Mīmāṃsā deontic reasoning using specificity: a proof theoretic approach

Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. (in: TABLEAUX 2015, volume 9323 of LNCS, Springer, 2015) from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic $$\mathsf {MD}$$ . Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for Mīmāṃsā philosophy and, more generally, for the formal interpretation of normative statements.