What Twitter web apps can automatically filter my tweets?

Tweetdeck has a filter that you can apply to any column with four options: Text, Name, Source, and Time. I use the "text" filter to remove tweets with the word "Archives", for example, because one account that I like to follow has a bot setup that also sends out tweets promoting old blog posts that I've already read. The problem is you can only apply one filter per column, so it's somewhat limited. And it doesn't do any automatic training as you've suggested -- it's an input-output system that does only what you tell it. I'm not aware of any apps that have more full featured organizational filtering.

You can try Twtboardpro... It's a nice twitter automation tool, we prefer for generating business leads and managing multiple Twitter accounts. It will help you organize your Twitter feed, provide nice and get valuable information. You can easily connect with your target audience by its amazing search options. It also have nice Optimized Management, follow and unfollow management features. http://twtboardpro.com

I've been working on solving this problem for a little while. So far my best solution has been a browser extension that helps you hide what you don't want to see by specifying keywords. You can check it out at http://slipstre.am/ and I'm always happy to hear feedback: Automatica solutions are a little harder to come by. I know of the Cadmus and my6sense but am not sure how actively developed they are.