a mathematical model for file system We are supposed to come up with a mathematical model describing a file system and its operations. The file system stores metadata in a database, and retrieves it when necessary. How does one go about modelling this in set theory?
eg: F : Set of all Files, T : Set of all Tags
f belongs to F, t belongs to T
g(f) gives t where all the associated tags for that file are returned
h(t) gives f where all the associated files for that tag(s) are returned
then how does one model it using set theory? any hint, clue, links?

The following dynamic and variable sets are defined as, 

$F$  : Set of Files 
  $T$  : Set of Tags 
  $S$  : Set of Tags in query ( $S \subseteq T$ )
$$ R = \{(f,t) \mid f \,\, has \,\, tag \,\,t; f \in F, t \in T\}$$
$$g(f) = \{t : f \, R \, t\}$$
$g$ is an operation which takes input as a file $f$ and returns the set of tags ($t \in S$) related by $R$ to that file.
$$h(t) = \{f : f \, R \, t\}$$
$h$ is an operation which takes input as a tag $t$ and returns the set of files ($f \in F_{S}$) related by $R$ to that tag. 
The relation $R$ is stored as a set of ordered pairs $(f,t)$, where $R \subseteq F \times T$. 
A query operation on a single tag is expressed as:
$$q(t) = F_{S} \,\, where \,\, \{f \in F_{S} \mid h(t) = f\}$$
