## Measuring inconsistency in knowledge via quasi-classical models (2002)

Venue: | In Proceedings of the National Conference on Artificial Intelligence (AAAI’02 |

Citations: | 28 - 16 self |

### BibTeX

@INPROCEEDINGS{Hunter02measuringinconsistency,

author = {Anthony Hunter},

title = {Measuring inconsistency in knowledge via quasi-classical models},

booktitle = {In Proceedings of the National Conference on Artificial Intelligence (AAAI’02},

year = {2002},

pages = {68--73},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

The language for describing inconsistency is underdeveloped. If a knowledgebase (a set of formulae) is inconsistent, we need more illuminating ways to say how inconsistent it is, or to say whether one knowledgebase is “more inconsistent” than another. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap’s four-valued logic, and unlike other paraconsistent logics, allows the connectives to appear to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasi-classical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a preference ordering, called the compromise relation, over knowledgebases. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge.

### Citations

873 | A theory of diagnosis from first principles
- Reiter
- 1987
(Show Context)
Citation Context ...oped. Some approaches touch on the topic. In diagnostic systems, there are proposals that offer preferences for certain kinds of consistent subsets of inconsistent information (Kleer & Williams 1987; =-=Reiter 1987-=-); in proposals for belief revision, epistemic entrenchment is an ordering over formulae which reCopyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved... |

304 |
Knowledge in Flux
- Gardenfors
- 1988
(Show Context)
Citation Context ...formulae which reCopyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. flects the preference for which formulae to give up in case of inconsistency (=-=Gardenfors 1988-=-); in proposals for drawing inferences from inconsistent information there is a preference for inferences from some consistent subsets (e.g. (Brewka 1989; Benferhat, Dubois, & Prade 1993)); in proposa... |

292 |
A useful four-valued logic
- Belnap
- 1977
(Show Context)
Citation Context ...to quasi-classical logic, a form of paraconsistent logic, to model inconsistent sets of formulae. There are other paraconsistent logics that we could consider, for example Belnap’s four-valued logic (=-=Belnap 1977-=-), or Levesque’s 3interpretations (Levesque 1984), or Grant’s generalizations of classical satisfaction (Grant 1978), but these, as we will illustrate, involve the consideration of too many models. Th... |

267 |
A logic of implicit and explicit belief
- Levesque
- 1984
(Show Context)
Citation Context ...tent logic, to model inconsistent sets of formulae. There are other paraconsistent logics that we could consider, for example Belnap’s four-valued logic (Belnap 1977), or Levesque’s 3interpretations (=-=Levesque 1984-=-), or Grant’s generalizations of classical satisfaction (Grant 1978), but these, as we will illustrate, involve the consideration of too many models. This increases the number of models that need to b... |

240 | Investigations into a Theory of Knowledge Base Revision: Preliminary Report
- Dalal
- 1988
(Show Context)
Citation Context ...theory, and the related field of knowledgebase merging, there are some proposals that do provide some description of the degree of inconsistency of a set of formulae. For example, the Dalal distance (=-=Dalal 1988-=-), essentially the Hamming distance between two propositional interpretations, can be used to give a profile of an inconsistent knowledgebase. Let dalal(w, w ′) denote the Dalal distance from w to w ′... |

209 | Possibilistic logic - Lang, Prade - 1994 |

199 | Preferred Subtheories: An Extended Logical Framework for Default Reasoning
- Brewka
- 1989
(Show Context)
Citation Context ...mulae to give up in case of inconsistency (Gardenfors 1988); in proposals for drawing inferences from inconsistent information there is a preference for inferences from some consistent subsets (e.g. (=-=Brewka 1989-=-; Benferhat, Dubois, & Prade 1993)); in proposals for approximating entailment, two sequences of entailment relation are defined (the first is sound but not complete, and the second is complete but no... |

112 | On the logic of merging - Konieczny, Pérez |

93 | Tractable reasoning via approximation
- Schaerf, Cadoli
- 1995
(Show Context)
Citation Context ... for approximating entailment, two sequences of entailment relation are defined (the first is sound but not complete, and the second is complete but not sound) which converge to classical entailment (=-=Schaerf & Cadoli 1995-=-); and in proposals for partial consistency checking, checking is terminated after the search space exceeds a threshold which gives a measure of partial consistency of the data. However, none of these... |

82 | On the theory of inconsistent formal systems - Costa - 1977 |

74 | Merging databases under constraints
- Lin, Mendelzon
- 1998
(Show Context)
Citation Context ...tency in a given set of formulae, and it is not clear how we could compare sets of formulae using this approach. Furthermore, operators for aggregating these distances, such as the majority operator (=-=Lin & Mendelzon 1998-=-), egalitarist operator (Revesz 1997), or the leximax operator (Konieczny & Pino Perez 1998), do not seem to be appropriate summaries of the degree of inconsistency in the original knowledgebase since... |

66 | On the semantics of arbitration
- Revesz
- 1997
(Show Context)
Citation Context ...ot clear how we could compare sets of formulae using this approach. Furthermore, operators for aggregating these distances, such as the majority operator (Lin & Mendelzon 1998), egalitarist operator (=-=Revesz 1997-=-), or the leximax operator (Konieczny & Pino Perez 1998), do not seem to be appropriate summaries of the degree of inconsistency in the original knowledgebase since they seek to find the most appropri... |

65 | Argumentative inference in uncertain and inconsistent knowledge bases - Benferhat, Dubois, et al. - 1993 |

52 | The complexity of model checking for circumscriptive formulae
- Cadoli
- 1992
(Show Context)
Citation Context ... to turn a QC satisfaction problem into a classical satisfaction problem, and on the coNP-complete property of checking whether a given classical interpretation is a minimal model of a given formula (=-=Cadoli 1992-=-). Measuring coherence of QC models We now consider a measure of inconsistency called coherence. The opinionbase of a QC model X is the set of atomic beliefs (atoms) for which there are reasons for or... |

32 | Quasi-classical Logic: Non-trivializable classical reasoning from inconsistent information. Symbolic and Quantitative Approaches to Reasoning and
- Besnard, Hunter
- 1995
(Show Context)
Citation Context ...nsistencies in models, and we extend this semantic framework to preference relations over sets of formulae. Review of QC Logic We review the propositional version of quasi-classical logic (QC Logic) (=-=Besnard & Hunter 1995-=-; Hunter 2000). Definition 1 The language of first-order QC logic is that of classical propositional logic. We let L denote a set of formulae formed in the usual way from a set of atom symbols A, and ... |

23 |
Information and evidence in logic systems
- Lozinskii
- 1994
(Show Context)
Citation Context ... propositional formulae Γ, that has been composed from n different atom symbols, is the logarithm of the number of models (2n) divided by the number of models for the maximum consistent subsets of Γ (=-=Lozinskii 1994-=-). This information theoretic measure increases with additions of consistent information and decreases with additions of inconsistent information. However, as highlighted by Wong and Besnard, the meas... |

21 |
Classifications for inconsistent theories’, Notre Dame
- Grant
- 1978
(Show Context)
Citation Context ...raconsistent logics that we could consider, for example Belnap’s four-valued logic (Belnap 1977), or Levesque’s 3interpretations (Levesque 1984), or Grant’s generalizations of classical satisfaction (=-=Grant 1978-=-), but these, as we will illustrate, involve the consideration of too many models. This increases the number of models that need to be analysed and it underspecifies the nature of the conflicts. In th... |

8 | Reasoning with conflicting information using quasi-classical logic - Hunter |

8 |
Computational aspects of quasi-classical entailment
- Marquis, Porquet
- 2001
(Show Context)
Citation Context ...logic (Hunter 2001). Entailment for QC logic for propositional CNF formulae is coNP-complete, and via a linear time transformation these formulae can be handled using classical logic theorem provers (=-=Marquis & Porquet 2001-=-). Why measure inconsistency with QC models? The definitions for QC models and for strong satisfaction provide us with the basic concepts for measuring inconsistency. QC logic exhibits the nice featur... |

7 | A semantic tableau version of first-order quasi-classical logic. In Quantitative and Qualitative Approaches to Reasoning with Uncertainty, LNCS - Hunter |

6 |
Diagnosing mulitple faults
- Kleer, Williams
- 1987
(Show Context)
Citation Context ...formulae are underdeveloped. Some approaches touch on the topic. In diagnostic systems, there are proposals that offer preferences for certain kinds of consistent subsets of inconsistent information (=-=Kleer & Williams 1987-=-; Reiter 1987); in proposals for belief revision, epistemic entrenchment is an ordering over formulae which reCopyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All ri... |