Math

Mathematical relations are not expressible with existing XML-Schema, RDF, or OWL techniques. It's missing an effective mathematical ontology. A simple approach might be to express the relation between semantical entities just as Relation:

is related to::...

But this has just the same meaning then a plain link. Instead we need a feature rich mathematical Approach to define constructs like Acceleration and define there Relation to Speed, Time, Distance, and the according Units Meter, inch, yard, etc., and Second, Minute, Hour, etc..

Therefore we need a way to express formulas in a semantic parseable way.

Basic Functions
Mathematical Functions for a ontologic wiki should support:


 * Mathematical
 * (important)
 * add, neg, minus
 * times, frac, mod
 * exp, root, nroot
 * e, log, ln
 * Fences (needs only '(' and ')')


 * Trigonometric functions
 * (important)
 * Sinus (sin, asin, sinh, asinh)
 * Cosinus (cos, acos, cosh, acosh)
 * Tangens (tan, atan, tanh, atanh)


 * Frontier functions
 * (min and max important)
 * lim
 * min
 * max


 * Derivates
 * (at least one important)
 * Delta
 * delta
 * partial


 * Dataset
 * (implicit part of the rdf/owl-syntax)
 * forall, in (programming loops)
 * exists
 * empty (rdf:nothing)
 * intersection (owl:intersectionOf)
 * union (owl:unionOf)


 * Logic
 * (implicit part of the rdf/owl-syntax)
 * True, False
 * and, or, not
 * nand, nor, xor


 * Relations
 * (important)
 * equal, notEqual
 * lessThan, greaterThan
 * plusMinus, minusPlus
 * approx
 * proportionalTo


 * Matrix
 * (optional)
 * Matrix Datatype
 * Vector Datatype
 * indexing
 * transposing


 * Summing
 * (optional)
 * Sum
 * Product
 * Coproduct
 * Integral
 * Binominal Coefficient (optional)
 * see also: lim


 * Functions
 * (optional)
 * definition of new functions
 * processing of a list of instuctions
 * ie. needed for the definition of prime numbers