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An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency

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In this paper, I present the modal adaptive logic AJ r (based on S5) as well as the discussive logic D r 2 that is defined from it. D r 2 is a (non-monotonic) alternative for Jaśkowski’s paraconsistent system D 2 . Like D 2 , D r 2 validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, D r 2 moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D 2 , this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.

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Correspondence to Joke Meheus*.

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*Research for this paper was indirectly supported by the Flemish Minister responsible for Science and Technology (contract BIL1/8). The author is indebted to Leon Horsten, João Marcos, Jerzy Perzanowski, Liza Verhoeven, and especially to the referee and to Diderik Batens for comments and suggestions.

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Meheus*, J. An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency. J Philos Logic 35, 539–567 (2006). https://doi.org/10.1007/s10992-005-9004-9

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