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The complexity of logic-based abduction
Open accessAbstract
Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction . Candidates for abductive explanations are usually subjected to minimality criteria such as subset-minimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.
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Cited by
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Dantsin, E., Eiter, T., Gottlob, G., & Voronkov, A. (2001) · ACM Computing Surveys · doi:10.1145/502807.502810 · Cited by 739
Self-citationAbductive reasoning in logistics research
Kovács, G., & Spens, K. M. (2005) · International Journal of Physical Distribution & Logistics Management · doi:10.1108/09600030510590318 · Cited by 688
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Solé, M., Muntés-Mulero, V., Rana, A. I., & Estrada, G. (2017) · arXiv · doi:10.48550/arxiv.1701.08546 · Cited by 74
Readiness of Quantum Optimization Machines for Industrial Applications
Perdomo-Ortiz, A., Feldman, A., Ozaeta, A., Isakov, S. V., Zhu, Z., O’Gorman, B., Katzgraber, H. G., Diedrich, A., Neven, H., de Kleer, J., et al. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.014004 · Cited by 62
Abduction-Based Explanations for Machine Learning Models
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Metadata
- Authors
- Eiter, T., & Gottlob, G.
- Venue
- Journal of the ACM
- Published
- 1995-01-03
- Volume
- 42
- Issue
- 1
- Pages
- 3-42
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2100657934
- Cited by
- 422
- References
- 0
- FWCI
- 10.05
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Eiter, T., & Gottlob, G. (1995). The complexity of logic-based abduction. Journal of the ACM. https://doi.org/10.1145/200836.200838
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