Thanks Leo and John, (01)
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. (02)
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. (03)
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? (04)
-Rich (05)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (06)
-----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 (07)
John, (08)
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. (09)
One might even consider IKL similar to a hybrid
logic, I guess, as Pat Hayes suggests [5]. (010)
[1] Gabbay, Dov. 1996. Labelled Deductive Systems;
Principles and Applications. Vol 1: Introduction.
Oxford University Press. (011)
[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. (012)
[3] Hybrid Logic.
http://en.wikipedia.org/wiki/Hybrid_logic. (013)
[4] Hybrid Logic.
http://plato.stanford.edu/entries/logic-hybrid/. (014)
[5] Hayes, Pat. Contexts and modalities in IKL.
http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.ht
ml#ContextsModalities. (015)
>-----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.
>
>JLC
>> 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.
>
>RC
>> 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:
>http://plato.stanford.edu/entries/logic-combining
/
>
>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.
>
>TA
>> 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.
>
>John
>
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