A Family of Neighborhood Contingency Logics

Notre Dame Journal of Formal Logic 60 (4):683-699 (2019)

Abstract

This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in 1995. We show that Kuhn’s function is actually equal to a related function originally given by Humberstone.

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References found in this work

Universal Grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
Contingency and Knowing Whether.Jie Fan, Yanjing Wang & Hans van Ditmarsch - 2015 - Review of Symbolic Logic 8 (1):75-107.
Minimal Non-Contingency Logic.Steven T. Kuhn - 1995 - Notre Dame Journal of Formal Logic 36 (2):230-234.
Necessity and Contingency.M. J. Cresswell - 1988 - Studia Logica 47 (2):145 - 149.

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Citations of this work

A Family of Kripke Contingency Logics.Jie Fan - 2020 - Theoria 86 (4):482-499.
A Unified Logic for Contingency and Accident.Jie Fan - 2022 - Journal of Philosophical Logic 51 (4):693-720.
A Logic for Disjunctive Ignorance.Jie Fan - 2021 - Journal of Philosophical Logic 50 (6):1293-1312.

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