A road to ultrafilter extensions

TL;DR

This paper introduces a unified method for constructing ultrafilter extensions from canonical models, enhancing understanding of their structure in modal and contingency logics.

Contribution

It presents a novel, uniform approach to build ultrafilter extensions, applicable to various modal and contingency logics, clarifying their foundational construction.

Findings

Unified method for ultrafilter extensions derived from canonical models

Application of the method to Kripke contingency logics

Application of the method to neighborhood contingency logics

Abstract

We propose a uniform method of constructing ultrafilter extensions from canonical models, which is based on the similarity between ultrafilters and maximal consistent sets. This method can help us understand why the known ultrafilter extensions of models for normal modal logics and for classical modal logics are so defined. We then apply this method to obtain ultrafilter extensions of models for Kripke contingency logics and for neighborhood contingency logics.