1,397 research outputs found
Two-Dimensional Tableaux
We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed
The Logic of Sequence Frames
This paper investigates and develops generalizations of two-dimensional 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 n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction
Actuality and the a priori
We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the âAppendixâ section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal
A Two-Dimensional Logic for Two Paradoxes of Deontic Modality
In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Rossâs Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions Fuscoâs account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to âliftâ a Kripke frame for a one- dimensional modal logic into two dimensions
Two-Dimensional Tableaux
We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed
Logics and Their Galaxies
This article introduces some concepts that help exploring the ontological
import of universal logic. It studies the notions of an antilogic and counterlogic associated
to each logic and shows some of their properties. It presents the notion of
galaxy, as the class of possible worlds compatible with a given logic.We explore some
consequences of these developments
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