Logic Society of Delhi

World Logic Day Celebration 2025

January 15, 7:00 PM

One Hundred Prisoners and a Light Bulb - and other Knowledge Puzzles (Abstract). I will talk about logic puzzles involving knowledge and ignorance, and their history, and how such puzzles influenced my research in the logic of knowledge. The following puzzle that came to me by way of Moshe Vardi: "A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light-switch (and that is the only way in which they can communicate). The light is initially switched off. There is no fixed order of interrogation, or interval between interrogations, and the same prisoner will be interrogated again at any stage. When interrogated, a prisoner can either do nothing, or toggle the light-switch, or announce that all prisoners have been interrogated. If that announcement is true, the prisoners will (all) be set free, but if it is false, they will all be executed. While still in the dining room, and before the prisoners go to their isolation cells (forever), can the prisoners agree on a protocol that will set them free?" I will, obviously, present a solution. But I will mainly address such puzzles of knowledge in general. There are many others, such as the 'Muddy Children Puzzle' (also known as the 'Wisemen Puzzle' or the 'Hats Problem') of which the history goes back (at least) two centuries, 'Surprise Examination', 'Monty Hall', 'The telephone problem' (Gossip), etc. They often involve a (seemingly) paradoxical aspect making agents knowledgeable by announcements of their ignorance. There is a strong relation between such puzzles and the area in logic known as 'dynamic epistemic logic'. More information on such puzzles is found on http://personal.us.es/hvd/lightbulb.html.
Speaker: Hans van Ditmarsch, Senior Researcher at CNRS, France.
Zoom Link here.

January 20, 7:30 PM

Making Necessity Relevant (Abstract). In classically based modal logic, there are three common conceptions of necessity, the universal conception, the equivalence relation conception, and the axiomatic conception. They provide distinct presentations of the modal logic S5, all of which coincide in the basic modal language. We explore these different conceptions in the context of the relevant logic R, demonstrating where they come apart. This reveals that there are many options for being an S5-ish extension of R. It further reveals a divide between the universal conception of necessity on the one hand, and the axiomatic conception on the other: The latter is consistent with motivations for relevant logics while the former is not. For the committed relevant logician, necessity cannot be the truth in all possible worlds.
Speaker: Shawn Standefer, Assistant Professor, National Taiwan University, Taiwan.
Zoom Link here.

January 21, 7:30 PM

Generalised Geometric Logic and its Applications (Abstract). In this talk, we will discuss the notion of generalised geometric logic, which can interpret situations where the truth values are incomparable. In [3], we have already indicated how the extension of 3-valued geometric logic (a fragment of generalised geometric logic) can be seen as the stepping stone to propose the logic of ethics. We will discuss this in detail. Moreover, if time permits, we will discuss how this study enhances the results of M. J. Healy [2] in [1] for the LAPART architecture.

References:

[1] R. Das and P. Jana, Generalised Geometric Logic: A Logic for expressing a Neural Network Architecture (submitted).

[2] M. J. Healy, Continuous functions and neural network semantics, Non-linear Analysis: Theory, Methods & Applications 30(3), 1997, pp. 1335-1341.

[3] N. Hwang, P. Jana and R. Parikh, Ethical agents, The 34th Stony Brook International Conference on Game Theory, JULY 24-27, 2023.

[4] S. J. Vickers, Topology Via Logic, 5, Cambridge Tracts Theoret. Comput. Sci., 1989.
Speaker: Purbita Jana, Assistant Professor, Madras School of Economics, India.
Zoom Link here.

January 22, 7:00 PM

Logic Society of Delhi Meet-up!
Please join us at Cafe Lota (at National Crafts Museum & Hastkala Academy, New Delhi) and meet your fellow Delhi NCR logic enthusiasts!