Entity Modelling

www.entitymodelling.org - entity modelling introduced from first principles - relational database design theory and practice - dependent type theory

The mathematical notions of
(a) Contextual Categories and (b) Generalised Algebraic Theories encapsulate the idea
of
types dependent on contexts which in turn are constructed from types^{1}^{,}^{2} .
Now types of things are equally concepts and (c) Entity Modelling
as described here is about modelling the types of things of interest in a particular
situation or or as part of a particular endeavour (the chosen perspective); in an
entity model,
composition relationships model dependencies between types of things. (a), (b) and
(c) are therefore closely related.
An introduction to types that vary (aka dependent types) is given here:
TypesThatVary.pdf.

Two mathematical papers follow. Firstly, here are some relatively recent notes on
the *generalised algebraic theory* of *contextual categories*:
theGATofCCs.pdf. I wrote these after having learnt of the definition of C-system given
by Vladimir Voevodsky.

Secondly, here is a recent write up of some work that I did at the time of my thesis, basically it is a variation on contextual categories — in brief, meta-GAT algebras are to a contexual category as a clones are to Lawvere theories. I wrote these notes suspecting, as was subsequently confirmed, that Voevodsky was producing a paper describing similar structures to my meta-GAT algebras (he calls them B-systems): MetaGAT and MetaGAT algebras.pdf.

One of my ongoing projects is to produce confluent rewriting systems for both of the above theories and to prove equivalence automatically.

Another ongoing project is to find a generalisation of contextual category which explicitly
includes
conjunctive dependencies such as we find them in entity modelling and as described
here in section
conjunctive dependencies.
So far this has proved elusive. If such can be found then
it would give a more practical diagramming approach than contextual categories for
the depiction of concepts.
A paper I published on this in 1986^{1} called
"Formalising the Network and Hierarchical Data Models "
is quite a long way off the mark.