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Abstract

In this paper, the correspondence between derivability (syntactic consequences obtained from ⊢) and convertibility in rewriting \( \left( {\mathop \leftrightarrow \limits^* } \right) \) , the so-called logicality, is studied in a generic way (i.e. logic-independent). This is achieved by giving simple conditions to characterise logics where (bidirectional) rewriting can be applied. These conditions are based on a property defined on proof trees, that we call semi-commutation. Then, we show that the convertibility relation obtained via semi-commutation is equivalent to the inference relation ⊢ of the logic under consideration.

Keywords

Formal system semi-commutation abstract rewrite tree abstract convertibility relation logicality 

Topics

Term Rewriting Reasoning Integration of Logical Reasoning and Computer Algebra 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marc Aiguier
    • 1
  • Diane Bahrami
    • 1
  • Catherine Dubois
    • 2
  1. 1.CNRS UMR 8042, LaMIUniversité d’Évry Val d’EssonneÉvryFrance
  2. 2.Institut d’Informatique d’EntrepriseCEDRICÉvryFrance

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