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