Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-08T08:32:57.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparative uncertainty: theory and automation

Published online by Cambridge University Press:  01 February 2008

ANDREA CAPOTORTI  and
ANDREA FORMISANO
ANDREA CAPOTORTI
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, I-06123 Perugia, Italy Email: capotorti@dipmat.unipg.it; formis@dipmat.unipg.it
ANDREA FORMISANO
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, I-06123 Perugia, Italy Email: capotorti@dipmat.unipg.it; formis@dipmat.unipg.it Dipartimento di Informatica, Università di L'Aquila, Via Vetoio, I-67010 L'Aquila, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In recent decades, qualitative approaches to probabilistic uncertainty have received more and more attention. We propose a characterisation of partial preference orders through a uniform axiomatic treatment of a variety of qualitative uncertainty notions. To this end, we prove a representation result that connects qualitative notions of partial uncertainty to their numerical counterparts. We describe an executable specification, in the declarative framework of Answer Set Programming, that constitutes the core engine for qualitative management of uncertainty. Some basic reasoning tasks are also identified.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 57 - 79
Copyright
Copyright © Cambridge University Press2008

References

Baral, C. (2003) Knowledge representation, reasoning and declarative problem solving, Cambridge University Press.CrossRefGoogle Scholar
Bilgiç, T. (2001) Fusing interval preferences. In: Proc. of EUROFUSE Workshop on Preference Modelling and Applications. 253–258.Google Scholar
Brafman, R. I. and Tennenholtz, M. (1997) Modeling agents as qualitative decision makers. Artif. Intel. 94 217–268.Google Scholar
Capotorti, A., Coletti, G. and Vantaggi, B. (1998) Non additive ordinal relations representable by lower or upper probabilities. Kybernetika 34 (1)79–90.Google Scholar
Capotorti, A. and Vantaggi, B. (2000) Axiomatic characterization of partial ordinal relations. Internat. J. Approx. Reason. 24 207–219.CrossRefGoogle Scholar
Cheeseman, P. (1988) Discussion on the Paper by Lauritzen and Spiegelhalter. J. R. Statist. Soc. B 50 (2).Google Scholar
Choquet, G. (1954) Theory of capacities. Annales de l'institut Fourier 5 131–295.CrossRefGoogle Scholar
Coletti, G. (1990) Coherent qualitative probability. J. Math. Psych. 34 297–310.Google Scholar
Coletti, G. and Vantaggi, B. (2006) Representability of Ordinal Relation on a Set of Conditional Events. Theory and Decision 60 137–174.Google Scholar
Dantsin, E., Eiter, T., Gottlob, G. and Voronkov, A. (2001) Complexity and expressive power of logic programming. ACM Computing Surveys 33 (3)374–425.Google Scholar
deCooman, G. Cooman, G. (1997) Confidence relations and ordinal information. Inform. Sci. 104 241–278.Google Scholar
de Finetti, B. (1931) Sul significato soggettivo della probabilità. Fund. Math. 17 298–321. (English translation in Induction and Probability, CLUEB, Bologna, 1993.)CrossRefGoogle Scholar
de Finetti, B. (1974) Theory of Probability, Wiley.Google Scholar
Dovier, A., Formisano, A. and Pontelli, E. (2005) A comparison of CLP(FD) and ASP solutions to NP-complete problems. In: Proc. of ICLP05. Springer-Verlag Lecture Notes in Computer Science 3662.Google Scholar
Dubois, D. (1986) Belief structure, possibility theory and decomposable confidence measures on finite sets. Comput. Artif. Intell. 5 403–416.Google Scholar
Dubois, D., Fargier, H. and Perny, P. (2003) Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach. Artif. Intel. 148 219–260.CrossRefGoogle Scholar
Dubois, D., Fargier, H. and Prade, H. (1997a) Decision-making under ordinal preferences and uncertainty. In: AAAI Spring Symposium on Qualitative Preferences in Deliberation and Practical Reasoning 41–46.Google Scholar
Dubois, D., Fargier, H., Prade, H. and Perny, P. (2002)Qualitative decision theory: From Savage's axioms to nonmonotonic reasoning. JACM 49 455–495.Google Scholar
Dubois, D. and Prade, H. (1980) Fuzzy sets and systems: theory and applications, Academic Press.Google Scholar
Dubois, D., Prade, H. and Sabbadin, R. (1997b) A possibilistic logic machinery for qualitative decision. In: AAAI Spring Symposium on Qualitative Preferences in Deliberation and Practical Reasoning 47–54.Google Scholar
Ellsberg, D. (1961) Risk, ambiguity, and the Savage axioms. Quart. J. Econ. 75 643–669.Google Scholar
Fishburn, P. (1986) The axioms of subjective probability. Statist. Sci. 1 335–358.Google Scholar
Fox, C. R. (1999) Strength of evidence, judged probability, and choice under uncertainty. Cognitive Psych. 38 167–189.CrossRefGoogle ScholarPubMed
Fox, C. R. and See, K. E. (2003) Belief and preference in decision under uncertainty. In: Hardman, D. and Macchi, L. (eds.) Thinking: Psychological perspectives on reasoning, judgment and decision making, Wiley 273–314.Google Scholar
Gelfond, M. and Lifschitz, V. (1988) The stable model semantics for logic programming. In: Proc. of 5th ILPS Conf. 1070–1080.Google Scholar
Giang, P. H. and Shenoy, P. P. (2001) A comparison of axiomatic approaches to qualitative decision making under possibility theory. In: Proc. of 17th Conf. on Uncertainty in Artificial Intelligence UAI01162–170.Google Scholar
Halpern, J. Y. (1997) Defining relative likelihood in partially-ordered structures. J. of Artif. Intell. Res. 7 1–24.CrossRefGoogle Scholar
Jaumard, B., Hansen, P. and Poggi de Aragão, M. (1991) Column Generation Methods for Probabilistic Logic. J. on Computing 3 (2)135–148.Google Scholar
Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement under uncertainty: Heuristics and biases, Cambridge University Press.CrossRefGoogle Scholar
Kaplan, M. and Fine, T. (1977) Joint orders in comparative probability. Annals Prob. 5 161–179.Google Scholar
Klir, G. J. and Folger, T. A. (1988) Fuzzy sets, uncertainty, and information, Prentice-Hall.Google Scholar
Lehmann, D. (1996) Generalized qualitative probability: Savage revisited. In: Proc. of 12th Conf. on Uncertainty in Artificial Intelligence UAI96 381–388.Google Scholar
Lifschitz, V. (1999) Answer set planning. In: DeSchreye, D. Schreye, D. (ed.) Proc. of ICLP'99, The MIT Press 23–37.Google Scholar
Marek, W. and Truszczyński, M. (1999) Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, Springer-Verlag 375–398.CrossRefGoogle Scholar
Nguyen, H. T. and Walker, E. A. (1997) A first course in fuzzy logic, CRC Press.Google Scholar
Parsons, S. (1994) Some qualitative approaches to applying the Dempster-Shafer theory. Inform. Decis. Tech. 19 321–337.Google Scholar
Pradhan, M., Henrion, M., Provan, G., delFavero, B. Favero, B. and Huang, K. (1996) The sensitivity of belief networks to imprecise probabilities: An experimental investigation. Artif. Intel. 85 363–397.Google Scholar
Redelmeier, D. A., Koehler, D. J., Liberman, V. and Tversky, A. (1995) Probability judgment in medicine: Discounting unspecified possibilities. Med. Decis. Mak. 15 (3)227–230.Google Scholar
Savage, L. J. (1972) The foundations of statistics, Dover.Google Scholar
Shafer, G. (1976) A mathematical theory of evidence, Princeton University Press.CrossRefGoogle Scholar
Simons, P. (2000) Extending and implementing the stable model semantics, Ph.D. thesis, Helsinki University, Department of Computer Science and Engineering. (Tech. report HUT-TCS-A58.)Google Scholar
Suppes, P. (1974) The measurement of belief. J. R. Statist. Soc. B 36Google Scholar
Syrjänen, T. (1999) Lparse 1.0 user's manual. Available at http://www.tcs.hut.fi/Software/smodels.Google Scholar
Tversky, A. (1974) Assessing Uncertainty. J. R. Statist. Soc. B 36.CrossRefGoogle Scholar
Tversky, A. and Simonson, I. (1993) Context-dependent preferences. Manag. Sci. 39 (10).Google Scholar
Walley, P. (1996) Measures of uncertainty in expert systems. Artif. Intel. 83 1–58.CrossRefGoogle Scholar
Walley, P. and Fine, T. (1979) Varieties of modal (classificatory) and comparative probability. Synthese 41 321–374.Google Scholar
Wong, S. K. M., Yao, Y. Y., Bollmann, P. and Bürger, H. C. (1991) Axiomatization of qualitative belief structure. IEEE Trans. Sys. Man. Cyber. 21 726–734.CrossRefGoogle Scholar
Zadeh, L. A. (1965) Fuzzy sets. InfoR. and Control 8 338–353.CrossRefGoogle Scholar