Incorporating uncertainty into bidirectional model transformations and their delta-lens formalization

In Model-Driven Engineering, bidirectional transformations are key to managing consistency and synchronization of related models. Delta-lenses are a exible algebraic framework designed for specifying delta-based synchronization operations. Since model consistency is usually not a one-to-one correspondence, the synchronization process is inherently ambiguous, and consistency restoration can be achieved in many different ways. This can be seen as an uncertainty reducing process:the unknown uncertainty at design-time is translated into known un-certainty at run-time by generating multiple choices. However, many current tools only focus on a specific strategy (an update policy) to select only one amongst many possible alternatives, providing developers with little control over how models are synchronized. In this paper, we propose to extend the delta-lenses framework to cover incomplete transformations producing a multitude of possible solutions to consistency restoration. This multitude is managed in an intentional manner via models with built-in uncertainty.