

Inconsistency-tolerant logics - wslh
http://en.m.wikipedia.org/wiki/Paraconsistent_logic

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StefanKarpinski
Interesting idea, although I find the motivation a little unconvincing. In
particular, the quotation

"... natural language abounds with directly or indirectly self-referential yet
apparently harmless expressions—all of which are excluded from the Tarskian
framework"

used in this article to motivate the concept of inconsistency-tolerant logic
is actually much better support for non-well-founded set theories [1] allowing
hypersets (i.e. sets which contain themselves), e.g. by assuming Aczel's anti-
foundation axiom [2]. Since these set theories _are_ compatible with standard
the set theory, extending it, rather than replacing it, they don't throw out
the notion of consistency, but have no problem dealing with self-referential
sets and such. "Vicious Circles" [3] is a great exposition of the subject of
hypersets and their applications to computer science and logic, among other
things and is quote accessible for such a theoretical subject.

[1] [http://en.wikipedia.org/wiki/Non-well-
founded_set_theory](http://en.wikipedia.org/wiki/Non-well-founded_set_theory)

[2] [http://en.wikipedia.org/wiki/Aczel%27s_anti-
foundation_axiom](http://en.wikipedia.org/wiki/Aczel%27s_anti-
foundation_axiom)

[3] [http://www.amazon.com/Vicious-Circles-Center-Language-
Inform...](http://www.amazon.com/Vicious-Circles-Center-Language-
Information/dp/1575860082)

