Analytic proof theory for deontic Mīmāṃsā logic

Abstract

Deontic logic is the branch of logic that deals with obligations,prohibitions, permissions, and other normative concepts.It has become increasingly relevant in domains such as Ethics,Law and AI. Deontic Logic is a relatively recent field of study,with its inception traced back to von Wright's 1951 paper. By constrast, Mīmāṃsā -- a prominent school of Sanskrit philosophy --has thoroughly discussed for more than two Millennia deontic concepts almost in a formal way. As such, Mīmāṃsā offers a treasure trove of 2000years of deontic investigations. This thesis focuses son the Mīmāṃsā authors Prabhakara and Kumarila and discusses two modal logics that formalize their deontic theories. The analyticity of their respective proof theories, based on the hypersequent calculus, is established through the process of cut-elimination. Further, soundness and completeness are proven.