Probabilistic Argumentation Systems with Decision Variables

The general concept of probabilistic argumentation systems PAS is restricted to the two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Here, we introduce a third kind into PAS: so-called decision variables. This new kind allows to describe the decisions a user can make to react on some state of the system. Such a decision allows then possibly to reach a certain goal state of the system. Further, we present an algorithm, which exploits the special structure of PAS with decision variables. Some results related with this paper were published in (Anrig and Baziukaite, 2003a).

[1]  Jürg Kohlas,et al.  Zuverlässigkeit und Verfügbarkeit , 1987 .

[2]  Jürg Kohlas,et al.  Propositional Information Systems , 1999, J. Log. Comput..

[3]  Jürg Kohlas,et al.  Probabilistic Argumentation and Decision System An Application to Reliability Theory , 2002 .

[4]  Bernhard Anrig,et al.  Probabilistic Argumentation and Decision System , 2003 .

[5]  Klaus D. Heidtmann.  Zuverlässigkeitsbewertung technischer Systeme , 1997 .

[6]  Jürg Kohlas,et al.  Model-Based Diagnostics and Probabilistic Assumption-Based Reasoning , 1998, Artif. Intell..

[7]  Adnan Darwiche,et al.  A compiler for deterministic, decomposable negation normal form , 2002, AAAI/IAAI.

[8]  Rolf Haenni,et al.  Probabilistic Argumentation Systems , 2003 .

[9]  Klaus D. Heidtmann,et al.  Smaller sums of disjoint products by subproduct inversion , 1989 .

[10]  Jürg Kohlas,et al.  Probabilistic Argumentation Systems and Abduction , 2002, Annals of Mathematics and Artificial Intelligence.

[11]  Rolf Haenni,et al.  Implementing belief function computations , 2003, Int. J. Intell. Syst..

[12]  Rolf Haenni,et al.  Probabilistic Argumentation Systems : a New Perspective on Dempster-Shafer Theory ∗ , 2001 .

[13]  Bernhard Anrig,et al.  Probabilistic model-based diagnostics , 2000 .

[14]  Frank Beichelt.  Zuverlässigkeits- und Instandhaltungstheorie , 1993 .

[15]  Prakash P. Shenoy,et al.  COMPUTING MARGINALS USING LOCAL COMPUTATION , 1996 .

[16]  J. Abraham.  An Improved Algorithm for Network Reliability , 1979, IEEE Transactions on Reliability.

[17]  Pierre Marquis,et al.  A Perspective on Knowledge Compilation , 2001, IJCAI.

[18]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[19]  Jürg Kohlas.  Information algebras - generic structures for inference , 2003, Discrete mathematics and theoretical computer science.

[20]  Jürg Kohlas,et al.  Model‐based reliability and diagnostics: A common framework for reliability and diagnostics , 2003, Int. J. Intell. Syst..

[21]  P. Monney,et al.  A generalization of the algorithm of Heidtmann to non-monotone formulas , 1996 .

[22]  J. Kohlas,et al.  A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence , 1995 .

[23]  Rolf Haenni,et al.  Cost-bounded argumentation , 2001, Int. J. Approx. Reason..

[24]  Jürg Kohlas,et al.  A Mathematical Theory of Hints , 1995 .

[25]  Prakash P. Shenoy,et al.  Computation in Valuation Algebras , 2000 .

[26]  Gregory M. Provan,et al.  A logic-based analysis of Dempster-Shafer theory , 1990, Int. J. Approx. Reason..

[27]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[28]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[29]  A Query-Driven Anytime Algorithm For Assumption-Based Reasoning Subjects , 2001 .

[30]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .