Logics of relations on graphs: Automating correspondence theory
BISKT is a bi-intuitionistic modal logic introduced in a study of the logical foundations of generalising the idea of relations of sets to relations on graphs and exposing connections to mathematical morphology.
This setting is very general and complex and has provided successful application of mechanisms for automating logics. This project seeks to investigate, automate and extend the correspondence theory introduced for BISKT. Correspondence results are an essential part of understanding classical modal logics and the connections to mathematical structures which provide interpretations for the logics. The project will bring tools from the study of automated correspondence theory of modal logic to the task and explore ways of extending these tools and obtain new results for BISKT and other logics of relations on graphs.
The project is part of a research collaboration between the Department of Computer Science at the University of Leeds and the group of the proposer. The results are expected to advance also methods of classical correspondence theory and non-classical reasoning tasks such as abstraction.