X201601: Ciná, Giovanni and Enqvist, Sebastian (2016) Bisimulation and path logic for sheaves: contextuality and beyond. [Report]

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Abstract
In the setting of concurrency theory, Joyal, Winskel and Nielsen introduced a general notion of path bisimulation and showed that path bisimulations can be characterized as spans of open maps between presheaves. A modal logic for presheaves, called path logic, was shown to be expressive for such notion of bisimilarity. We consider the special case where the presheaves are defined over a topological space, and in particular where they are sheaves. We illustrate how natural properties of sheaves can be expressed in path logic and show how to encode the key concepts of the sheaftheoretic treatment of contextuality. We further investigate the associated notion of path bisimulation on sheaves, proving a characterization result for cospans of open maps. Finally, we introduce a “hybrid path logic” and show that the notion of a sheaf itself can be captured by an axiom of this enriched logic.
Item Type:  Report 

Report Nr:  X201601 
Series Name:  Technical Notes (X) Series 
Year:  2016 
Uncontrolled Keywords:  Bisimulation, Modal logic, Sheaves 
Subjects:  Logic 
Depositing User:  Giovanni Cina 
Date Deposited:  12 Oct 2016 14:38 
Last Modified:  12 Oct 2016 14:38 
URI:  https://eprints.illc.uva.nl/id/eprint/693 
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