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Re: [ontolog-forum] Paraconsistent Logic

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Obrst, Leo J." <lobrst@xxxxxxxxx>
Date: Sat, 26 Jul 2014 19:09:07 +0000
Message-id: <FDFBC56B2482EE48850DB651ADF7FEB035239193@xxxxxxxxxxxxxxxxxx>
John,    (01)

RE: combining logics, you might also look at Labelled Deduction, which when 
pushed into the object language is a so-called "Hybrid Logic" [1-4], i.e., an 
extended modal logic.    (02)

One might even consider IKL similar to a hybrid logic, I guess, as Pat Hayes 
suggests [5].    (03)

[1] Gabbay, Dov. 1996. Labelled Deductive Systems; Principles and Applications. 
Vol 1: Introduction. Oxford University Press.    (04)

[2] Blackburn, Patrick. 1999. Internalizing Labelled Deduction. In Proceedings 
of Hylo'99, First International Workshop on Hybrid Logics. July 13th, 1999, 
Saarbrücken, Germany. Published in Journal of Logic and Computation, 2000 
10(1):137-168.    (05)

[3] Hybrid Logic. http://en.wikipedia.org/wiki/Hybrid_logic.     (06)

[4] Hybrid Logic. http://plato.stanford.edu/entries/logic-hybrid/.     (07)

[5] Hayes, Pat.  Contexts and modalities in IKL. 
http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html#ContextsModalities.     (08)

>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
>Sent: Saturday, July 26, 2014 12:18 PM
>To: ontolog-forum@xxxxxxxxxxxxxxxx
>Subject: Re: [ontolog-forum] Paraconsistent Logic
>Joel Luis, Rich, and Tara,
>Thanks for the references.
>> I think that I have found some applications...
>Yes, those are good examples of useful applications.  I did not
>track down all the references, but the first one contained the
>comment "last, we state our future development of EVALPSN for
>defeasible deontic control."
>That confirms my suspicion that this is an interesting research
>area, but the applications are still exploratory developments.
>It's mostly R with wishful thinking about practical D.
>> Here is an article that explains the basic math:
>> 3.3 On the Philosophy and Mathematics
>> of the Logics of Formal Inconsistency
>> which starts on page 19 of the following URL:
>> http://www.paraconsistency.org/book/Handbook-WCP5.pdf
>The book covers a wide range of topics on reasoning about inconsistency
>by computers *and* by humans.
>It led me to a good survey article about methods for combining logics:
>This is another example of heavy R and little or no D.  If I were
>advising an engineer with a limited budget and a tight deadline,
>I'd suggest something else.
>> Based on the Stanford article, I would say that that following
>> all qualify as paraconsistent logics (emphasis on the plural)
>> * Defeasible Logics
>> * Default Logics
>> * Fuzzy Logics
>> * Logic programming with negation as failure
>I agree that all of them are related ways of addressing similar
>problems.  In fact, the article mentioned above discusses the
>relationship between EVALPSN and "conventional logic programming".
>But these methods have been used in practical applications for
>over 3o years.  Perhaps the theories of paraconsistent logic may
>provide a unified foundation for them.  That would be useful.
>> It appears that paraconsistent logics must be non-monotonic.
>> I think it is important to bear in mind that paraconsistent
>> is a characteristic that a logic can have, but many different
>> logics can have this characteristic.
>I agree.
>I would add belief revision as a method of handling similar problems.
>BR methods use metalevel reasoning about possibly inconsistent FO
>theories to produce a revised and consistent FO theory.
>For a good 42-page intro and overview of belief revision methods,
>    Peppas, Pavlos (2008) Belief revision, _Handbook of KR_,
>    http://pavlos.bma.upatras.gr/papers/8.pdf
>The advantage of belief (or theory) revision is that the final
>result is FOL, which can be represented and implemented in a
>wide range of well supported systems.
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>    (09)

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