How to exclude taxonomy=term using url alone

This may have been answered somewhere but I may not be searching for the right wording or my concept is just way off 🙂

In a nutshell:
If I have a url like this:

http://mysite.com/?taxname=termvalue

wordpress dutifully parses that to arrive at http://mysite.com/taxname/termvalue and shows all posts having that taxonomy term equal to that term value.

But I would like to construct a url something like one of these:

http://mysite.com/?taxname=-termvalue
http://mysite.com/?taxname!=termvalue
http://mysite.com/?taxname<>termvalue
http://mysite.com/taxname/-termvalue/

which excludes any particular term value (or id).
(I know the syntax is wrong but wanted my meaning to be clear.)

I do know how to make a custom query with all the arguments as described here: http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters but am hoping for a shortcut where wordpress can directly parse a constructed url like that to exclude (and include) taxonomy terms.

Thanks!