Abstract

Simplicial Epistemic Semantics

All my working life as a logician epistemic logic came with Kripke models, in particular the kind for multiple agents with equivalence relations to interpret knowledge. Sure enough, I knew about enriched Kripke models, like subset spaces, or with topologies. But at some level of abstraction you get back your standard Kripke model. Imagine my surprise, around 2018, that there is an entirely dual sort of structure on which the epistemic logical language can be interpreted and that results in the same S5 logic: simplicial complexes. Instead of points that are worlds and links labeled with agents, we now have points that are agents and links labeled with worlds. Or, instead of edges (links), triangles, tetrahedrons, etcetera, that represent worlds. Simplicial complexes are well-known within combinatorial topology and have wide usage in distributed systems to model (a)synchronous computation. The link with epistemic modal logic is recent, spreading out from Mexico City and Paris to other parts of the world, like Bern, Prague and Vienna - where on May 5 Rojo Randrianomentsoa successfully defended her PhD thesis on this topic. Other logics are relevant too, for example KB4, in order to encode crashed processes/agents. Other epistemics are relevant too, and in particular distributed knowledge, which facilitates further generalizations from simplicial complexes to simplicial sets, and also belief instead of knowledge. It will be my pleasure to present my infatuation with this novel development connecting epistemic logic and distributed computing.

About Hans van Ditmarsch

Hans van Ditmarsch is senior researcher at CNRS, France. He is based at IRIT in Toulouse. He has previously been based at the Open University of the Netherlands, the University of Groningen, the University of Otago, the University of Aberdeen, the University of Sevilla, and CNRS (the University of Lorraine / LORIA). He has also been associated researcher at Institute of Mathematical Sciences, Chennai, India, for many years. His PhD is from the University of Groningen. His research is on the dynamics of knowledge and belief, information-based security protocols, modal logics, and combinatorics. He has frequently taught at ESSLLI summer schools, and he was an organizer or chair of events such as LOFT, M4M, ESSLLI, Tools for Teaching Logic, and LORI. He has been an editor of the Journal of Philosophical Logic. He is an author of the textbook and monograph Dynamic Epistemic Logic, an editor of the Handbook of Epistemic Logic, and an author of the logic puzzles book One Hundred Prisoners and a Light Bulb. He also received an ERC (European Research Council) starting grant on Epistemic Protocol Synthesis.

About Current Trends in Computer Science

This lecture is part of the Current Trends in Computer Science Lecture Series by the TU Wien Informatics Doctoral School, where renowned Guest Professors hold public lectures every semester. If you are studying with us, the lecture series can be credited as an elective course for students of master programs of computer science: 195.072 Current Trends in Computer Science. Additionally, you can join courses held by this year’s Guest Professors of our doctoral colleges and the TU Wien Informatics Doctoral School.

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