A Universal Technique for Relating Heterogeneous Data Models Nick Rossiter David Nelson Michael Heather email: d.a.nelson@sunderland.ac.uk

Introduction Looking at multi-level architecture for information systems Need to handle higher levels than intension Take object work two levels higher to achieve interoperability between heterogeneous systems Formalisation using category theory and adjoints Example using relational and object oriented databases

Outline IRDS Introduces concept of meta-meta data Four-level approach based on ISO/IEC Standards 10027 1990 Information Resource Dictionary System (IRDS) Four-level approach concepts constructions format data values

Extract IRDS Standard Framework

Relating Extension to Intension level example Application data Supplier(1,’Smith’) extension -direct addressing Schema data Supplier (supp_no, name) intension - addressing by name level pair:

Relating Intension to Constructs Schema data Supplier (supp_no, name) intension - addressing by name Meta data Table(supplier) data dictionary - addressing by concepts, constructs.

Relating Constructs to Abstractions Meta data Table(Supplier) data dictionary - addressing by concepts, constructs. Meta meta data Aggregation(Table) real-world abstractions - addressing by abstractions

Interpretation of IRDS in Schematic form concepts mission MetaMeta Policy constructs management Meta Organize intension enterprise Name Data extension information Information Resource Dictionary Definition Schema (IRDDS) Information Resource Dictionary Definition (IRDD) Information Resource Dictionary (IRD) Information Resource Data (APP)

Formalization of IRDS Approach Quality enhanced by formalization Can know more confidently the limits and behaviour of a system Which formalism is best-suited?

Category Theory? Need relations to represent level-pairs Multi-level construction (higher-order) Category theory seems appropriate: - categories for basic structures - functors relate categories - natural transformations relate functors

Adjointness

Relational/OO Example Concept (IRDDS) Inheritance Policy MetaMeta Constructs (IRDD) InherTable <Subtype, Supertype> Organize OrgUniDDR OrgUniDDO Meta Format (IRD) StudentR StudentO Postgrad Data DataUniDDR DataUniDDO Name Values StudentR{1234, ‘James’, {1234, ‘James’, {1234, ‘The Language X’} (APP) ‘15 Montfort Ave’, ‘The Language X’} ‘15 Montfort Ave’}

Conclusions Interoperability is considered in the context of ISO Information Resource Dictionary System Provides a complete definition of an information system from real world abstractions through constructs employed to real data Levels in IRDS can be mapped using category theory concept of adjoints Future work to develop model and test constructions for a variety of data models