Thesis defense

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Where and when

November 16, 10:00

1 rue Honoré d’Estienne d’Orves, Palaiseau

how to get there

What

Title: On Geometric Models of Epistemic Logic

Abstract: About 30 years ago, two major approaches to the study of distributed systems were developed. One approach established a topological perspective on distributed computing, expressing solvability of distributed tasks through standard notions of algebraic topology, by modeling spaces of states as simplicial complexes. In parallel, a prominent application of epistemic logic, a type of modal logic, provided an alternative point of view on the structure of distributed systems, by using the notion of knowledge to describe the behavior of processes in a system. It has recently been realized that these two approaches are closely related, and that the topological models can, in fact, serve as models of epistemic logic. This thesis continues a research program aimed at unification of these two approaches. Our first goal is to generalize the existing semantics of epistemic logic based on simplicial complexes to the case of simplicial sets. We show that with these models one can express non-standard group knowledge, that is situations when knowledge of a group seen as a whole is strictly greater than the union of knowledge of its members. We then proceed to study a many-sorted variant of epistemic logic, where properties of the environment and local properties of agents are expressed separately. This logic is interpreted in chromatic hypergraphs, which are a further generalization of simplicial complexes, allowing us to emphasize the role of local points of view of agents in distributed systems. We also investigate the dynamics of knowledge in distributed systems by introducing a dynamic variant of chromatic hypergraphs. In these models, local views of agents are supplemented with a temporal structure, which allows us to model the evolution of knowledge in time. Additionally, we discuss the relationship between knowledge and concurrency in this setting.

After

The drinks will be here: Le popup du label 14 Rue Abel, 75012 Paris