Top

Published in:

2015 | OriginalPaper | Chapter

Symbolic Possibilistic Logic: Completeness and Inference Methods

Authors : Claudette Cayrol, Didier Dubois, Fayçal Touazi

Published in: Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Learning Contextual Discounting and Contextual Reinforcement from Labelled Data

next chapter Probabilistic Common Knowledge Among Infinite Number of Agents

Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D., Hogger, C., Robinson, J., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)

Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Smets, P. (ed.) Handbook on Defeasible Reasoning and Uncertainty Management Systems. Quantified Representation of Uncertainty and Imprecision, vol. 1, pp. 169–226. Kluwer Academic Publ., Dordrecht (1998)

Dubois, D., Prade, H.: Possibilistic logic - an overview. In: Gabbay, D., Siekmann, J., Woods, J., (eds.): Computational Logic. Handbook of the History of Logic. vol. 9, pp. 283–342. Elsevier (2014)

Benferhat, S., Prade, H.: Encoding formulas with partially constrained weights in a possibilistic-like many-sorted propositional logic. In: Kaelbling, L.P., Saffiotti, A., (eds.): IJCAI, pp. 1281–1286 Professional Book Center (2005)

Halpern, J.Y.: Defining relative likelihood in partially-ordered preferential structures. J. Artif. Intell. Res. 7, 1–24 (1997)MathSciNetMATH

Benferhat, S., Lagrue, S., Papini, O.: A possibilistic handling of partially ordered information. In: Proceedings 19th Conference on Uncertainty in Artificial Intelligence UAI 2003, pp. 29–36 (2003)

Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32, 57–95 (1987)MathSciNetCrossRefMATH

Dubois, D., Fargier, H., Prade, H.: Ordinal and probabilistic representations of acceptance. J. Artif. Intell. Res. (JAIR) 22, 23–56 (2004)MathSciNetMATH

Benferhat, S., Dubois, D., Prade, H.: Nonmonotonic reasoning, conditional objects and possibility theory. Artif. Intell. 92, 259–276 (1997)MathSciNetCrossRefMATH

10.

McAreavey, K., Liu, W., Miller, P.: Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases. IJAR 55, 1659–1693 (2014)MathSciNetMATH

11.

Liffiton, M.H., Sakallah, K.A.: On finding all minimally unsatisfiable subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 173–186. Springer, Heidelberg (2005)CrossRef

12.

De Kleer, J.: An assumption-based tms. Artif. Intell. 28, 127–162 (1986)CrossRef

13.

De Kleer, J.: A general labeling algorithm for assumption-based truth maintenance. AAAI 88, 188–192 (1988)

14.

Dubois, D., Prade, H., Touazi, F.: Conditional Preference Nets and Possibilistic Logic. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS, vol. 7958, pp. 181–193. Springer, Heidelberg (2013)CrossRef

Title: Symbolic Possibilistic Logic: Completeness and Inference Methods
Authors: Claudette Cayrol
Didier Dubois
Fayçal Touazi
Publisher: Springer International Publishing
Book: Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Print ISBN: 978-3-319-20806-0

Electronic ISBN: 978-3-319-20807-7

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-20807-7_44

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner