Strengthening Consistency Results in Modal Logic

TL;DR

This paper introduces generic theories in propositional modal logic to provide a more robust and standard approach for determining the consistency of theories, with implications for epistemology and modal reasoning.

Contribution

It proposes the concept of generic theories as a foundational tool for consistency analysis in modal logic, improving upon traditional background axiom choices.

Findings

Generic theories serve as standard building blocks for background knowledge.

The approach clarifies the consistency determination process in modal logic.

Potential applications in epistemology and modal reasoning problems.

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.