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Nonmonotonic inference operations

Michael Freund & Daniel Lehmann

Logic Journal of the IGPL 1 (1):23-68 (1993)

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(1 other version)Nonmonotonic reasoning: From finitary relations to infinitary inference operations.Michael Freund & Daniel Lehmann - 1994 - Studia Logica 53 (2):161 - 201.details 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 (...) Download Export citation Bookmark 7 citations
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.details Since the earliest formalisation of default logic by Reiter many contributions to this appealing approach to nonmonotonic reasoning have been given. The different formalisations are here presented in a general framework that gathers the basic notions, concepts and constructions underlying default logic. Our view is to interpret defaults as special rules that impose a restriction on the juxtaposition of monotonic Hubert-style proofs of a given logicL. We propose to describe default logic as a logic where the juxtaposition of default proofs (...) Download Export citation Bookmark
(1 other version)Nonmonotonic reasoning: from finitary relations to infinitary inference operations.Michael Freund & Daniel Lehmann - 1994 - Studia Logica 53 (2):161-201.details 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 (...) Download Export citation Bookmark 3 citations
Characterizations of Preferential Entailments.Yves Moinard & Raymond Rolland - 2002 - Logic Journal of the IGPL 10 (3):245-272.details The “preferential entailments” considered in this text are all defined in the same way, by a binary relation, or “preference relation”. This relation can be among interpretations, or sets of interpretations, or among “states” which are copies of interpretations or copies of sets of interpretations. This provides four kinds of preferential entailments. What we do here is to provide a characterization result for these four kinds of preferential entailments. We choose properties as simple and natural as possible, and sometimes we (...) Download Export citation Bookmark 2 citations
Generalized compactness of nonmonotonic inference operations.Heinrich Herre - 1995 - Journal of Applied Non-Classical Logics 5 (1):121-135.details The aim of the present paper is to analyse compactness properties of nonmonotonic inference operations within the framework of model theory. For this purpose the concepts of a deductive frame and its semantical counterpart, a semantical frame are introduced. Compactness properties play a fundamental in the study of non-monotonic inference, and in the paper several new versions of compactness are studied. Download Export citation Bookmark 1 citation

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