Is there an algorithm that tells the semantic similarity of two phrases

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You might want to check out this paper:

Sentence similarity based on semantic nets and corpus statistics (PDF)

I've implemented the algorithm described. Our context was very general (effectively any two English sentences) and we found the approach taken was too slow and the results, while promising, not good enough (or likely to be so without considerable, extra, effort).

You don't give a lot of context so I can't necessarily recommend this but reading the paper could be useful for you in understanding how to tackle the problem.

Regards,

Matt.

There's a short and a long answer to this.

The short answer:

Use the WordNet::Similarity Perl package. If Perl is not your language of choice, check the WordNet project page at Princeton, or google for a wrapper library.

The long answer:

Determining word similarity is a complicated issue, and research is still very hot in this area. To compute similarity, you need an appropriate represenation of the meaning of a word. But what would be a representation of the meaning of, say, 'chair'? In fact, what is the exact meaning of 'chair'? If you think long and hard about this, it will twist your mind, you will go slightly mad, and finally take up a research career in Philosophy or Computational Linguistics to find the truth™. Both philosophers and linguists have tried to come up with an answer for literally thousands of years, and there's no end in sight.

So, if you're interested in exploring this problem a little more in-depth, I highly recommend reading Chapter 20.7 in Speech and Language Processing by Jurafsky and Martin, some of which is available through Google Books. It gives a very good overview of the state-of-the-art of distributional methods, which use word co-occurrence statistics to define a measure for word similarity. You are not likely to find libraries implementing these, however.