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Four-level Architecture for Closure in Interoperability

Four-level Architecture for Closure in Interoperability. EFIS, 17th-18th July 2003 Nick Rossiter & Michael Heather Informatics, Northumbria University http://computing.unn.ac.uk/staff/CGNR1/ nick.rossiter@unn.ac.uk. Interoperability. Interoperability:

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Four-level Architecture for Closure in Interoperability

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  1. Four-level Architecture for Closure inInteroperability EFIS, 17th-18th July 2003 Nick Rossiter & Michael Heather Informatics, Northumbria University http://computing.unn.ac.uk/staff/CGNR1/ nick.rossiter@unn.ac.uk

  2. Interoperability • Interoperability: the ability to request and receive services between various systems and use their functionality. • More than data exchange. • Implies a close integration

  3. Motivations • Diversity of modelling techniques • Data warehousing requires heterogeneous systems to be connected • Semantic Web/RDF/Ontologies • GRID • MOF/MDA

  4. Mappings in Systems are two-way MetaMetaPolicy Meta Organize Classify Instantiate Concepts Constructs Schema Types Named Data Values Downward arrows are intension-extension pairs

  5. Formalising the Architecture • Requirements: • mappings within levels and across levels • bidirectional mappings • closure at top level • open-ended logic • relationships (product and coproduct) • Candidate: category theory as used in mathematics as a workspace for relating different constructions

  6. Choice: category theory • Requirements: • mappings within levels and across levels • arrows: function, functor, natural transformation • bidirectional mappings • adjunctions • closure at top level • four levels of arrow, closed by natural transformation • open-ended logic • Heyting intuitionism • relationships (product and coproduct) • Cartesian-closed categories (like 2NF): pullback and pushout

  7. Comparing one System with Another CCCSSMDT CCCS´SM´DT´ P O I    P´ O ´ I ´ ,,  are natural transformations (comparing functors)

  8. Godement Calculus • Rules showing: • composition of functors and natural transformations is associative • natural transformations can be composed with each other • For example: • (I´O´)  = I´(O´); (OP) = (O)P •   = (O) o (I´ );  = P o (O´)

  9. Four Levels are Sufficient • In category theory: • objects are identity arrows • categories are arrows from object to object • functors are arrows from category to category • natural transformations are arrows from functor to functor • An arrow between natural transformations is a composition of natural transformations, not a new level

  10. Analogous Levels for Interoperability

  11. Pullbacks are used extensively for database relationships Here of S and M in Context of IMG S = source, M = medium, IMG = image, W = world

  12. Discussion • Category theory shows that: • four levels are ideal for interoperability • more than four yields no benefits • less than four gives only local interoperability • Categorical approach provides: • an architecture for universal interoperability • a calculus (Godement) for composing mappings at any level • adjunctions for evaluating two-way mappings

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