The abnormality predicate

The author has suggested earlier that the various nonmonotonic reasoning formalisms are converging towards probability. Here, he discusses the idea of randomness: using a definition by Kyburg as a benchmark, he describes how it appears in various nonmonotonic reasoning formalisms, in particular, circumscription. It is argued that behind the complexity of circumscription lie the simple notions of random sampling and statistically founded beliefs. The latter is implemented through a device known as the abnormality predicate which appears in various guises in the nonmonotonic reasoning literature. Another view of this study is that randomness provides a universal conjecture for nonmonotonic theories. Default theories can be interpreted as jumping to the conclusion that an entity is a random member of a certain class.<<ETX>>

[1]  David Poole,et al.  What the Lottery Paradox Tells Us About Default Reasoning , 1989, KR.

[2]  Henry E. Kyburg,et al.  Probabilistic inference and non-monotonic inference , 1988, UAI.

[3]  James P. Delgrande,et al.  An Approach to Default Reasoning Based on a First-Order Conditional Logic: Revised Report , 1987, Artif. Intell..

[4]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[5]  Gerhard Brewka,et al.  Tweety - Still Flying: Some Remarks on Abnormal Birds Applicable Rules and a Default Prover , 1986, AAAI.

[6]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[7]  Raymond Reiter,et al.  On Interacting Defaults , 1981, IJCAI.

[8]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[9]  Eric Neufeld,et al.  Defaults and Probabilities; Extensions and Coherence , 1989, KR.

[10]  Judea Pearl,et al.  Probabilistic Semantics for Nonmonotonic Reasoning: A Survey , 1989, KR.

[11]  Eric Neufeld,et al.  Conditioning on Disjunctive Knowledge: Simpson's Paradox in Default Logic , 1989, UAI.

[12]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[13]  Robert C. Moore.  Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[14]  B. Sauphanor.  The logical foundations of statistical inference , 1974 .

[15]  Fahiem Bacchus.  A Modest, but Semantically Well Founded, Inheritance Reasoner , 1989, IJCAI.

[16]  Henry E. Kyburg,,et al.  The Reference Class , 1983, Philosophy of Science.