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 . (03)
 Gabbay, Dov. 1996. Labelled Deductive Systems; Principles and Applications.
Vol 1: Introduction. Oxford University Press. (04)
 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
 Hybrid Logic. http://en.wikipedia.org/wiki/Hybrid_logic. (06)
 Hybrid Logic. http://plato.stanford.edu/entries/logic-hybrid/. (07)
 Hayes, Pat. Contexts and modalities in IKL.
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
>Sent: Saturday, July 26, 2014 12:18 PM
>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:
>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 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_,
>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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