The Varieties of Ought-Implies-Can and Deontic STIT Logic
This work addresses a foundational issue in formal logic and philosophy for researchers in multi-agent systems and deontic reasoning, but it is incremental as it builds on existing STIT frameworks.
The paper tackles the problem of formalizing multiple interpretations of the Ought-implies-Can principle in deontic STIT logic, resulting in a modular framework that accounts for ten such readings and provides sound and complete calculi for the corresponding logics.
STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings.