I´m Software Architect and I´m not very familiarized with standard notation in mathematics but I would like to write a paper explaning a normalization of computing model for expert systems. It has a very deep background on geometrics, logic and group theory, so I have to define some [new] unusual mathematical objects, and in order to get it accepted by the reader (some of them scientists of different disciplines) I would like to be as clear and correct as possible. How can I improve this definitions? Does anyone or any company offer this "help" as a service?

I have about 20 definitions like this (only for instance) to be improved.

The m-Crown of a set S, denoted by $S^m$, is the family of sets of every subset of its index set of cardinality $m$ no containing its index, such that

$\forall(X_i \in S^m : i \in S) \rightarrow X_i = \{ x \subset S :(i\notin x \land|x|=m) \} $

(Note: I am sure that it is a correct definition but may be not easy to understand with a not very standarized notation)