2022/09/17 by Michael Benedikt, Benedikt, Michael, Christoph Wernhard +2 · 1 citation
Computer Science · #Advanced Database Systems and Queries #Databases (cs.DB) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2209.08299
openalex publication_date 2022/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I) is a logical specification involving the source data I and the interface data O. It is a valid definition of O in terms of I, if any two models of the specification agreeing on I agree on O. In contrast, an explicit definition is a query that produces O from I. Variants of Beth's theorem state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus NRC. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.