Abstract. Starting with the deontic principles in Mīmām . sā texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results and neighbourhood semantics. The latter is used to analyse a well known example of conflicting obligations from the Vedas.

The Mīmāṁ sā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṁ sā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṁ sā theory of Vedic injunctions from a logical and philosophical point of view. The theory at issue can be regarded as a system of reasoning based on certain fundamental principles, such as the distinction between strong and weak duties, and on a taxonomy of ritual actions. We start by reconstructing the conceptual framework of the theory and then move to a formalization of its core aspects. Our contribution represents a new perspective to study Mīmāṁ sā and outlines its relevance, in general, for deontic reasoning.

The Mīmāṃsā school of Indian philosophy elaborated complex ways of interpreting the prescriptive portions of the Vedic sacred texts. The present article is the result of the collaboration of a group of scholars of logic, computer science, European philosophy and Indian philosophy and aims at the individuation and analysis of the deontic system which is applied but never explicitly discussed in Mīmāṃsā texts. The article outlines the basic distinction between three sorts of principles-hermeneutic, linguistic and deontic. It proposes a mathematical formalization of the deontic principles and uses it to discuss a well-known example of seemingly conflicting statements, namely the prescription to undertake the malefic Śyena sacrifice and the prohibition to perform any harm.

Free will may not be a universal problem, but it is also not only confined to Christianity, as shown in the case of Viśiṣṭādvaita Vedānta. The authors of this school of Indian philosophy, founded in the 11th c. and still influential up until today, had to face the challenge of accounting for human autonomy and God's omnipotence. Their solution was to create a precinct for free will in human minds, whereas all actions depend on God. Thus, God does not interfere with the initial determination of human free will and it later supports human intentions, thus permitting that they are turned into action.