LFCS Seminar: Friday 21 June - Hans van Ditmarsch Title: Epistemic logic and simplicial complexes Abstract 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 Vienna and Bern. 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. It will be my pleasure to present my infatuation with this novel development connecting epistemic logic and distributed computing. Suggested introductory reading is: https://arxiv.org/abs/2002.08863 Jun 21 2024 15.10 - 16.00 LFCS Seminar: Friday 21 June - Hans van Ditmarsch Hans van Ditmarsch, CNRS, IRIT, University of Toulouse https://sites.google.com/site/hansvanditmarsch/ Note unusual day and time.
LFCS Seminar: Friday 21 June - Hans van Ditmarsch Title: Epistemic logic and simplicial complexes Abstract 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 Vienna and Bern. 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. It will be my pleasure to present my infatuation with this novel development connecting epistemic logic and distributed computing. Suggested introductory reading is: https://arxiv.org/abs/2002.08863 Jun 21 2024 15.10 - 16.00 LFCS Seminar: Friday 21 June - Hans van Ditmarsch Hans van Ditmarsch, CNRS, IRIT, University of Toulouse https://sites.google.com/site/hansvanditmarsch/ Note unusual day and time.
Jun 21 2024 15.10 - 16.00 LFCS Seminar: Friday 21 June - Hans van Ditmarsch Hans van Ditmarsch, CNRS, IRIT, University of Toulouse https://sites.google.com/site/hansvanditmarsch/
