Strengthening Consistency Results in Modal Logic
Abstract
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces **generic theories** for propositional modal logic to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making.
Cite
@article{arxiv.2307.05053,
title = {Strengthening Consistency Results in Modal Logic},
author = {Samuel Allen Alexander and Arthur Paul Pedersen},
journal= {arXiv preprint arXiv:2307.05053},
year = {2023}
}
Comments
In Proceedings TARK 2023, arXiv:2307.04005. The authors thank three anonymous reviewers as well as Rineke Verbrugge for valuable comments and suggestions to help improve this manuscript. The authors also extend their gratitude to Alessandro Aldini, Michael Grossberg, Ali Kahn, Rohit Parikh, and Max Stinchcombe, for their generous feedback on prior drafts of this manuscript