On Generation of Cumulative Inference Operators by Default Deduction Rules

The paper deals with the question how a cumulative inference operator can be generated by default deduction rules. After discussing the “classical” ways (i.e. the sceptical and the credulous definition as well as Brewka's approach) we propose a new approach, the socalled codiagonal generation of cumulative inference operator by default deduction rules.

[1]  Matthew L. Ginsberg,et al.  Readings in Nonmonotonic Reasoning , 1987, AAAI 1987.

[2]  George Gratzer,et al.  Universal Algebra , 1979 .

[3]  G. Birkhoff,et al.  On the Structure of Abstract Algebras , 1935 .

[4]  Dov M. Gabbay,et al.  Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems , 1989, Logics and Models of Concurrent Systems.

[5]  A. Tarski.  Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I , 1930 .

[6]  Krzysztof R. Apt,et al.  Logics and Models of Concurrent Systems , 1989, NATO ASI Series.

[7]  David Makinson,et al.  General Theory of Cumulative Inference , 1988, NMR.

[8]  Gerhard Brewka.  Cumulative Default Logic: In Defense of Nonmonotonic Inference Rules , 1991, Artif. Intell..

[9]  Jürgen Schmidt,et al.  ber die Rolle der transfiniten Schluweisen in einer allgemeinen Idealtheorie , 1952 .

[10]  G. Birkhoff,et al.  On the combination of subalgebras , 1933, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Raymond Reiter,et al.  On Reasoning by Default , 1978, TINLAP.

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

[13]  小口 武彦,et al.  D.C. Mattis: The Theory of Magnetism, Harper and Row, New York, Evanston, and London, John Weatherhill, Inc. Tokyo, 1965, 303頁, 15×23cm, 約1,700円. , 1969 .

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

[15]  Martin D. Davis,et al.  The Mathematics of Non-Monotonic Reasoning , 1980, Artif. Intell..