Abstract
In the framework of quantitative possibility theory, two representation modes were developed: logical representation in term of quantitative possibilistic base and graphical representation in term of product-based possibilistic network. This article deals with logical and graphical representations of uncertain information around quantitative possibility theory. First, a deep analysis of relationships between these two forms of representational frameworks is provided. Then, in the logical setting, syntactical relations between penalty logic and quantitative possibilistic base are developed. Afterward, the relationship which exists between UCP networks and product-based possibilistic networks is pointed out in the graphical setting. These translations are useful for different applications and are interesting by taking advantage from each format at the inferential level. From these translations, we also exhibit the relation which is deduced, between UCP networks and penalty logic.
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
Preview
Unable to display preview. Download preview PDF.
References
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publ. Inc., San Mateo (1988)
Jensen, V.F.: An introduction to Bayesian Networks. UCL Press, University College London (1996)
Ben Amor, N., Benferhat, S., Mellouli, K.: Anytime propagation algorithm for min-based possibilistic graphs. Soft Computing, A fusion of foundations: methodologies and applications 8(2), 150–161 (2003)
Fonk, P.: Réseaux d’inférence pour le raisonnement possibiliste, PHD thesis, Université de liège, Faculté des sciences (1994)
Gebhardt, J., Kruse, R.: POSSINFER - A Software Tool for Possibilistic Inference. In: Dubois, D., Prade, H., Yager, R. (eds.) Fuzzy set Methods in Information Engineering, A Guided Tour of Applications (1997)
Dubois, D., Lang, J., Prade, H.: Possibilistic Logic. In: Gabbay, D., et al. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)
Pinkas, G.: Propositional nonmonotonic reasoning and inconsistency in symmetric neural networks. In: 12th IJCAI, Sydney Australia, pp. 525–530. Morgan-Kaufmann, San Francisco (1991)
Dupin De Saint-Cyr, F., Lang, J., Schiex, T.: Penalty logic and its link with Dempster-Shafer theory. In: Proceedings of 10th International Conference on Uncertainty in Artificial Intelligence (UAI 1994), pp. 204–211 (1994)
Gebhardt, J., Kruse, R.: Background and perspectives of possibilistic graphical models. In: 4th European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 1997). LNCS (LNAI), vol. 2143, pp. 108–121. Springer, Heidelberg (1997)
Gebhardt, J., Kruse, R.: Background and perspectives of possibilistic graphical models. In: 4th European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 1997). LNCS (LNAI), vol. 2143, pp. 108–121. Springer, Heidelberg (1997)
Dubois, D., Prade, H.: The logical view of conditioning and its application to possibility and evidence theorie. International Journal of Approximate Reasoning 4(1), 23–46 (1990)
De Campos, L.M., Huete, J.F.: Independence concepts in possibility theory. Fuzzy Sets and Systems (1998)
Ben Amor, N., Benferhat, S., Dubois, D., Geffner, H., Prade, H.: Independence in Qualitative Uncertainty Frameworks. In: Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), Breckenridge, Colorado, pp. 235–246. Morgan Kaufmann, San Francisco (April 2000)
Boutilier, C., Bacchus, F., Brafman, R.I.: UCP-Networks: A directed Graphical Representation of Conditional Utilities. In: Proceedings of the Seventeenth Annual Conference on Uncertainty Artificial Intelligence (UAI), Seattle, pp. 56–64 (2001)
Bacchus, F., Grove, A.: Graphical models for preference and utility. In: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI), Montreal, pp. 3–10 (1995)
Boutilier, C., Brafman, R.I., Hoos, H., Poole, D.: Reasoning with conditional ceteris paribus preference statements. In: Proceedings of 15th Conference on Uncertainty in Artificial Intelligence (UAI), Stockholm, pp. 71–80 (1999)
Benferhat, S., Dubois, D., Garcia, L., Prade, H.: On the transformation between possibilistic logic bases and possibilistic causal networks. International Journal of Approximate Reasoning 29, 135–173 (2002)
Benferhat, S., Khellaf-Haned, F., Mokhtari, A.: Product-based causal networks and quantitative possibilistic bases. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 13(5), 469–493 (2005)
Shenoy, P.P.: A valuation-based language for expert systems. International Journal of Approximate Reasoning 3, 383–411 (1989)
Shenoy, P.P.: Valutions-based systems for propositional logic. Methodologies for Intelligent Systems 5, 305–312 (1990)
Benferhat, S., Dubois, D., Prade, H.: From semantic to syntactic approaches to information combinaison in possibilistic logic. In: Bouchon-Meunier, B. (ed.) Aggregation and Fusion of Imperfect Information, pp. 141–161. Physica-Verlag, Heidelberg (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khellaf-Haned, H.F. (2011). Transformations around Quantitative Possibilistic Logic. In: Benferhat, S., Grant, J. (eds) Scalable Uncertainty Management. SUM 2011. Lecture Notes in Computer Science(), vol 6929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23963-2_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-23963-2_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23962-5
Online ISBN: 978-3-642-23963-2
eBook Packages: Computer ScienceComputer Science (R0)