Abstract
Possibilistic logic is a weighted logic for dealing with incomplete and uncertain information by assigning weights to propositional formulas. A possibilistic knowledge base (KB) is a finite set of such formulas. The problem of revising a possibilistic KB by possibilistic formula is not new. However, existing approaches are limited in two ways. Firstly, they suffer from the so-called drowning effect. Secondly, they handle certain and uncertain formulas separately and most only handle certain inputs. In this paper, we propose a unified approach that caters for revision by both certain and uncertain inputs and relieves the drowning effect. The approach is based on a refined inconsistency degree function called compatibility degree which provides a unifying framework (called cd-revision) for defining specific revision operators for possibilistic KBs. Our definition leads to an algorithm for computing the result of the proposed revision. The revision operators defined in cd-revision possess some desirable properties including those from classic belief revision and some others that are specific to possibilistic revision. We also show that several major revision operators for possibilistic, stratified and prioritised KBs can be embedded in cd-revision.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50(2), 510–530 (1985)
Bauters, K., Schockaert, S., Cock, M., Vermeir, D.: Possible and necessary answer sets of possibilistic answer set programs. In: Proceedings of the 24th International Conference on Tools with Artificial Intelligence, ICTAI, pp. 836–843 (2012)
Bauters, K., Schockaert, S., Cock, M., Vermeir, D.: Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions. Int. J. Approx. Reason. 55(2), 739–761 (2014)
Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. IJCAI 93, 640–645 (1993)
Benferhat, S., da Costa Pereira, C., Tettamanzi, A.: Hybrid possibilistic conditioning for revision under weighted inputs. In: 20th European Conference on Artificial Intelligence, pp. 151–156 (2012)
Benferhat, S., da Costa Pereira, C., Tettamanzi, A.: Syntactic computation of hybrid possibilistic conditioning under uncertain inputs. In: Proceedings of the Twenty-Third international joint conference on Artificial Intelligence, pp. 739–745 (2013)
Benferhat, S., Dubois, D., Prade, H., Williams, M.: A practical approach to revising prioritized knowledge bases. Stud. Logica 70(1), 105–130 (2002)
Benferhat, S., Dubois, D., Prade, H., Williams, M.: A framework for iterated belief revision using possibilistic counterparts to jeffrey’s rule. Fundamenta Informaticae 99(2), 147 (2010)
Brewka, G.: Preferred subtheories: an extended logical framework for default reasoning. IJCAI 89, 1043–1048 (1989)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic (1994)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., et al. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, New York (1997)
Dubois, D., Prade, H.: A synthetic view of belief revision with uncertain inputs in the framework of possibility theory. Int. J. Approx. Reason. 17, 295–324 (1997)
Dubois, D., Prade, H.: Generalized Possibilistic Logic, pp. 428–432. Springer, Berlin (2011)
Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artif. Intell. 52(3), 263–294 (1992)
Ma, J., Liu, W.: A framework for managing uncertain inputs: an axiomization of rewarding. Int. J. Approx. Reason. 52(7), 917–934 (2011)
Nebel, B.: Belief revision and default reasoning: syntax-based approaches. In: KR, pp. 417–428 (1991)
Nebel, B.: How hard is it to revise a belief base? In: Dubois, D., Prade, H. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Springer, Netherlands (1998)
Qi, G.: A semantic approach for iterated revision in possibilistic logic. In: Proceedings of the 23rd AAAI Conference on Artificial Intelligence, pp. 523–528 (2008)
Qi, G., Wang, K.: Conflict-based belief revision operators in possibilistic logic. In: AAAI (2012)
Acknowledgement
We would like to thank three anonymous referees for their constructive comments. This work was supported by Australian Research Council (ARC) under grant DP130102302.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Jin, Y., Wang, K., Wang, Z., Zhuang, Z. (2016). Revising Possibilistic Knowledge Bases via Compatibility Degrees. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-48758-8_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48757-1
Online ISBN: 978-3-319-48758-8
eBook Packages: Computer ScienceComputer Science (R0)