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Which style of reasoning to choose in the face of conflicting information?

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Abstract
In the context of non-monotonic reasoning different kinds of consequence relations are defined for reasoning from (possibly) inconsistent information. Examples are consequence relations that are characterized in terms of maximal consistent subsets of the premise set. The strong consequences are those formulas that follow by Classical Logic from every maximal consistent subset. The weak consequences follow from some maximal consistent subset. The free consequences follow from the set of formulas that belong to every maximal consistent subset. In this paper the question is discussed which of these consequence relations should be applied in which reasoning context. First the concerns that are expressed in the literature with respect to the usefulness of the weak consequences are addressed. Then it is argued that making weak inferences is sensible for some application contexts, provided one has a (dynamic) proof theory for the corresponding consequence relation. Such a dynamic proof theory is what adaptive logics offer. Finally, all this is illustrated by means of a very simple adaptive logic reconstruction of the free, strong, and weak consequences.
Keywords
defeasible reasoning, reasoning from inconsistent information, Rescher-Manor consequences, Adaptive logics, maximal consistent subsets, dynamic proofs, FLOATING CONCLUSIONS, INFERENCE

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MLA
Meheus, Joke, et al. “Which Style of Reasoning to Choose in the Face of Conflicting Information?” JOURNAL OF LOGIC AND COMPUTATION, vol. 26, no. 1, Oxford Journals, 2016, pp. 361–80, doi:10.1093/logcom/ext030.
APA
Meheus, J., Strasser, C., & Verdée, P. (2016). Which style of reasoning to choose in the face of conflicting information? JOURNAL OF LOGIC AND COMPUTATION, 26(1), 361–380. https://doi.org/10.1093/logcom/ext030
Chicago author-date
Meheus, Joke, Christian Strasser, and Peter Verdée. 2016. “Which Style of Reasoning to Choose in the Face of Conflicting Information?” JOURNAL OF LOGIC AND COMPUTATION 26 (1): 361–80. https://doi.org/10.1093/logcom/ext030.
Chicago author-date (all authors)
Meheus, Joke, Christian Strasser, and Peter Verdée. 2016. “Which Style of Reasoning to Choose in the Face of Conflicting Information?” JOURNAL OF LOGIC AND COMPUTATION 26 (1): 361–380. doi:10.1093/logcom/ext030.
Vancouver
1.
Meheus J, Strasser C, Verdée P. Which style of reasoning to choose in the face of conflicting information? JOURNAL OF LOGIC AND COMPUTATION. 2016;26(1):361–80.
IEEE
[1]
J. Meheus, C. Strasser, and P. Verdée, “Which style of reasoning to choose in the face of conflicting information?,” JOURNAL OF LOGIC AND COMPUTATION, vol. 26, no. 1, pp. 361–380, 2016.
@article{7251335,
  abstract     = {{In the context of non-monotonic reasoning different kinds of consequence relations are defined for reasoning from (possibly) inconsistent information. Examples are consequence relations that are characterized in terms of maximal consistent subsets of the premise set. The strong consequences are those formulas that follow by Classical Logic from every maximal consistent subset. The weak consequences follow from some maximal consistent subset. The free consequences follow from the set of formulas that belong to every maximal consistent subset. In this paper the question is discussed which of these consequence relations should be applied in which reasoning context. First the concerns that are expressed in the literature with respect to the usefulness of the weak consequences are addressed. Then it is argued that making weak inferences is sensible for some application contexts, provided one has a (dynamic) proof theory for the corresponding consequence relation. Such a dynamic proof theory is what adaptive logics offer. Finally, all this is illustrated by means of a very simple adaptive logic reconstruction of the free, strong, and weak consequences.}},
  author       = {{Meheus, Joke and Strasser, Christian and Verdée, Peter}},
  issn         = {{0955-792X}},
  journal      = {{JOURNAL OF LOGIC AND COMPUTATION}},
  keywords     = {{defeasible reasoning,reasoning from inconsistent information,Rescher-Manor consequences,Adaptive logics,maximal consistent subsets,dynamic proofs,FLOATING CONCLUSIONS,INFERENCE}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{361--380}},
  publisher    = {{Oxford Journals}},
  title        = {{Which style of reasoning to choose in the face of conflicting information?}},
  url          = {{http://doi.org/10.1093/logcom/ext030}},
  volume       = {{26}},
  year         = {{2016}},
}

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