Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uunet!meaddata!gordon
From: gordon@meaddata.com (Gordon Edwards)
Newsgroups: comp.databases
Subject: Re: errors and 4-valued logic
Message-ID: <1602@meaddata.meaddata.com>
Date: 12 Oct 90 12:48:09 GMT
Sender: usenet@meaddata.com
Distribution: comp
Organization: Mead Data Central, Dayton OH
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In article <30999@netnews.upenn.edu>, aaron@grad2.cis.upenn.edu (Aaron
Watters) writes:
|> In response to my brief account of one variety of 4-valued logic
|> where I claimed:
|> 
|> `the king of North America is bald' is error.
|> 
|> Chuck Phillips  writes:
|> :Clairification: A statement requiring the existance of the non-existant to
|> :be true, is simply false, not an error.  However, a domain violation _is_
|> :an error.  (e.g. "I am green years old.")
|> :
|> :If "king" is an out-of-band attribute, then the statement is an error; if
|> :"king" is within the defined domain, then the statement is simply:
|> :false.
|> 
|> Now I'm willing to admit that this may be what the Prophet Codd says, but
|> I respectfully disagree.
|> 
|> if ``The king of North America is bald'' is false then we infer
|> that ``The king of North America has hair'' must be true, right?

I respectfully disgree with your disagreement. :-)  You treat the statement,
"The king of North America is bald" as  having a single semantic.
What you really have is:

assertion :-
	is_ruled_by(North_America, king),
	is(king, bald).  /* read as pseudo prolog */

Both predicates must evaluate to true for the assertion to be true.  North
America does not have a king, but North America could potentially be ruled by
a king.  Any land mass that supports human life can have any form of government
so I don't think we have a domain problem.  Since the first predicate is false,
the assertion is false without saying anything about the baldness predicate.  

|> However neither statement can be meaningfully asserted to be true
|> because there is no king of North America.  My favorite
|> version of 4-valued logic resolves this difficulty by calling
|> both statements `overdefined' or `erroneous.'  I would argue that
|> treating either statement as having a truth value is 
|> actually illogical. -aaron.
|> 
|> PS: I also claim that `I am green years old' can reasonably be
|> treated as false.

OK, I'll bite.  How?

-- Gordon     (gordon@meaddata.com)