Routley Star and Hyperintensionality

Journal of Philosophical Logic 50 (1):33-56 (2021)
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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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Heinrich Wansing
Ruhr-Universität Bochum

References found in this work

The Impossible: An Essay on Hyperintensionality.Mark Jago - 2014 - Oxford, United Kingdom: Oxford University Press.
HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.

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