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We consider a naturallanguage sentence that cannot be formally represented in a firstorder language for epistemic twodimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the firstorder language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal. 

In a recent paper, Pruss proves the validity of the rule beta2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counterexamples to beta2 formulated with the actuality operator and rigidified descriptions. We offer a novel and twodimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can (...) 

This paper investigates and develops generalizations of twodimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional ndimensional modal logics and show them to be decidable by means of a systematic tableau construction. 

In this paper, we axiomatize the deontic logic in Fusco, which uses a Stalnakerinspired account of diagonal acceptance and a twodimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunctioninvolving validities are a priori rather than necessary. We show how to axiomatize twodimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as onedimensional projections of more general twodimensional rules. These completeness results help make explicit the restrictions Fusco’s (...) 

Graeme Forbes (2011) raises some problems for twodimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong twodimensionalism. We call the problem of handling nested environments within twodimensional semantics “the nesting problem”. We show that the twodimensional (...) 

Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modalepistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles. 

This article surveys recent developments in the epistemology of modality. 

We present a sound and complete Fitchstyle natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is twodimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...) 

In this paper we present tableau methods for twodimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain firstorder quantifiers with identity, and all the formulas in the language are doublyindexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...) 