Normative statements, which involve concepts such as obligation and prohibition, are enormously important in a variety of fields, from law and ethics to artificial intelligence. Reasoning with and about them requires deontic logic, which is a quite recent area of research. By contrast, for more than two millennia, one of the most important systems of Indian philosophy focused on analyzing normative statements. Mimamsa, as it is called, looks at these statements found in the Vedas, the sacred texts of (what it is now called) Hinduism, and interprets them by explaining precisely what course of action they require. This talk will describe the findings in [1] on the deontic reasoning of \mimamsa{}, and preliminary ideas on how to apply them to design autonomous agents sensitive to legal, social and ethical norms, see [2].

The results I will present arise from a collaboration between logicians, sanskritists and computer scientists.

Bibliography

1. Reasoning Tools for Deontic Logic and Applications to Indian Sacred Texts. Research project (with Elisa Freschi) funded by the Vienna Science and Technology Funds WWTF – 2017-2022.https://mimamsa.logic.at/
2. TAIGER: Training and Guiding AI Agents with Ethical Rules. Research project (with Ezio Bartocci and Thomas Eiter) funded by the Vienna Science and Technology Funds WWTF – 2023-2026.https://taiger.logic.at/

We examine the relationship between the ontological argument, in its original version provided by Anselm in Proslogion II, and theories of definite desriptions. Anselm’s ontological arguments, and its later variants proposed by such eminent philosophers as Descartes or Leibniz, still belong to the most discussed themes in the field of philosophy and theology. An advent of interest in these arguments in XXth century, among logicians and analytical philosophers, has thrown a new light on their structure and value. The prevailing approach to their formalisation is based on the application of modal logic, as in the works of Malcolm [3], Hartshorne [2], or Plantinga [6]. However, it seems that at least in the case of the version of the ontological argument formulated in Proslogion II, the crucial elements are contained in the description of God provided by Anselm. Therefore, following Barnes [1] or Oppenheimer and Zalta [4,5], we take as our basic assumption that the proper analysis of the Anselm’s argument should use some logic of definite descriptions. In fact, several theories of definite descriptions were developed and the problem is: which of them is the most suitable tool for its formalisation and evaluation.

Bibliography

1. J. Barnes, The Ontological Argument, London: Macmillan 1972.
2. C. Hartshorne, Anselm’s Discovery, LaSalle, IL: Open Court 1965.
3. N. Malcolm, Anselm’s Ontological Arguments, The PhilosophicalReview 69: 41–62 1960.
4. P. E. Oppenheimer and E. N. Zalta, On the Logic of the Ontological Argument,Philosophical Perspectives, 5: 509-529, 1991.
5. P. E. Oppenheimer and E. N. Zalta, A Computationally-Discovered Simplification of the Ontological Argument, Australasian Journal of Philosophy, 89: 333-349, 2011.
6. A. Plantinga, The Nature of Necessity, Oxford: Oxford UniversityPress 1974.

Tarski taught us that we cannot have both, a classical, semantically closed language and an adequate definition of truth. Kripke taught us that we can define a truth predicate for a semantically closed language, if we are willing to embrace a subclassical logic (at least on the sentential level). Yet, Tarski’s ghost is still with us, as these subclassical logics do not possess an attractive conditional connective, that is, a conditional that enables us to `carry on sustained ordinary reasoning’. In this talk we show how conditionals can be added to subclassical logics, in particular strong Kleene logic K3 and investigate the costs and consequences of such an addition. This leads us to a discussion of hyperintensionality in logics and truth theories.