Explicit non-normal modal logic

TL;DR

This paper introduces hyperintensional justification logics as a new approach to formalize deontic modals, addressing limitations of traditional modal logic.

Contribution

It develops novel justification logics for deontic modals, establishing their soundness, completeness, and exploring realization issues.

Findings

Justification logics effectively model hyperintensional deontic modalities.

Soundness and completeness are proven for the proposed logics.

The paper discusses realization problems in the new framework.

Abstract

Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completeness with respect to various models and we study the problem of realization.