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identifying classes in the Physics Derivation Graph for OWL (Web Ontology Language)

Published 2020-12-13T14:16:00.003Z by Physics Derivation Graph

Classes and subclasses of entities in the Physics Derivation Graph:

Some aspects of expressions and derivations I don't have names for yet:

Some aspects of expressions and derivations I don't need to label in the PDG:
See also

An equation is two expressions linked with an equal sign. 
What is the superclass above "equation" and "inequality"?
So far I'm settling on "statement".

I am intentionally staying out of the realm of {proofs, theorems, axioms} both because that is outside the scope of the Physics Derivation Graph and because the topic is already addressed by OMDoc. 

Suppose we have a statement like
y = x^2 + b where x = {5, 3, 1}
In that statement, 
What is the "where" relation in the statement? The "where" is a binary operator that relates two equations. There are other "statement operators" to relate equations, like "for all"; see the statement
a + c = 2*g + k for all g \in \Re
In that statement, "g \in \Re" is (an equation?) serving as a scope for the primary equation. 

All statements have supplemental scope/definition equations that are usually left as implicit. The reader is expected to deduce the scope of the statement from the surrounding context. 

The supplemental scope/definition equations describe both per-variable and inter-variable constraints. For example,
x*y + 3 = 94 where ((x \in \Re) AND (y \in \Re) AND (x<y))

More complicated statement:
f(x) = { 0 for x<0
       { 1 for 0<=x<=1
       { 0 for x>1
Here the LHS is a function and the RHS is an integer, but the value of the integer depends on x. 
Note that the "0<=x<=1" can be separated into "0<=x AND x<=1". Expanding this even more,
(f(x) = 0 for x<0) AND (f(x) = 1 for (0<=x AND x<=1)) AND (f(x) = 0 for x>1)