov 90 14:22:10 GMT
References: <694@creatures.cs.vt.edu>
Sender: news@netnews.upenn.edu
Reply-To: aaron@grad1.cis.upenn.edu (Aaron Watters)
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Organization: University of Pennsylvania
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The question at hand is:  What are the appropriate truth values
for the following statements
	B: `the king of north america is Bald.'
	H: `the king of north america has Hair.'
	G: `I am Green years old.'
About which...

In article <694@creatures.cs.vt.edu> holliday@csgrad.cs.vt.edu (Glenn Holliday) writes:
>Chuck Phillips  writes:
>	I think this is another example of Neat vs Scruffy, otherwise known
>as "What does logic _mean_" vs "How does the database work?".  

If you say so.

>The examples
>can be logically represented to model any domain you like.  Whether you
>want them to be false or errors depends completely on what domain you
>define.  

I don't agree at all.  B=not H.  If one is true then the other is
false and that's that.  Since at an intuitive level I can admit
neither B or H as a true statement, I am forced to consider an additional
truth value called `error' (or `overdefined') in order to deal with
such statements.  (I've had personal correspondence with a
constructivist who argues that B must be true since we cannot produce
a hair off the king's head -- I maintain this does violence to ordinary
common sense, even if it is an internally consistent position.)

>If any object can be in the domain, you can infer true statements
>or fail to infer them, which makes them false (_if_ you define your logical
>system to give that meaning to false!).

this is Reiter's closed world assumption, which I've always regarded
as a convenient technical assumption that is not really justifiable
in general.  Something is false if it is incorrect, not just because
I cannot prove it to be true.  To call mechanisms that do not make
this distinction `logical' is a perversion of language.

>	To call both of these [B and G?]
>false, your database wants rules that say
>1. The domain for every object/entity must be completely defined.
>2. Any purported value which does not fall within the appropriate domain is
>   reported as an error.
>3. Any reference to a value which does not exist (but would fall within an
>   appropriate domain if it did exist) is reported as an error.
>Glenn Holliday  holliday@csgrad.cs.vt.edu

I'm afraid I don't understand this.		-aaron

PS: recap of my position B=H=error. G=false.