Some Notes on Dyadic Contingency

Journal of Logic, Language and Information 32 (2):209-217 (2023)
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Abstract

In a recent work, Pizzi proposes a notion of dyadic non-contingency, and then gives an axiomatic system of dyadic non-contingency named \(\text {KD}\Delta ^2\), which is shown to be translationally equivalent to the deontic system KD and has the minimal system \(\text {K}\Delta \) of monadic contingency as a fragment. However, the reason why he defines dyadic non-contingency like that is unclear. In this article, inspired by the notion of relativized knowing-value in the literature, we give a plausible explanation for this. We also show that \(\text {KD}\Delta ^2\) is _not_ sound with respect to the class of serial frames, and then correct a mistake in the previous-mentioned Pizzi’s work.

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References found in this work

Contingency and Knowing Whether.Jie Fan, Yanjing Wang & Hans van Ditmarsch - 2015 - Review of Symbolic Logic 8 (1):75-107.
The Logic of Non-contingency.I. L. Humberstone - 1995 - Notre Dame Journal of Formal Logic 36 (2):214-229.
Minimal Non-contingency Logic.Steven T. Kuhn - 1995 - Notre Dame Journal of Formal Logic 36 (2):230-234.
Completeness and Definability in the Logic of Noncontingency.Evgeni E. Zolin - 1999 - Notre Dame Journal of Formal Logic 40 (4):533-547.

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