Impossible and Conflicting Obligations in Justification Logic

TL;DR

This paper explores how justification logic, with explicit reasons for obligations, offers a nuanced approach to consistency principles and addresses deontic paradoxes through a novel semantics.

Contribution

It introduces new consistency principles in justification logic and a novel semantics ensuring completeness for explicit axiom D with arbitrary constant specifications.

Findings

Justification logic's strength depends on constant specifications and operations for combining reasons.

A new semantics is proposed that makes justification logic with axiom D complete for any constant specification.

The work has philosophical implications for deontic paradoxes.

Abstract

Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification and on the available set of operations for combining different reasons. We present different consistency principles in justification logic and compare their logical strength. We propose a novel semantics for which justification logics with the explicit version of axiom D, jd, are complete for arbitrary constant specifications. We then discuss the philosophical implications with regard to some deontic paradoxes.