Known and Unknown Fields

Let $\mathbb{W}$ denote all named field values in a form and $\mathbb{F}$ denote a set of all form fields. Let $\mathbb{V}$ $\subseteq$ $\mathbb{W}$ denote a collection of named HTML form fields that have non-blank values and are accessible from DOM. A field v is known iff v $\in$ $\mathbb{V}$. Conversely, a field is unknown if v $\notin$ $\mathbb{V}$. Let $\mathbb{Z}$ be the collection of named field values and let val: $\mathbb{V}$ $\rightarrow$ $\mathbb{Z}$ be a function such that it maps a named field to its value then,

$$v \equiv \left\{\begin{array}{l@{\quad\quad}l} {\it known} & \mb... ...t val}(v) \neq null\\ {\it unknown} & \mbox{ } otherwise \end{array}\right.$$