Describing and quantifying contradiction between pieces of evidence via Belnap Dunn logic and Dempster-Shafer theory

Marta Bı́lková, Sabine Frittella, Daniil Kozhemiachenko, Ondrej Majer, Krishna Manoorkar
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:37-47, 2023.

Abstract

Belnap Dunn logic is a four-valued logic introduced to model reasoning with incomplete or contradictory information. In this article, we show how Dempster-Shafer theory can be used over Belnap Dunn logic in order to formalise reasoning with incomplete and/or contradictory pieces of evidence. First, we discuss how to encode different kinds of evidence, and how to interpret the resulting belief and plausibility functions. Then, we discuss the behaviour of Dempster’s rule in this framework and present a variation of the rule. Finally, we show how to construct credal sets of classical probability measures based on this kind of evidence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-bilkova23a, title = {Describing and quantifying contradiction between pieces of evidence via {B}elnap {D}unn logic and {D}empster-{S}hafer theory}, author = {B\'\ilkov\'a, Marta and Frittella, Sabine and Kozhemiachenko, Daniil and Majer, Ondrej and Manoorkar, Krishna}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {37--47}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/bilkova23a/bilkova23a.pdf}, url = {https://proceedings.mlr.press/v215/bilkova23a.html}, abstract = {Belnap Dunn logic is a four-valued logic introduced to model reasoning with incomplete or contradictory information. In this article, we show how Dempster-Shafer theory can be used over Belnap Dunn logic in order to formalise reasoning with incomplete and/or contradictory pieces of evidence. First, we discuss how to encode different kinds of evidence, and how to interpret the resulting belief and plausibility functions. Then, we discuss the behaviour of Dempster’s rule in this framework and present a variation of the rule. Finally, we show how to construct credal sets of classical probability measures based on this kind of evidence.} }
Endnote
%0 Conference Paper %T Describing and quantifying contradiction between pieces of evidence via Belnap Dunn logic and Dempster-Shafer theory %A Marta Bı́lková %A Sabine Frittella %A Daniil Kozhemiachenko %A Ondrej Majer %A Krishna Manoorkar %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-bilkova23a %I PMLR %P 37--47 %U https://proceedings.mlr.press/v215/bilkova23a.html %V 215 %X Belnap Dunn logic is a four-valued logic introduced to model reasoning with incomplete or contradictory information. In this article, we show how Dempster-Shafer theory can be used over Belnap Dunn logic in order to formalise reasoning with incomplete and/or contradictory pieces of evidence. First, we discuss how to encode different kinds of evidence, and how to interpret the resulting belief and plausibility functions. Then, we discuss the behaviour of Dempster’s rule in this framework and present a variation of the rule. Finally, we show how to construct credal sets of classical probability measures based on this kind of evidence.
APA
Bı́lková, M., Frittella, S., Kozhemiachenko, D., Majer, O. & Manoorkar, K.. (2023). Describing and quantifying contradiction between pieces of evidence via Belnap Dunn logic and Dempster-Shafer theory. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:37-47 Available from https://proceedings.mlr.press/v215/bilkova23a.html.

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