Abstract
Conditional probabilities are one promising and widely used approach to model uncertainty in information systems. This paper discusses the DUCK-calculus, which is founded on the cautious approach to uncertain probabilistic inference. Based on a set of sound inference rules, derived probabilistic information is gained by local bounds propagation techniques. Precision being always a central point of criticism to such systems, we demonstrate that DUCK need not necessarily suffer from these problems. We can show that the popular Bayesian networks are subsumed by DUCK, implying that precise probabilities can be deduced by local propagation techniques, even in the multiply connected case. A comparative study with INFERNO and with inference techniques based on global operations-research techniques yields quite favorable results for our approach. Since conditional probabilities are also suited to model nonmonotonic situations by considering different contexts, we investigate the problems of maximal and relevant contexts, needed to draw default conclusions about individuals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K.A. Anderson and J.N. Hooker, Bayesian logic.Uncertainty in Knowledge-Based Systems, Workshop at the FAW. Ulm. FAW-B-90025. Vol. 1 (1990) pp. 1–54.
S.K. Andersen, K.G. Olesen, F.V. Jensen and F. Jensen, HUGIN a shell for building Bayesian belief universes for expert systems,Proc. 10th Int. Joint Conf. on Artificial Intelligence (1989) pp. 1080–1086.
F. Bacchus,Representing and Reasoning with Probabilistic Knowledge: A Logic Approach to Probabilities (MIT Press, Cambridge, 1990).
G. Brewka,Nonmonotonic Reasoning: Logical Foundations of Commonsense (Cambridge University Press, 1991).
G.F. Cooper, The computational complexity of probabilistic inference using Bayesian networks, Art. Int. 42 (1990) 393–405.
D. Dubois, H. Prade, L. Godo and R.L. Mantaras, A symbolic approach to reasoning with linguistic quantifiers,8th Conf. on Uncertainty in Artificial Intelligence, Stanford (1992) pp. 74–82.
R. Fagin and J.Y. Halpern, Uncertainty, belief and probability, Comp. Int. 7 (1991) pp. 160–173.
U. Güntzer, W. Kießling and H. Thöne. New directions for uncertainty reasoning in deductive databases,Proc. ACM SIGMOD Int. Conf. on Management of Data, Denver (1991) pp. 178–187.
H. Geffner and J. Pearl, Conditional entailment: bridging two approaches to default reasoning, Art. Int. 53 (1992) 209–244.
P. Kotler,Principles of Marketing (Prentice Hall, 1989).
R. Kruse, E. Schwecke and J. Heinsohn,Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods (Springer, 1991).
W. Kießling, G. Köstler and U. Güntzer, Fixpoint evaluation with subsumption for probabilistic uncertainty,Conf on “Datenbanksysteme in Büro. Technik und Wissenschaft” (BTW), Braunschweig (Springer, 1993) pp. 316–333.
W. Kießling, H. Thöne and U. Güntzer, Database support for problematic knowledge,Proc. Int. Conf. on Extending Database Technology (EDBT), Vienna (Springer, 1992) pp. 421–436.
H.E. Kyburg, Jr., The reference class, Philos. Sci. 50 (1983) 374–397.
H.E. Kyburg, Jr., The choice of the reference class, J. Appl. Non-Classical Logics 1 (1991) 154–157.
S.L. Lauritzen and D.J. Spiegelhalter, Local computation with probabilities on graphical structures and their application to expert systems, J. Roy. Statist. Soc. Series B (1988) 157–224.
L. Sombe, Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example, Int. J. Intell. Syst. 5 (1990) 323–472.
X. Liu and A. Gammerman, On the validity and applicability of the Inferno systems, in:Research and Development in Expert Systems III, eds. M.A. Bramer (1987) pp. 47–56.
R.P. Loui, Computing reference classes, in:Uncertainty in Artificial Intelligence 2, eds. J.F. Lemmer and L.N. Kanal (1988) pp. 273–289.
J. Minker, An overview of non-monotonic reasoning and logic programming, Technical Report CS-TR-2736, Univ. of Maryland (1991).
R.T. Ng and V.S. Subrahmanian, Empirical probabilities in monadic deductive databases,8th Conf. on Uncertainty in Artificial Intelligence, Stanford (1992) pp. 215–222.
N.J. Nilsson, Probabilistic logic, Art. Int. 28 (1986) 71–87.
J. Pearl,Probabilistic Reasoning in Intelligent Systems (Morgan Kaufmann, San Mateo, 1988).
J. Pearl, D. Geiger and T. Verma, Conditional independence and its representations,Readings in Uncertain Reasoning, eds. G. Shafer and J. Pearl (Morgan Kaufmann, 1990) pp. 55–60.
J.R. Quinlan, INFERNO: A cautious approach to uncertain inference, Comp. J. 26 (1983) 255–269.
M. v. Rimscha, The determination of comparative and lower probability,Uncertainty in Knowledge-Based Systems, Workshop at the FAW, Ulm, FAW-B-90025, Vol. 2 (1990) pp. 344–376.
H. Reichenbach,Theory of Probability (University of California Press, Berkeley, 1949).
D. Saunders, Improvements to INFERNO,Proc. 7th Conf. of the Society for the Study of Artificial Intelligence and Simulation of Behaviour, England (1989) pp. 105–112.
H. Thöne, U. Güntzer and W. Kießling, Numerical uncertainty reasoning with database support3rd Int. Workshop on Data, Expert Knowledge and Decisions, FAW-B-91023, Ulm (1991) pp. 161–170.
H. Thöne, U. Güntzer and W. Kießling, Towards precision of probabilistic bounds propagatio8th Conf. on Uncertainty in Artificial Intelligence, Stanford (1992) pp. 315–322.
UMIS Workshop, Uncertainty in information systems: from needs to solutions,Invitation Workshop. Palma de Mallorca (1992) and Catalina Island (1993).
L. Wittgenstein,Tractatus logico-philosophicus, Tagebücher 1914–1916, Philosophische Unters chugnen (Suhrkamp, Werkausgabe 1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thöne, H., Kießling, W. & Güntzer, U. On cautious probabilistic inference and default detachment. Ann Oper Res 55, 195–224 (1995). https://doi.org/10.1007/BF02031721
Issue Date:
DOI: https://doi.org/10.1007/BF02031721