Nonmonotonic reasoning: From finitary relations to infinitary inference operations

Studia Logica 53 (2):161 - 201 (1994)

Abstract
A. Tarski [22] 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 defeasible 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 [12] on nonmonotonic inference relations, and relies on some of the definitions found there.
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DOI 10.1007/BF01054708
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References found in this work BETA

The Collected Papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam: North-Holland Pub. Co..
Nonmonotonic Inference Operations.Michael Freund & Daniel Lehmann - 1993 - Logic Journal of the IGPL 1 (1):23-68.
Supracompact Inference Operations.Michael Freund - 1993 - Studia Logica 52 (3):457 - 481.

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Citations of this work BETA

Infinitary Belief Revision.Dongmo Zhang & Norman Foo - 2001 - Journal of Philosophical Logic 30 (6):525-570.
Generalized Compactness of Nonmonotonic Inference Operations.Heinrich Herre - 1995 - Journal of Applied Non-Classical Logics 5 (1):121-135.
Defaults as Restrictions on Classical Hilbert-Style Proofs.Gianni Amati, Luigia Carlucci Aiello & Fiora Pirri - 1994 - Journal of Logic, Language and Information 3 (4):303-326.

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