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On a Generalised Logicality Theorem

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Artificial Intelligence, Automated Reasoning, and Symbolic Computation (AISC 2002, Calculemus 2002)

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.

This work was partially supported by the European Commission under WGs Aspire (22704) and is partially supported by the French research program “GDR Algorithmique-Langage-Programmation (ALP)”

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© 2002 Springer-Verlag Berlin Heidelberg

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Aiguier, M., Bahrami, D., Dubois, C. (2002). On a Generalised Logicality Theorem. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_8

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  • DOI: https://doi.org/10.1007/3-540-45470-5_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43865-6

  • Online ISBN: 978-3-540-45470-0

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