The Problem With Keyword Searching

Keyword searches have a tough time distinguishing between words that are spelled the same way, but mean something different (i.e. hard cider, a hard stone, a hard exam, and the hard drive on your computer). This often results in hits that are completely irrelevant to your query. Some search engines also have trouble with so-called stemming -- i.e., if you enter the word "big," should they return a hit on the word, "bigger?" What about singular and plural words? What about verb tenses that differ from the word you entered by only an "s," or an "ed"?
Search engines also cannot return hits on keywords that mean the same, but are not actually entered in your query. A query on heart disease would not return a document that used the word "cardiac" instead of "heart."