Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is, general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, especially characteristic of common-sense contexts. However, it is not easy for a modeller to choose a formalism that is a good fit for a particular domain from an ontological point of view. In this paper, we present a framework for formulating the characteristics of defeasibility and reasoning with exceptions which exploits and incorporates related fields of inquiry, including generics, ceteris paribus laws, and a truthmaking theory for generalisations. The resulting theory allows a grounded comparison of the various formalisms and reveals their ontological commitments. To illustrate and apply this framework, we compare the main systems of non-monotonic logics, showing the differences that may occur from an ontological perspective.
BochmanA. (2018). Nonmonotonic reasoning. In S. O. Hansson & V. F. Hendricks (Eds.), Introduction to formal philosophy (pp. 93–104). Springer International Publishing.
2.
BonattiP. A.LutzC.WolterF. (2006). Description logics with circumscription. In KR2006 (pp. 400–410). AAAI Press.
3.
BorgoS.PorelloD.TroquardN. (2014). Logical operators for ontological modeling. In FOIS. Frontiers in Artificial Intelligence and Applications, (Vol. 267, pp. 23–36). IOS Press.
4.
BrachmanR. J.LevesqueH. J. (2004). Chapter 11 - defaults. In Knowledge representation and reasoning, The Morgan Kaufmann Series in Artificial Intelligence (pp. 205–235). Morgan Kaufmann. ISBN 978-1-55860-932-7. https://doi.org/10.1016/B978-155860932-7/50096-0
5.
BritzK.CasiniG.MeyerT.MoodleyK.SattlerU.VarzinczakI. (2020). Principles of klm-style defeasible description logics. ACM Transactions on Computational Logic, 22(1), 1–46 .https://doi.org/10.1145/3420258
6.
CarnapR. (1937). Logical syntax of language. London: Routledge.
KonoligeK. (1994). Autoepistemic logic. In Handbook of logic in artificial intelligence and logic programming (Vol. 3): Nonmonotonic reasoning and uncertain reasoning (pp. 217–295). USA: Oxford University Press, Inc. ISBN 0198537476.
14.
KoonsR. (2021). Defeasible reasoning. In E. N. Zalta (Ed.) The stanford encyclopedia of philosophy, Fall 2021 edition. Metaphysics Research Lab, Stanford University.
KutzO.MossakowskiT.LückeD. (2010). Carnap, goguen, and the hyperontologies: Logical pluralism and heterogeneous structuring in ontology design. Logica Universalis, 4(2), 255–333.
17.
LehmannD.MagidorM. (1990). Preferential logics: the predicate calculus case. In: Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge, TARK ’90 (pp. 57–72). San Francisco, CA, USA: Morgan Kaufmann Publishers Inc. ISBN 1558801058.
LeslieS. J. (2007). Generics and the structure of the mind. Philosophical Perspectives, 21, 375–403.
20.
LeslieS. J.LernerA. (2022). Generic generalizations. In E. N. Zalta & U. Nodelman (Eds.), The stanford encyclopedia of philosophy, Fall 2022 edition. Metaphysics Research Lab, Stanford University.
21.
LifschitzV. (1994). Circumscription. In Handbook of logic in artificial intelligence and logic programming (Vol. 3): Nonmonotonic reasoning and uncertain reasoning (pp. 297–352). USA: Oxford University Press, Inc. ISBN 0198537476.
22.
LinneboØ. (2022). Generality explained. Journal of Philosophy, 119(7), 349–379.
Osta-VélezM.GärdenforsP. (2022). Nonmonotonic reasoning, expectations orderings, and conceptual spaces. The Journal of Logic, Language and Information, 31(1), 77–97. https://doi.org/10.1007/S10849-021-09347-6
27.
PelletierF. J.AsherN. (1997). Generics and defaults. In J. van Benthem & A. ter Meulen (Eds.), Handbook of logic and language (pp. 1125–1177). Amsterdam: North-Holland.
28.
PooleD. (1994). Default logic. In Handbook of logic in artificial intelligence and logic programming (Vol. 3): Nonmonotonic reasoning and uncertain reasoning (pp. 189–215). USA: Oxford University Press, Inc. ISBN 0198537476.
29.
ReiterR. (1977). On closed world data bases. In Logic and data bases, Advances in Data Base Theory (pp. 55–76). New York: Plemum Press.
ReutlingerA.SchurzG.HüttemannA.JaagS. (2024). Ceteris paribus laws. In E. N. Zalta & U. Nodelman (Eds.), The stanford encyclopedia of philosophy (Spring 2024 edition). Metaphysics Research Lab, Stanford University.
33.
SaccoG.BozzatoL.KutzO. (2023a). Defeasible reasoning with prototype descriptions: First steps. In Proceedings of the 36th international workshop on description logics (DL 2023) co-located with the 20th international conference on principles of knowledge representation and reasoning and the 21st international workshop on non-monotonic reasoning (KR 2023 and NMR 2023), Rhodes, Greece, September 2–4, 2023, CEUR Workshop Proceedings (Vol. 3739). CEUR-WS.org. https://ceur-ws.org/Vol-3739/paper-9.pdf
34.
SaccoG.BozzatoL.KutzO. (2023b). Generics in defeasible reasoning: Exceptionality, gradability and content sensitivity. In Proceedings of the joint ontology workshops 2023 Episode IX:co-located with the 13th international conference on formal ontology in information systems (FOIS 2023), Sherbrooke, Québec, Canada, July 19-20, 2023, CEUR Workshop Proceedings (Vol. 3637). CEUR-WS.org.
35.
SaccoG.BozzatoL.KutzO. (2024). Know your exceptions. In C. Trojahn, D. Porello & P. P. F. Barcelos (Eds.), Formal ontology in information systems - Proceedings of the 14th International conference (FOIS 2024), Enschede, The Netherlands, July 2024, Frontiers in Artificial Intelligence and Applications, (Vol. 394, pp. 254–267). IOS Press. https://doi.org/10.3233/FAIA241312
StrasserC.AntonelliG. A. (2019). Non-monotonic Logic. In E. N. Zalta (ed.) The stanford encyclopedia of philosophy, (Summer 2019 edition). Metaphysics Research Lab, Stanford University.
40.
ToyoshimaF.NikiS. (2021). Semantics matters: A new light on ontological commitments of logics. In JOWO. CEUR Workshop Proceedings, (Vol. 2969). CEUR-WS.org.
41.
WesterståhlD. (2024). Generalized quantifiers. In E. N. Zalta & U. Nodelman (Eds.), The stanford encyclopedia of philosophy, Fall 2024 edition. Metaphysics Research Lab, Stanford University.
42.
WheelerG. (2007). A review of the lottery paradox. In W. Harper & G. Wheeler (Eds.), Probability and inference: Essays in honour of henry E. Kyburg, Jr. College Publications.
