Routley Star and Hyperintensionality

Abstract

We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bi-modal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality.

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Acknowledgements

The work reported in this paper has been carried out as part of the joint research project “FDE-based modal logics,” supported by the Russian Foundation for Basic Research, RFBR, grant No. 18-501-12019 and the Deutsche Forschungsgemeinschaft, DFG, grant WA 936/13-1. We gratefully acknowledge this support. Moreover, we would like to thank the two anonymous referees for their very helpful comments.

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Correspondence to Sergei Odintsov.

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The work reported in this paper was supported by the Russian Foundation for Basic Research, RFBR, grant No. 18-501-12019 and the Deutsche Forschungsgemeinschaft, DFG, grant WA 936/13-1.

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Odintsov, S., Wansing, H. Routley Star and Hyperintensionality. J Philos Logic 50, 33–56 (2021). https://doi.org/10.1007/s10992-020-09558-5

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Keywords

  • Hyperintensional contexts
  • Routley star operation
  • Heyting-Ockham logic
  • Vakarelov’s theory of negation
  • HYPE