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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 19:58:01 +0000
Message-id: <FDFBC56B2482EE48850DB651ADF7FEB0352391E5@xxxxxxxxxxxxxxxxxx>
Sure. Ruth Kempson did some early work in linguistics/nlp using labelled 
deduction:    (01)

Finger, Marcelo; Rodger Kibble; Dov Gabbay; Ruth Kempson. 1997. Parsing Natural 
Language Using LDS: a 
http://citeseerx.ist.psu.edu/viewdoc/download?doi=    (02)

I had also mentioned this before: 
http://ontolog.cim3.net/forum/ontolog-forum/2012-08/msg00020.html.     (03)

Leo    (04)

>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
>Sent: Saturday, July 26, 2014 3:41 PM
>To: '[ontolog-forum] '
>Subject: Re: [ontolog-forum] Paraconsistent Logic
>Thanks Leo and John,
>The phrase "Labeled Deductive Systems" sounds very
>interesting, but the Gabbay book costs $50 used.
>PDFs I found covered the topic but only in the
>math, nothing intuitive in the way of explaining
>the what how and why of labeled deductive systems.
>There seems to be a dual system in play, one
>called the Labels and the other the deduction
>rules.  That reminds me of the Link Grammar
>Parser, which applies at least two layers of
>labels to its syntax rules and matches the labels
>against other labels stored as properties of the
>language's vocabulary.
>So with only the LGP as the exemplar, can anyone
>shed some more light on why how and what you would
>use a labeled deductive system for?
>Rich Cooper
>Rich AT EnglishLogicKernel DOT com
>9 4 9 \ 5 2 5 - 5 7 1 2
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On
>Behalf Of Obrst, Leo J.
>Sent: Saturday, July 26, 2014 12:09 PM
>To: [ontolog-forum]
>Subject: Re: [ontolog-forum] Paraconsistent Logic
>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.
>One might even consider IKL similar to a hybrid
>logic, I guess, as Pat Hayes suggests [5].
>[1] Gabbay, Dov. 1996. Labelled Deductive Systems;
>Principles and Applications. Vol 1: Introduction.
>Oxford University Press.
>[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
>[3] Hybrid Logic.
>[4] Hybrid Logic.
>[5] Hayes, Pat.  Contexts and modalities in IKL.
>>-----Original Message-----
>>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>>bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F
>>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
>>defeasible deontic control."
>>That confirms my suspicion that this is an
>interesting research
>>area, but the applications are still exploratory
>>It's mostly R with wishful thinking about
>practical D.
>>> Here is an article that explains the basic
>>> 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
>>> I think it is important to bear in mind that
>>> 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
>>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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