Handling conditionals adequately in uncertain reasoning and belief revision

Conditionals (“if-then-rules”) are most important objects in knowledge representation, commonsense reasoning and belief revision. Due to their non-classical nature, however, they are not easily dealt with. This paper presents a new approach to conditionals, which is apt to capture their dynamic power particularly well. We show how this approach can be applied to represent conditional knowledge inductively, and to guide revisions of epistemic states by sets of (propositional or conditional) beliefs. In particular, we generalize system-Z* as an appropriate counterpart to maximum entropy-representations in a semi-quantitative setting, and provide a theoretical justification to make its basic ideas usable also for belief revision.

[1]  Gabriele Kern-Isberner,et al.  Characterizing the Principle of Minimum Cross-Entropy Within a Conditional-Logical Framework , 1998, Artif. Intell..

[2]  Gabriele Kern-Isberner.  Representing and Learning Conditional Information in Possibility Theory , 2001, Fuzzy Days.

[3]  P. Calabrese.  Deduction and Inference Using Conditional Logic and Probability , 1991 .

[4]  I. Good.  Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables , 1963 .

[5]  Emil Weydert.  Rankings we prefer: a rational minimal construction semantics for default reasoning , 2001 .

[6]  Didier Dubois,et al.  Non-standard theories of uncertainty of plausible reasoning , 1997 .

[7]  Emil Weydert.  SYSTEM JZ - How to Build a Canonical Ranking Model of a Default Knowledge Base , 1998, KR.

[8]  Emil Weydert,et al.  System J - Revision Entailment. Default Reasoning through Ranking Measure Updates , 1996, FAPR.

[9]  Judea Pearl,et al.  On the Logic of Iterated Belief Revision , 1994, Artif. Intell..

[10]  Gabriele Kern-Isberner.  Postulates for Conditional Belief Revision , 1999, IJCAI.

[11]  Craig Boutilier,et al.  Revision by Conditional Beliefs , 1993, AAAI.

[12]  Gabriele Kern-Isberner,et al.  Solving the Inverse Representation Problem , 2000, ECAI.

[13]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[14]  Didier Dubois,et al.  Nonmonotonic Reasoning, Conditional Objects and Possibility Theory , 1997, Artif. Intell..

[15]  H. Jeffreys,et al.  Theory of probability , 1896 .

[16]  Moisés Goldszmidt,et al.  A Maximum Entropy Approach to Nonmonotonic Reasoning , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Alessandro Saffiotti,et al.  Belief functions and default reasoning , 1995, Artif. Intell..

[18]  R. Lyndon,et al.  Combinatorial Group Theory , 1977 .

[19]  Gabriele Kern-Isberner.  A Structural Approach to Default Reasoning , 2002, KR.

[20]  Simon Parsons,et al.  Maximum Entropy and Variable Strength Defaults , 1999, IJCAI.

[21]  Gabriele Kern-Isberner.  The Principle of Conditional Preservation in Belief Revision , 2002, FoIKS.

[22]  J. Paris.  The Uncertain Reasoner's Companion: A Mathematical Perspective , 1994 .

[23]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision , 2001, Lecture Notes in Computer Science.

[24]  Emil Weydert.  Default epistemology rankings, reasoning and revision (a very preliminary account) , 2002, NMR.