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

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... 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 proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. §1. Introduction. Epistemic two-dimensional semantics as proposed by David Chalmers, e.g., in Chalmers (2004) , provides an account of meaning that allows a possible world semantics of necessity as well as apriority. The notions of necessity and apriority intended here are those distinguished by Kripke (1972) ; the first is sometimes called metaphysical necessity. They can roughly be paraphrased by saying that necessary is what could not have failed to be the case, and a priori is what can be known in an a priori way. In Fritz (2013), a propositional modal logic with operators for necessity, actuality and apriority is defined which captures the relevant ideas of epistemic two-dimensional semantics. In particular, a class of relational structures is defined, and it is argued that it represents the evaluation of sentences according to epistemic two-dimensional semantics, and that therefore, the logic characterized by this class captures the relations of the three modalities according to epistemic two-dimensional semantics. Epistemic two-dimensional semantics is a controversial theory, and philosophers who do not want to commit themselves to it can't justify the correctness of this logic using its semantics. This raises the question whether there is a way of arguing for its correctness that is not based on epistemic two-dimensional semantics. The main aim of this paper is to outline such an argument.