Frontiers of Philosophy in China 1 (4):688-709 (2006)

Abstract
Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between "local inferences"(to infer a conclusion from a subset of given premises) and "global inferences"(to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved
Keywords default reasoning  default implication  default Modus Ponens  local inference  global inference  set-selection function  set-selection frame  set-selection model  set-selection semantics
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DOI 10.1007/s11466-006-0032-5
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A Logic for Default Reasoning.Ray Reiter - 1980 - Artificial Intelligence 13 (1-2):81-137.
Circumscription — A Form of Non-Monotonic Reasoning.John McCarthy - 1980 - Artificial Intelligence 13 (1-2):27–39.
A Formalism for Nonmonotonic Reasoning Encoded Generics.Yi Mao - 2003 - Dissertation, The University of Texas at Austin

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