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Splitting and relevance : broadening the scope of Parikh's concepts

Frederik Van De Putte (UGent)
(2016) LOGIQUE ET ANALYSE. 59(234). p.173-205
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Abstract
When our current beliefs face a certain problem e.g. when we receive new information contradicting them, then we should not remove beliefs that are not related to this problem. This principle is known as "minimal mutilation" or "conservativity" [21]. To make it formally precise, Rohit Parikh [32] defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas [27]. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from [25] and the least letter-set theorem from [27]. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from [14, 36, 24].
Keywords
MODAL LOGIC, CONTRACTION, REVISION, CONTRACTION, LOGIC

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Citation

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MLA
Van De Putte, Frederik. “Splitting and Relevance : Broadening the Scope of Parikh’s Concepts.” LOGIQUE ET ANALYSE, vol. 59, no. 234, 2016, pp. 173–205, doi:10.2143/LEA.234.0.3159740.
APA
Van De Putte, F. (2016). Splitting and relevance : broadening the scope of Parikh’s concepts. LOGIQUE ET ANALYSE, 59(234), 173–205. https://doi.org/10.2143/LEA.234.0.3159740
Chicago author-date
Van De Putte, Frederik. 2016. “Splitting and Relevance : Broadening the Scope of Parikh’s Concepts.” LOGIQUE ET ANALYSE 59 (234): 173–205. https://doi.org/10.2143/LEA.234.0.3159740.
Chicago author-date (all authors)
Van De Putte, Frederik. 2016. “Splitting and Relevance : Broadening the Scope of Parikh’s Concepts.” LOGIQUE ET ANALYSE 59 (234): 173–205. doi:10.2143/LEA.234.0.3159740.
Vancouver
1.
Van De Putte F. Splitting and relevance : broadening the scope of Parikh’s concepts. LOGIQUE ET ANALYSE. 2016;59(234):173–205.
IEEE
[1]
F. Van De Putte, “Splitting and relevance : broadening the scope of Parikh’s concepts,” LOGIQUE ET ANALYSE, vol. 59, no. 234, pp. 173–205, 2016.
@article{8511794,
  abstract     = {{When our current beliefs face a certain problem e.g. when we receive new information contradicting them, then we should not remove beliefs that are not related to this problem. This principle is known as "minimal mutilation" or "conservativity" [21]. To make it formally precise, Rohit Parikh [32] defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. 

I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas [27]. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from [25] and the least letter-set theorem from [27]. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from [14, 36, 24].}},
  author       = {{Van De Putte, Frederik}},
  issn         = {{0024-5836}},
  journal      = {{LOGIQUE ET ANALYSE}},
  keywords     = {{MODAL LOGIC,CONTRACTION,REVISION,CONTRACTION,LOGIC}},
  language     = {{eng}},
  number       = {{234}},
  pages        = {{173--205}},
  title        = {{Splitting and relevance : broadening the scope of Parikh's concepts}},
  url          = {{http://doi.org/10.2143/LEA.234.0.3159740}},
  volume       = {{59}},
  year         = {{2016}},
}
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