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Proof theories for superpositions of adaptive logics

(2015) LOGIQUE ET ANALYSE. 58(230). p.307-346
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Abstract
The standard format for adaptive logics offers a generic and unifying formal framework for defeasible reasoning forms. One of its main distinguishing features is a dynamic proof theory by means of which it is able to explicate actual reasoning. In many applications it has proven very useful to superpose sequences of adaptive logics, such that each logic treats the consequence set of its predecessor as premise set. Although attempts have been made to define dynamic proof theories for some of the resulting logics, no generic proof theory is available yet. Moreover, the existing proof theories for concrete superpositions are suboptimal in various respects: the derivability relations characterized by these proposals are often not adequate with respect to the consequence relation of the superposed adaptive logics and in some cases they even trivialize premise sets. An adequate and generic proof theory is needed in order to meet the requirement of explicating defeasible reasoning in terms of superpositions of adaptive logics. This paper presents two equivalent generic proof theories for superpositions of adaptive logics in standard format. By means of simple examples, the basic ideas behind these proof theories are illustrated and it is shown how the older proposals are inadequate.

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MLA
Strasser, Christian, and Frederik Van De Putte. “Proof Theories for Superpositions of Adaptive Logics.” LOGIQUE ET ANALYSE, vol. 58, no. 230, 2015, pp. 307–46, doi:10.2143/LEA.230.0.3141812.
APA
Strasser, C., & Van De Putte, F. (2015). Proof theories for superpositions of adaptive logics. LOGIQUE ET ANALYSE, 58(230), 307–346. https://doi.org/10.2143/LEA.230.0.3141812
Chicago author-date
Strasser, Christian, and Frederik Van De Putte. 2015. “Proof Theories for Superpositions of Adaptive Logics.” LOGIQUE ET ANALYSE 58 (230): 307–46. https://doi.org/10.2143/LEA.230.0.3141812.
Chicago author-date (all authors)
Strasser, Christian, and Frederik Van De Putte. 2015. “Proof Theories for Superpositions of Adaptive Logics.” LOGIQUE ET ANALYSE 58 (230): 307–346. doi:10.2143/LEA.230.0.3141812.
Vancouver
1.
Strasser C, Van De Putte F. Proof theories for superpositions of adaptive logics. LOGIQUE ET ANALYSE. 2015;58(230):307–46.
IEEE
[1]
C. Strasser and F. Van De Putte, “Proof theories for superpositions of adaptive logics,” LOGIQUE ET ANALYSE, vol. 58, no. 230, pp. 307–346, 2015.
@article{8511803,
  abstract     = {{The standard format for adaptive logics offers a generic and unifying formal framework for defeasible reasoning forms. One of its main distinguishing features is a dynamic proof theory by means of which it is able to explicate actual reasoning.

In many applications it has proven very useful to superpose sequences of adaptive logics, such that each logic treats the consequence set of its predecessor as premise set. Although attempts have been made to define dynamic proof theories for some of the resulting logics, no generic proof theory is available yet. Moreover, the existing proof theories for concrete superpositions are suboptimal in various respects: the derivability relations characterized by these proposals are often not adequate with respect to the consequence relation of the superposed adaptive logics and in some cases they even trivialize premise sets. An adequate and generic proof theory is needed in order to meet the requirement of explicating defeasible reasoning in terms of superpositions of adaptive logics.

This paper presents two equivalent generic proof theories for superpositions of adaptive logics in standard format. By means of simple examples, the basic ideas behind these proof theories are illustrated and it is shown how the older proposals are inadequate.}},
  author       = {{Strasser, Christian and Van De Putte, Frederik}},
  issn         = {{0024-5836}},
  journal      = {{LOGIQUE ET ANALYSE}},
  language     = {{eng}},
  number       = {{230}},
  pages        = {{307--346}},
  title        = {{Proof theories for superpositions of adaptive logics}},
  url          = {{http://doi.org/10.2143/LEA.230.0.3141812}},
  volume       = {{58}},
  year         = {{2015}},
}

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