Exploring modal worlds

• Different applications of modal idempotent semirings.
• Modal algebra of bisimulations and a proof of closure.
• Modal algebra of formal concept analysis and database preferences.
• Modal algebra of total and partial program correctness, including abortion.
• Modal algebra of structured modules in feature oriented software development.

Modal idempotent semirings cover a large set of different applications. The paper presents a small collection of these, ranging from algebraic logics for program correctness over bisimulation refinement, formal concept analysis, database preferences to feature oriented software development. We provide new results and/or views on these domains; the modal semiring setting allows a concise and unified treatment, while being more general than, e.g., standard relation algebra.