Unknown Truths and False Beliefs: Completeness and Expressivity Results for the Neighborhood Semantics

Studia Logica 110 (1):1-45 (2021)
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Abstract

In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various classes of neighborhood frames. Most importantly, by adopting the intersection semantics and the subset semantics in the literature, we extend the results to the case of public announcements, which gives us the desired reduction axioms and has good applications related to Moore sentences, successful formulas and self-refuting formulas. Also, we can say something about the comparative merits of the intersection semantics and the subset semantics.

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References found in this work

Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
Universal grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
A logical analysis of some value concepts.Frederic Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.
Ignorance of ignorance.Kit Fine - 2018 - Synthese 195 (9):4031-4045.

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