Understanding Dijkstra's notation $f.x.y$
I think this would read as follows in modern notation (although  field-local variations are possible):

$$\forall x y. x &lt; y \Rightarrow f(x,y) &lt; f(y,x).$$

Read aloud: for all x and y, x is less than y implies that f of x and y 
is less than f of y and x.

If you read the first sentence of the linked document, it says that square brackets represent universal quantification over $x$ and $y$. The second states that $f$ is a function. =&gt; is ASCII art for $\Rightarrow$ (logical implication).

The main problem here is missing context (and detective skills). This article refers to EWD878. Perhaps looking there would have helped. Indeed, looking at that article, you see notation slightly closer to what is used today (at least, by Haskell programmers: f.x.y becomes f\ x\ y).