=Paper=
{{Paper
|id=Vol-3835/invited1
|storemode=property
|title=Interval Orders and Biorders: Under-explored Playgrounds for NMR and Belief Revision (Invited Talk, Abstract)
|pdfUrl=https://ceur-ws.org/Vol-3835/invited1.pdf
|volume=Vol-3835
|authors=Richard Booth
|dblpUrl=https://dblp.org/rec/conf/nmr/Booth24
}}
==Interval Orders and Biorders: Under-explored Playgrounds for NMR and Belief Revision (Invited Talk, Abstract)==
<pdf width="1500px">https://ceur-ws.org/Vol-3835/invited1.pdf</pdf>
<pre>
                         Interval Orders and Biorders: Under-explored Playgrounds for
                         NMR and Belief Revision (Invited Talk, Abstract)
                         Richard Booth
                         School of Computer Science and Informatics, Cardiff University


                                         Abstract
                                         The notion of orderings over possible worlds to represent comparative normality or plausibility is a fundamental tool in the study
                                         of semantics for nonmonotonic reasoning (NMR) and belief revision (BR). The dominant model is that of a total preorder, which is
                                         central to AGM belief revision and to rational consequence in KLM-style preferential reasoning. Other, more general, types of orderings,
                                         specifically interval orders and biorders, have been studied in the theory of rational choice, but have received less attention in NMR and
                                         BR. Interval orders, introduced by Fishburn, associate to each possible world a non-negative interval of plausibility, while biorders,
                                         studied by Aleskerov, Bouyssou and Monjardet, generalise interval orders by allowing the intervals to be have negative length. This talk,
                                         based on recent and ongoing collaboration with Ivan Varzinczak, will focus on these lesser-known kinds of ordering. Specifically we
                                         will look at how interval orders can be used to address the problem of conditional inference, and how biorders offer a fresh perspective
                                         on credibility-limited belief revision.




                          22nd International Workshop on Nonmonotonic Reasoning, November 2-4,
                          2024, Hanoi, Vietnam
                          $ BoothR2@cardiff.ac.uk (R. Booth)
                          € https://profiles.cardiff.ac.uk/staff/boothr2 (R. Booth)
                           0000-0002-6647-6381 (R. Booth)
                                     © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License
                                     Attribution 4.0 International (CC BY 4.0).



CEUR
                  ceur-ws.org
Workshop      ISSN 1613-0073
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