LUW Dec 8, 4pm CET / Measuring Inconsistency in Generalized Propositional Logic

[jean-yves beziau]

The next Logica Universalis Webinar session will take place next
Wednesday,  Dec 8, at 4pm CET with the talk
 "Measuring Inconsistency in Generalized Propositional Logic"
by John Grant (University of Maryland, USA)

Abstract: Consistency is one of the key concepts of logic; logicians have
put a great deal of effort into proving the consistency of many logics.
Understanding what causes inconsistency is also important; some logicians
have developed paraconsistent logics that, unlike classical logics, allow
some contradictions without making all formulas provable. Another direction
of research studies inconsistency by measuring the amount of inconsistency
of sets of formulas. While the initial attempt in 1978 was too ambitious in
trying to do this for first-order logic, this research got a substantial
boost when an inconsistency measure was proposed for propositional logic in
2002. Since then, researchers in logic and artificial intelligence (AI
systems need the capability to deal with inconsistency) have made many
interesting proposals and found related issues. Almost all of this work has
been done for propositional logic. The purpose of this paper is to extend
inconsistency measures to logics that also contain operators, such as modal
operators. We use the terminology “generalized propositional logic” for
such logics. We show how to extend propositional inconsistency measures to
sets of formulas in any such generalized propositional logic. Examples are
used to illustrate how various modal operators, including spatial and tense
operators, fit into this framework. We also show that the addition of
operators leads to a weak type of inconsistency. In all cases, the
calculations for several inconsistency measures are given.
https://link.springer.com/article/10.1007/s11787-020-00256-z

Associate Organization: World Association of Paraconsistency (WAP)
http://www.paraconsistency.org/
presented by Maria Martinez-Ordaz
https://www.mariamartinezordaz.com/

To attend, register here:
https://www.springer.com/journal/11787/updates/18988758

Best Wishes
Jean-Yves Beziau
Organizer of the Logica Universalis Webinar
President of Logica Universalis Association
http://www.logica-universalis.org/LUAD
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