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Logic Journal of IGPL 1993 1(1):23-68; doi:10.1093/jigpal/1.1.23
© 1993 by Oxford University Press
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Original Articles

Nonmonotonic inference operations

MICHAEL FREUND and DANIEL LEHMANN

Département de Mathématiques, Université d'Orléans 45067 Orléans, Cédex 2 (France)
Institute of Computer Science, Hebrew University Jerusalem 91904 (Israel)E-mail: lehmann{at}cs.huji.ac.il

A. Tarski [21] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering dofeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations is inspired by the results of [11] on finitary nonmonotonic operations, but this paper is self-contained.

Key Words: Nonmonotonic reasoning


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