On the complexity of inconsistency measurement

Thimm, Matthias; Wallner, Johannes

doi:10.1016/j.artint.2019.07.001

Cited by 22 publications

(26 citation statements)

References 78 publications

(142 reference statements)

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“…While this view is simply phrased and of intuitive appeal, reasoning with (maximally) consistent subsets is computationally demanding, as already [in]consistency detection in classical logic is a [co]NP-complete problem. Moreover, the number of the maximally inconsistent subsets of a premise set S may grow exponentially in the size of S, and as shown in [32], computing the size of MCS(S) is beyond the second level of the polynomial hierarchy.…”

Section: Resultsmentioning

confidence: 99%

Reasoning with maximal consistency by argumentative approaches

Arieli

Borg

Straßer

2018

Journal of Logic and Computation

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Reasoning with the maximally consistent subsets (MCS) of the premises is a well-known approach for handling contradictory information. In this paper we consider several variations of this kind of reasoning, for each one we introduce two complementary computational methods that are based on logical argumentation theory. The difference between the two approaches is in their ways of making consequences: one approach is of a declarative nature and is related to Dung-style semantics for abstract argumentation, while the other approach has a more proof-theoretical flavor, extending Gentzen-style sequent calculi. The outcome of this work is a new perspective on reasoning with MCS, which shows a strong link between the latter and argumentation systems, and which can be generalized to some related formalisms. As a by-product of this we obtain soundness and completeness results for the dynamic proof systems with respect to several of Dung's semantics. In a broader context, we believe that this work helps to better understand and evaluate the role of logic-based instantiations of argumentation frameworks.

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Section: Resultsmentioning

confidence: 99%

Reasoning with maximal consistency by argumentative approaches

Arieli

Borg

Straßer

2018

Journal of Logic and Computation

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“…Our idea focuses mainly on consistent KBs. Also, it is possible to use variable forgetting techniques in inconsistency reasoning, for which there is also an extensive literature [39][40][41].…”

Section: Forgettingmentioning

confidence: 99%

Towards a Notion of Basis for Knowledge-Based Systems—Applications

et al. 2021

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In the paradigm of Knowledge-Based Systems (KBS), the design of methods to simplify the reasoning leads to more efficient processes. A point of view that provides valuable insights is the algebraic one. In this work, a notion of basis (and dimension) for Knowledge Bases in Propositional Logic associated with knowledge forgetting is introduced. It is based on ideas that come from the translation of such logic in (Computer) Algebra, particularly from the interpretation of variable forgetting. In this paper, the concept of weak base is defined as a set of variables sufficient to decide the consistency using variable forgetting. Several applications of weak bases are presented in order to show their usefulness in KBS reasoning and to justify their study and use in solving problems within this topic.

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“…The problem of measuring inconsistency in knowledge bases over logical languages has increasingly received attention during recent years (for a survey, see [42,43]). An inconsistency measure is a function I : K → [0, ∞) ∪ {∞} 7 , which takes knowledge bases and returns non-negative real numbers or ∞.…”

Section: New Inconsistency Measuresmentioning

confidence: 99%

“…To answer the second question in a qualitative way, inconsistent knowledge bases were classified by the severity of their inconsistency [17]. Recently, to numerically quantify the extent to which a knowledge base is inconsistent, many inconsistency measures have been proposed [29,24,25,19,28,27,20,42,43]. In contrast, the first question appears quite underdeveloped, and it is the subject of the present work.…”

Section: Introductionmentioning

confidence: 99%

Localising iceberg inconsistencies

Bona

Hunter

2017

Artificial Intelligence

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In artificial intelligence, it is important to handle and analyse inconsistency in knowledge bases. Inconsistent pieces of information suggest questions like "where is the inconsistency?" and "how severe is it?". Inconsistency measures have been proposed to tackle the latter issue, but the former seems underdeveloped and is the focus of this paper. Minimal inconsistent sets have been the main tool to localise inconsistency, but we argue that they are like the exposed part of an iceberg, failing to capture contradictions hidden under the water. Using classical propositional logic, we develop methods to characterise when a formula is contributing to the inconsistency in a knowledge base and when a set of formulas can be regarded as a primitive conflict. To achieve this, we employ an abstract consequence operation to "look beneath the water level", generalising the minimal inconsistent set concept and the related free formula notion. We apply the framework presented to the problem of measuring inconsistency in knowledge bases, putting forward relaxed forms for two debatable postulates for inconsistency measures. Finally, we discuss the computational complexity issues related to the introduced concepts.

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On the complexity of inconsistency measurement

Cited by 22 publications

References 78 publications

Reasoning with maximal consistency by argumentative approaches

Reasoning with maximal consistency by argumentative approaches

Towards a Notion of Basis for Knowledge-Based Systems—Applications

Localising iceberg inconsistencies

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