1. 21st May 2004Informatics Research Conference, Northumbria University 1 Some Fundamental Questions in Databases Nick Rossiter (with Michael Heather)

2. 21st May 2004Informatics Research Conference, Northumbria University 2 Questions Why so many database models? What is their rationale? Are there undiscovered new models? Is there an ultimate data model? Do all models have to be reductionist?

3. 21st May 2004Informatics Research Conference, Northumbria University 3 Meaning of Database Model A model is a representation of reality according to some perceived view. A database model for representing this view has: –a structure –a manipulation language –rules for controlling the structure

4. 21st May 2004Informatics Research Conference, Northumbria University 4 Classical Database Models 1

5. 21st May 2004Informatics Research Conference, Northumbria University 5 Classical Database Models 2

6. 21st May 2004Informatics Research Conference, Northumbria University 6 Classical Relationships Relationships are often performed in a separate process: –Entity-Relationship Modelling – Unified Modelling (UML) Normalisation is needed to verify schema design: –particularly to relate key and non-key attributes. The levels, mappings and relationships all have to be integrated in a consistent database design.

7. 21st May 2004Informatics Research Conference, Northumbria University 7 Developing non-classical Areas The new developing areas are: –quantum computation, exploiting quantum mechanics principles in physics, –nanoscale chemistry, –bio- and molecular-computing processing as in genetics Collectively referred to as natural computing Natural computing is: –Real-world processing does not rely on any model. –Data can be input neat without any reductionist pre-processing.

8. 21st May 2004Informatics Research Conference, Northumbria University 8 Non-classical Database Design Not layered (Theory of Categories) Use Dolittle approach (push me-pull you creature of High Lofting): A database design is a topos -- a Dolittle diagram subsuming the pullback/pushout relationships as: X+ f* Cartesian Closed Category

9. 21st May 2004Informatics Research Conference, Northumbria University 9 What is f*? f* is an examination and re-indexing functor –organises the data into a key for storage and applies a query for interrogation of the database. –puts together a key by concatenation as in the relational model. –looks up information for retrieval by inspecting the key. In quantum theory: –the key (X) is entanglement, –the colimit (+) is superposition, In genetics it is a DNA strand.

10. 21st May 2004Informatics Research Conference, Northumbria University 10 Enriched Pullback In terms of the Dolittle diagram: –f* is the same operation in classical and natural computation. What then corresponds to the database schema in natural computing? The pullback diagram contains many more arrows than in the Dolittle diagram. This enriched diagram satisfies our needs.

11. 21st May 2004Informatics Research Conference, Northumbria University 11 S = source, M = medium, IMG = image, W = world Pullback of S and M in Context of IMG

12. 21st May 2004Informatics Research Conference, Northumbria University 12 Contents of Enriched Dolittle The Dolittle diagram relates binary categorial limits (X) and colimits (+) for types Logic is Heyting -- intuitionistic logic. Godement calculus can be used for composing arrows across levels pullback functor (f* or  ): –emulates the join operation of databases Other arrows represent: –projection  ; membership  –existential  or  quantification –universal  or  quantification

13. 21st May 2004Informatics Research Conference, Northumbria University 13 Higher-level Arrows for Semantics/DB Design Originality with the unit of adjunction  –Example:  gives properties of relationship onto limit –  = 0, no creativity, mapping S to S X IMG M is 1:1 –  = 1, maximum creativity, mapping S to S  IMG M is from S to cartesian product of S  M. Style with the counit  of adjunction. –Example:  gives properties of relationship onto colimit –  = 1, preservation of style, each S is found exactly once in S X IMG M –  = 0, loss of style, each S occurs in S  IMG M maximum number of times (S  M).

14. 21st May 2004Informatics Research Conference, Northumbria University 14 Normalisation and Defeasance Not captured at the data model level –except for 1NF in some models A complex topic jargon-wise Perhaps related to defeasibility or nonmonotonic reasoning: –A kills B implies A has committed murder –A kills B AND B attacked A implies A has committed manslaughter –strengthening of antecedent changes conclusion

15. 21st May 2004Informatics Research Conference, Northumbria University 15 Integration of Normalisation within the model Many normalisation definitions say: –A table is normalised if condition X holds and additional conditions B, C,, D etc do not hold Normalisation failure is due to defeasance Exploring incorporation of defeasance into topos

16. 21st May 2004Informatics Research Conference, Northumbria University 16 Non-classical Database Model ModelMathsManip- ulation Non- procedural Design Cite ToposCate- gories Comp- osition/ Intuit- ionistic/ Godement YesInte- grated (topos, defeas- ance) Nelson & Rossiter (1996); Rossiter & Heather (2003, 2004)

17. 21st May 2004Informatics Research Conference, Northumbria University 17 Questions Why so many database models? What is their rationale? Are there undiscovered new models? Is there an ultimate data model? Do all models have to be reductionist?