Abstract
Inductive inference operators generate non-monotonic inference relations on the basis of a set of conditionals. Examples include rational closure, system P and lexicographic inference. For most of these systems, inference has a high worst-case computational complexity. Recently, the notion of syntax splitting has been formulated, which allows restricting attention to subsets of conditionals relevant for a given query. In this paper, we define algorithms for inductive inference that take advantage of syntax splitting in order to obtain more efficient decision procedures. In particular, we show that relevance allows to use the modularity of knowledge base is a parameter that leads to tractable cases of inference for inductive inference operators such as lexicographic inference.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In [24], conditionals can be assigned an additional rank \(\infty \) to allow for the modelling of strict conditionals. For simplicity, we do not consider strict conditionals, but the results here can be easily adapted to allow them.
References
Britz, K., Casini, G., Meyer, T., Moodley, K., Sattler, U., Varzinczak, I.: Rational defeasible reasoning for description logics. University of Cape Town, Technical report (2018)
Britz, K., Casini, G., Meyer, T., Varzinczak, I.: A KLM perspective on defeasible reasoning for description logics. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, A.-Y., Wolter, F. (eds.) Description Logic, Theory Combination, and All That. LNCS, vol. 11560, pp. 147–173. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22102-7_7
Casini, G., Meyer, T., Varzinczak, I.: Taking defeasible entailment beyond rational closure. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 182–197. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_12
Casini, G., Straccia, U.: Lexicographic closure for defeasible description logics. In: Proceedings of Australasian Ontology Workshop, vol. 969, pp. 28–39 (2012)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity, vol. 4. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4471-5559-1
Eiter, T., Lukasiewicz, T.: Default reasoning from conditional knowledge bases: complexity and tractable cases. Artif. Intell. 124(2), 169–241 (2000)
de Finetti, B.: Theory of Probability, 2 vols. (1974)
Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. AI 84(1–2), 57–112 (1996)
Gottlob, G., Szeider, S.: Fixed-parameter algorithms for artificial intelligence, constraint satisfaction and database problems. Comput. J. 51(3), 303–325 (2008)
Haldimann, J., Beierle, C.: Inference with system W satisfies syntax splitting. arXiv preprint arXiv:2202.05511 (2022)
Heyninck, J., Kern-Isberner, G., Meyer, T.: Lexicographic entailment, syntax splitting and the drowning problem. In: Raedt, L.D. (ed.) Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI-22, pp. 2662–2668. International Joint Conferences on Artificial Intelligence Organization (2022). https://doi.org/10.24963/ijcai.2022/369
Kern-Isberner, G.: Handling conditionals adequately in uncertain reasoning and belief revision. J. Appl. Non-Classical Logics 12(2), 215–237 (2002)
Kern-Isberner, G., Beierle, C., Brewka, G.: Syntax splitting= relevance+ independence: new postulates for nonmonotonic reasoning from conditional belief bases. In: Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning, vol. 17, pp. 560–571 (2020)
Kern-Isberner, G., Brewka, G.: Strong syntax splitting for iterated belief revision. In: Sierra, C. (ed.) Proceedings International Joint Conference on Artificial Intelligence, IJCAI 2017, pp. 1131–1137. ijcai.org (2017)
Komo, C., Beierle, C.: Nonmonotonic reasoning from conditional knowledge bases with system W. Ann. Math. Artif. Intell. 90, 1–38 (2021). https://doi.org/10.1007/s10472-021-09777-9
Konev, B., Lutz, C., Ponomaryov, D.K., Wolter, F.: Decomposing description logic ontologies. In: KR (2010)
Konev, B., Lutz, C., Walther, D., Wolter, F.: Model-theoretic inseparability and modularity of description logic ontologies. Artif. Intell. 203, 66–103 (2013)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)
Kutsch, S.: InfOCF-Lib: a java library for OCF-based conditional inference. In: DKB/KIK@ KI, pp. 47–58 (2019)
Lehmann, D.: Another perspective on default reasoning. Ann. Math. Artif. Intell. 15(1), 61–82 (1995). https://doi.org/10.1007/BF01535841
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992)
Makinson, D.: General theory of cumulative inference. In: Reinfrank, M., de Kleer, J., Ginsberg, M.L., Sandewall, E. (eds.) NMR 1988. LNCS, vol. 346, pp. 1–18. Springer, Heidelberg (1989). https://doi.org/10.1007/3-540-50701-9_16
Marek, V.W.: Introduction to Mathematics of Satisfiability. Chapman and Hall/CRC, London (2009)
Morris, M., Ross, T., Meyer, T.: Algorithmic definitions for KLM-style defeasible disjunctive datalog. South African Comput. J. 32(2), 141–160 (2020)
Parikh, R.: Beliefs, belief revision, and splitting languages. Logic Lang. Comput. 2(96), 266–268 (1999)
Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics. The University of Western Ontario Series in Philosophy of Science, vol. 42, pp. 105–134. Springer, Heidelberg (1988). https://doi.org/10.1007/978-94-009-2865-7_6
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Heyninck, J., Meyer, T. (2022). Relevance in the Computation of Non-monotonic Inferences. In: Pillay, A., Jembere, E., Gerber, A. (eds) Artificial Intelligence Research. SACAIR 2022. Communications in Computer and Information Science, vol 1734. Springer, Cham. https://doi.org/10.1007/978-3-031-22321-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-031-22321-1_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-22320-4
Online ISBN: 978-3-031-22321-1
eBook Packages: Computer ScienceComputer Science (R0)