Neighborhood Contingency Logic
A formula is contingent, if it is possibly true and possibly false; a formula is non-contingent, if it is not contingent, i.e., if it is necessarily true or necessarily false. In this paper, we propose a neighborhood semantics for contingency logic, in which the interpretation of the non-contingency operator is consistent with its philosophical intuition. Based on this semantics, we compare the relative expressivity of contingency logic and modal logic on various classes of neighborhood models, and investigate the frame definability of contingency logic. We present a decidable axiomatization for classical contingency logic (the obvious counterpart of classical modal logic), and demonstrate that for contingency logic, neighborhood semantics can be seen as an extension of Kripke semantics.
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