ergophobe - 4:21 pm on Dec 23, 2011 (gmt 0)
The DTD does not, as far as I know, specify a visual style (that is usually the case, even with elements like EM and STRONG which browsers universally map to italic and bold. Lots of decisions are left to the user agent (because if you specify dotted underline or italic, this leaves no clue how to handle the element in a screen reader, for example).
So yes, the visual style varies. Firefox and Opera will underline the abbreviation IF you have defined a title for it. Webkit browsers (Safari and Chrome) will not.
In the case of a webkit browser, it's up to you to specify the visual style with CSS.
I don't think it would be correct to say that the "bottom-border property value dotted does not render under Google Chrome" because as far as I know, it's not set.
You would need to set it in your stylesheet.
It believe it would be correct to say (subject to testing): "By default, Firefox and Opera style the ABBR element with a dotted underline if a title is present, and display the title on hover. Webkit browsers (Chrome and Safari) display the title on hover, but leave it to the designer to provide visual styling for the element."