input: phrase 1, phrase 2
output: semantic similarity value (between 0 and 1), or the probability these two phrases are talking about the same thing
For anyone just coming at this, i would suggest taking a look at SEMILAR - http://www.semanticsimilarity.org/ . They implement a lot of the modern research methods for calculating word and sentence similarity. It is written in Java.
SEMILAR API comes with various similarity methods based on Wordnet, Latent Semantic Analysis (LSA), Latent Dirichlet Allocation (LDA), BLEU, Meteor, Pointwise Mutual Information (PMI), Dependency based methods, optimized methods based on Quadratic Assignment, etc. And the similarity methods work in different granularities - word to word, sentence to sentence, or bigger texts.
Sorry to dig up a 6 year old question, but as I just came across this post today, I'll throw in an answer in case anyone else is looking for something similar.
cortical.io has developed a process for calculating the semantic similarity of two expressions and they have a demo of it up on their website. They offer a free API providing access to the functionality, so you can use it in your own application without having to implement the algorithm yourself.
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.
You might want to check into the WordNet project at Princeton University. One possible approach to this would be to first run each phrase through a stop-word list (to remove "common" words such as "a", "to", "the", etc.) Then for each of the remaining words in each phrase, you could compute the semantic "similarity" between each of the words in the other phrase using a distance measure based on WordNet. The distance measure could be something like: the number of arcs you have to pass through in WordNet to get from word1 to word2.
Sorry this is pretty high-level. I've obviously never tried this. Just a quick thought.
One simple solution is to use the dot product of character n-gram vectors. This is robust over ordering changes (which many edit distance metrics are not) and captures many issues around stemming. It also prevents the AI-complete problem of full semantic understanding.
To compute the n-gram vector, just pick a value of n (say, 3), and hash every 3-word sequence in the phrase into a vector. Normalize the vector to unit length, then take the dot product of different vectors to detect similarity.
This approach has been described in J. Mitchell and M. Lapata, “Composition in Distributional Models of Semantics,” Cognitive Science, vol. 34, no. 8, pp. 1388–1429, Nov. 2010., DOI 10.1111/j.1551-6709.2010.01106.x
I would look into latent semantic indexing for this. I believe you can create something similar to a vector space search index but with semantically related terms being closer together i.e. having a smaller angle between them. If I learn more I will post here.