Abstract
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.
Highlights
The Mımam. sais a philosophical school which originated in ancient India in the last centuries BCE and whose main focus was the exegesis of the prescriptive portions of the Vedas—the Sacred Texts of Hinduism
Some can be transformed into properties (Hilbert axioms) for the operators corresponding to the deontic concepts in Mımam. sa; this method led to the introduction of the non-normal dyadic deontic logic bMDL, which was used in Ciabattoni et al (2015) to formally analyze a famous controversial passage in the Vedas
Focusing on the specificity principle, we have explored connections between the Mımam. saschool of Indian philosophy and symbolic deontic logic
Summary
The Mımam. sais a philosophical school which originated in ancient India in the last centuries BCE and whose main focus was the exegesis of the prescriptive portions of the Vedas—the Sacred Texts of (what is called) Hinduism. Additional rules to derive all possible prescriptions are defined using limited (downwards) monotonicity on the conditions of the (non-nested) prescriptions in the Vedas (prima-facie deontic statements) “up to conflicting deontic statements” relative to the given set of facts. Saauthors considered applications of vikalpa to be “the last resort” and to be avoided as much as possible In our system this criterium can be evaluated by checking how many of the prima-facie deontic statements are derivable. 3. The base logic is extended with prohibitions and recommendations, and the complete set of rules for reasoning using specificity is introduced in Sect. The technical proof of cut elimination is contained in the “Appendix”
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