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Abstract

In this paper I present a range of substructural logics for a conditional connective ↦. This connective was original introduced semantically via restriction on the ternary accessibility relation R for a relevant conditional. I give sound and complete proof systems for a number of variations of this semantic definition. The completeness result in this paper proceeds by step-by-step improvements of models, rather than by the one-step canonical model method. This gradual technique allows for the additional control, lacking in the canonical model method, that is required.

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Authors and Affiliations

  1. School of Philosophy, Anthropology and Social Inquiries, University of Melbourne, Melbourne, Australia

    C. M. Asmus

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  1. C. M. Asmus
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Correspondence to C. M. Asmus.

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Asmus, C.M. Restricted Arrow. J Philos Logic 38, 405–431 (2009). https://doi.org/10.1007/s10992-008-9094-2

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  • DOI: https://doi.org/10.1007/s10992-008-9094-2

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