Semantic distance between excerpts of text. I'm wondering how far along the natural language processing is in determining the semantic distance between two excerpts of text.

For instance, consider the following phrases


Early this morning I got up and washed my car.
I cleaned my truck up this morning.
Bananas are an excellent source of potassium.


Clearly (to the human reader) the first two statements are much more similar to one another than they are to the third statement.  Does there exist any theory that would allow a computer to draw the same conclusion?  What about if we allow longer excerpts such as new articles?

Meta info: this is my first post here, so feel free to direct me to a better forum for asking such a question if this isn't where I should be.  Also, feel free to retag my question with anything more appropriate.
You are looking for "lexical cohesion". Try searching for this term and you will get tons of literature. After constructing the so-called "lexical chains", well-known graph partitioning and information retrieval algorithms can be used to group them into semantic classes. There is in fact a lot of theory and algorithms behind this "post-processing". Dictionary of synonyms and antonyms is often used to construct these chains. I worked on such extraction algorithms during my undergraduate days, about 10 years back. So this field must be more advanced now.