2017

- A. Ciabattoni, E. Freschi, F. Genco and B. Lellmann

*Understanding Prescriptive Texts: Rules and Logic as elaborated by the Mīmāṃsā school.*Published in Online Journal of World Philosophies 2 (2017): https://scholarworks.iu.edu/iupjournals/index.php/jwp/index.

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 formalisation 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.The paper is addressed to historians of (Indian) philosophy. It proposes a first classification of the principles contained in the Mīmāṃsā texts as hermeneutic, linguistic and deontic. Section 5 describes in a non-technical way the results obtained in the paper (Ciabattoni et al. 2015) where a logic formalization of some of the deontic principles is used to analyze the seemingly conflicting statements around the Śyena sacrifice. - M. Pascucci

*Anderson's restriction of deontic modalities to contingent propositions.*Theoria. Swedish Journal of Philosophy, 83(4), pp.440-470 (2017).

The deontic status of tautologies and contradictions is one of the major puzzles for authors of early works on deontic logic. It is well-known that von Wright (1951) addresses this problem by adopting a Principle of Deontic Contingency, which says that tautologies are not necessarily obligatory and contradictions are not necessarily forbidden. A more radical solution is proposed by Anderson (1956) within a reductionist approach to deontic logic and consists in restricting the range of application of deontic modalities to contingent propositions. Anderson’s solution has not received much attention in the literature, despite reflecting a typical feature of ordinary deontic reasoning, where non-contingent propositions are rarely, if ever, taken into account. In the present article we explore some of its formal consequences, providing a taxonomy of the properties of the Andersonian operators of obligation and permission for contingent propositions, O' and P', in the class of normal alethic systems.This article is addressed to logicians. It analyses the relation between alethic and deontic modal notions (e.g., between necessity and obligation); in particular it investigates the formal consequences of the idea that all propositions having a relevant deontic status are contingent. The facts observed can be used, in general, as a philosophical basis for logical systems in which only formulas having some specified properties are allowed to be in the scope of a deontic (or modal) operator. - A. Ciabattoni and F. Genco

*Hypersequents and Systems of Rules: Embeddings and Applications.*ACM Transaction on Computational Logic. To appear.

We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of the benefits of locality for 2-systems, analyticity results for a large class of such systems, and a rewriting of hypersequent rules as natural deduction rules.There are many proof theoretic formalisms to define reasoning tools for logics. This paper, addressed to proof theorists, investigates two such formalisms: hypersequents and a subclass of systems of rules called 2-systems. We show that the two formalisms have the same expressive power (= they can capture the same logics), and derivations in one formalism can be effectively trasformed into derivations in the other formalism. In the context of the project the result is useful to understand which Hilbert axioms (that are tipically used to introduce/describe logics) can be captured using hypersequents; moreover it sheds light on how to generalize the hypersequent framework. - E. Freschi, M. Keating

*How Do We Gather Knowledge Through Language?*Published in Online Journal of World Philosophies 2 (2017): https://scholarworks.iu.edu/iupjournals/index.php/jwp/index.

How do we gather knowledge from language? The present article introduces Mīmāṃsā and European theories about epistemology of language. According to several theories in India and Europe, linguistic communication is only a case of inference. The present article discusses alternative strategies to avoid this reductionism of linguistic communication as instrument of knowledge to inference. This antireductionism enables the possibility of interpreting texts independently of their authors. The same principle is at play in the case of deontic logic, since Mīmāṃsā authors are committed to the idea of intepreting commands independently of their source.The paper is addressed to philosophers and historians of philosophy and linguistics. How do we gather knowledge from language? The present article introduces Mīmāṃsā and European theories about epistemology of language. According to several theories in India and Europe, linguistic communication is only a case of inference. The present article discusses alternative strategies to avoid this reductionism of linguistic communication as instrument of knowledge to inference.

Preliminary results

- A. Ciabattoni, E. Freschi, F. Genco and B. Lellmann

*Mīmāṃsā Deontic Logic: Proof Theory and Applications.*Proceedings of TABLEAUX 2015. Lecture Notes in Computer Science 9323. pp. 323-338. 2015.

Starting with the deontic principles in the Mīmāṃsā 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 paper is addressed to logicians. Using some deontic principles (metarules) contained in the Mīmāṃsā texts, it introduces a new deontic logic which is used to analyze the seemingly conflicting statements around the Śyena sacrifice. In particular, the interpretation of the mathematical structure validating these statements turns out to coincide with the controversial interpretation of Prābhākara, which can be reformulated as the lesser of two evils principle.