What is the correct logic of necessity, actuality and apriority?

Abstract
This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two different proof systems with respect to the semantics is proven (Theorems 2.11. and 2.15.), as well as a normal form theorem (Theorem 3.23.), an elimination theorem for the actuality operator (Corollary 3.27.), and the decidability of the logic (Corollary 3.28.).
Keywords Modal logic  Necessity  Apriority  Actuality  Two-Dimensional Semantics  Nesting Problem
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