[FOM] "Hidden" contradictions

Kreinovich, Vladik vladik at utep.edu
Sun Aug 25 18:00:00 EDT 2013

While there are non-logical way to deal with this problem, there is also a known logic-based solution to this problem, 4-valued logic of Belnap; when one treats all facts in the database as correct and unleash usual logical reasoning on these fact, then the fact that we have both a plane leaving at 12:00 pm and a (typo-induced) statement that the same plane will leave at 12:01 pm, we get a contradiction, and thus, the ability to conclude everything. Belnap avoids the rule that A and not A imply B, and he adds two new truth values: unknown and "true and false" (meaning that we have a record of this statement being true and a record or it being false -- or that we can deduce both true and false). 

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Dennis E. Hamilton
Sent: Sunday, August 25, 2013 11:29 AM

It's not clear to me that the problem is one that applies to logic systems.  I see it as a computer-science problem involving representation of assertions that are not mutually consistent and that are of a contingent/empirical nature.

If one desired to train some form of machine intelligence that could reason over such a corpus, it would require a robust means for dealing with such conditions including, first of all, a means of distinguishing them.  

Accepting all of the observations as asserted propositions in the usual manner (i.e., accepted hypotheses) is not going to work, not least of all because temporality and belief come into it along with pure inaccuracy.  Having some more-applicable formalized/heuristic inference system would certainly be valuable in such an undertaking.  That's probably not going to be a logic in the sense logic is ordinarily understood.  Mistaken conclusions will be an issue.  To make this the duty of a system of logic strikes me as some sort of category mistake.

I don't think that any of this is new news.  It doesn't seem to me that it's logic's fault that these situations do not satisfy the core requirements of conventional logic (and mathematics) for well-definedness.  


 - Dennis

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