Computing with Epistemic and Spatial Modalities

Sophia Knight (1) , Prakash Panangaden (2) , Frank Valencia (3)

1 UMD - University of Minnesota [Duluth]
2 McGill University = Université McGill [Montréal, Canada]
3 COMETE - Concurrency, Mobility and Transactions

This paper describes the role which epistemic reasoning can play in concurrency theory. The idea of using epistemic modalities as programming constructs has been largely unexplored. Logic programming emerged under the slogan ``Logic as a programming language'' and the connection was manifest in a very clear way in the concurrent constraint programming paradigm. In this paper we explore the role of epistemic, and closely related spatial modalities, as part of the programming language and not just as part of the meta-language for reasoning about protocols. We introduce spatial and epistemic process calculi for reasoning about spatial information and knowledge distributed among the agents of a system. We introduce domain-theoretical structures to represent spatial and epistemic information. We provide operational and denotational techniques for reasoning about the potentially infinite behaviour of spatial and epistemic processes. Finally, we develop the analogue of Scott's information systems for the modal case and show an equivalence of categories between modal information systems and spatial constraint systems, and between epistemic information systems and epistemic constraint systems.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Sophia Knight, Prakash Panangaden, Frank Valencia. Computing with Epistemic and Spatial Modalities. 2020. ⟨hal-03148149⟩