Strengthening Consistency Results in Modal Logic

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 consiste...

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Bibliographic Details
Published inarXiv.org
Main Authors Samuel Allen Alexander, Pedersen, Arthur Paul
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.07.2023
Subjects
Axioms
Codification
Computer Science - Artificial Intelligence
Computer Science - Logic in Computer Science
Consistency
Decision making
Epistemology
Logic
Mathematics - Logic
Questions
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2307.05053