Abstract
Partially preordered belief bases are very convenient for an efficient representation of incomplete knowledge. They offer flexibility and avoid to compare unrelated pieces of information. A number of inference relations for reasoning from partially preordered belief bases have been proposed. This paper sheds light on the following approaches: the partial binary lexicographic inference, the compatible-based lexicographic inference, the democratic inference, the compatible-based inclusion inference, the strong possibilistic inference and the weak possibilistic inference. In particular, we propose to analyse these inference relations according to two key dimensions: the computational complexity and the cautiousness. It turns out that almost all the corresponding decision problems are located at most at the second level of the polynomial hierarchy. As for the cautiousness results, they genereally extend those obtained in the particular case of totally preordered belief bases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benferhat, S., Dubois, D., Cayrol, C., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: IJCAI 1993, pp. 640–645 (1993)
Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: the prioritized case, vol. 24, pp. 473–511. Physica-Verlag, Heidelberg (1998)
Benferhat, S., Lagrue, S., Papini, O.: Reasoning with partially ordered information in a possibilistic framework. Fuzzy Sets and Systems 144, 25–41 (2004)
Brewka, G.: Preferred sutheories: an extende logical framework for default reasoning. In: IJCAI 1989, pp. 1043–1048 (1989)
Cayrol, C., Lagasquie-Schiex, M.-C., Schiex, T.: Nonmonotonic reasoning: From complexity to algorithms. Ann. Math. Artif. Intell 22(3-4), 207–236 (1998)
Cayrol, C., Royer, V., Saurel, C.: Management of preferences in assumption-based reasoning. In: Valverde, L., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 1992. LNCS, vol. 682, pp. 13–22. Springer, Heidelberg (1993)
da Costa, N.C.A.: Theory of inconsistent formal systems. Notre Dame Journal of Formal Logic 15, 497–510 (1974)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Handbook of Logic in Articial Intelligence and Logic Programming, vol. 3, pp. 439–513 (1994)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, New York (1979)
Junker, U., Brewka, G.: Handling partially ordered defaults in TMS. In: IJCAI 1989, pp. 1043–1048 (1989)
Lehmann, D.J.: Another perspective on default reasoning. Ann. Math. Artif. Intell 15(1), 61–82 (1995)
Nebel, B.: Belief revision and default reasoning: Syntax-based approaches. In: KR 1991, pp. 417–428 (1991)
Nebel, B.: How hard is it to revise a belief base? In: Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 77–145 (1998)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Resher, N., Manor, R.: On inference from inconsistent premises. Theory and Decision 1, 179–219 (1970)
Yahi, S., Benferhat, S., Lagrue, S., Sérayet, M., Papini, O.: A lexicographic inference for partially preordered belief bases. In: KR 2008, pp. 507–517 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benferhat, S., Yahi, S. (2009). Complexity and Cautiousness Results for Reasoning from Partially Preordered Belief Bases. In: Sossai, C., Chemello, G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science(), vol 5590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02906-6_70
Download citation
DOI: https://doi.org/10.1007/978-3-642-02906-6_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02905-9
Online ISBN: 978-3-642-02906-6
eBook Packages: Computer ScienceComputer Science (R0)