Is provenance logical? [Invited Keynote]

Research on provenance in databases (or other settings) sometimes has an arbitrary flavor. Once we abandon the classical semantics of queries there is a large design space for alternative semantics that could provide some useful provenance information, but there is little guidance for how to explore this space or justify or compare different proposals. Topics from mathematical or philosophical logic could be used as a way of inspiring, justifying or comparing different approaches to provenance in databases. This paper and invited talk will present several topics in logic that may be less familiar to database researchers and that could bear upon provenance techniques. These areas include nonclassical logics (e.g. relevance logic), algebraic logic (cylindric algebras), substructural logic (e.g. linear logic) and logics of knowledge, belief or causality.