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Strong inconsistency.

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Title: Strong inconsistency.
Authors: Brewka, Gerhard1, Thimm, Matthias1,2, Ulbricht, Markus1 mulbricht@informatik.uni-leipzig.de
Source: Artificial Intelligence. Feb2019, Vol. 267, p78-117. 40p.
Subjects: Set theory, Subset selection, Knowledge base, Genetic algorithms, Combinatorial optimization
Abstract: Abstract Minimal inconsistent subsets of knowledge bases play an important role in propositional logic, most notably for diagnosis, axiom pinpointing, and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play a similar role as minimal inconsistent subsets in propositional logic. In particular, we show that the well-known duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on axiom pinpointing and inconsistency measurement. [ABSTRACT FROM AUTHOR]
Copyright of Artificial Intelligence is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
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  Data: Abstract Minimal inconsistent subsets of knowledge bases play an important role in propositional logic, most notably for diagnosis, axiom pinpointing, and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play a similar role as minimal inconsistent subsets in propositional logic. In particular, we show that the well-known duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on axiom pinpointing and inconsistency measurement. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Artificial Intelligence is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.artint.2018.11.002
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      – SubjectFull: Set theory
        Type: general
      – SubjectFull: Subset selection
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      – SubjectFull: Knowledge base
        Type: general
      – SubjectFull: Genetic algorithms
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      – SubjectFull: Combinatorial optimization
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      – TitleFull: Strong inconsistency.
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              Text: Feb2019
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              Value: 267
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