Towards a Logic of Dilation

We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a semantic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, and a generalized notion of forgetting in propositional logic on the other hand. We place our work in the context of existing theories of approximation spaces and forgetting, and show that neighbourhoods obtained by combining collective and selective dilation provide a suitable semantic framework within which to reason computationally with uncertainty in a classical setting.