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. from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic \. (...) 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. (shrink)

Realism for agents with unconditional beliefs, desires and intentions has been analyzed in modal logic. This paper provides a logical analysis of realism for agents with conditional beliefs and desires in a rule based approach analogous to Reiter's default logic. We distinguish two types of realism, which we call ‘a priori' and ‘a posteriori' realism. We analyze whether these two new properties are compatible with other properties discussed in the literature, such as existence of extensions. We show that Reiter's default (...) logic is too strong, in the sense that a weaker notion of maximality of extensions is needed to satisfy realism. Finally we show that several existing approaches do not satisfy the new realism properties, and we introduce a new construction that does satisfy them. (shrink)