I am trying to formally formulate the definition of the co-occurrence of two concepts in a document. Is the next mathematical equation correct?
Mathematically a word co-occurrence is defined as:
$Co-occurrence(c_i,c_j )= \sum_{c_i,c_j∈d}d_{c_i∩c_j}$
where $c_i$ and $c_j$ represent concepts mentioned in the collection of a documents $D$, and D is defined as
$D=\{d_1,d_2....d_n\}$ where $d$ represent each document of the collection.
In ordinary language what i am trying to formulate is the following: a $Co-occurrence$ of two cocepts, $c_i$ and $c_j$, (words) for a set of documents $D$ is equal to the number of documents that contains $c_i$ and also contains $c_j$. Note that $c_i$ and $c_j$ not could be the same word.
If there is one or more documents that contain the two concepts $c_i$ and $c_j$, at same time, this means that there is a relation between them $R{c_i c_j}$:
$$R{c_i c_j} = \begin{cases} ∃, & \text{if $Co-occurrence(c_i,c_j )>0$} \\ ∄, & \text{otherwise} \end{cases}$$
There appear to be some mismatches and unexplained notations. For example, what is lowercase d with no subscript? Why is it written as though it is a function applied to an intersection? What is the meaning of the intersection of two words?
We could try the following: $$Co-occurrence(c_1,c_2 )= \sum_{k=0}^n f(k, D)$$
where f is defined as follows:
$$f(k, D) = \begin{cases} 1, & \text{if $[c_1 \in d_k \land c_2 \in d_k ]$} \\ 0, & \text{otherwise} \end{cases}$$
To write formulas like the above one for f, use "Find ..." in your browser to look for the title "Definitions by cases (piecewise functions)" at the following link: MathJax basic tutorial and quick reference