DERIVATION S RULES USEDPROBABILITY P(s) = j P(T,S) where t is a parse of s = j P(T) P(T) The probability of a tree T is the product of the probabilities of the rules used to generate it. P(s) The probability of the string s is the sum of the probabilities of the trees which have that string as their yield Tree and String Probabilities s = people fish tanks with rods P(t 1 ) = 1.0 0.7 0.4 0.5 0.6 0.7 1.0 0.2 1.0 0.7 0.1 = P(t 2 ) = 1.0 0.7 0.6 0.5 0.6 0.2 0.7 1.0 0.2 1.0 0.7 0.1 = P(s) = P(t 1 ) + P(t 2 ) = = Overview An introduction to the parsing problem Context free grammars A brief(!) sketch of the syntax of English Examples of ambiguous structures PCFGs, their formal properties, and useful algorithms Weaknesses of PCFGs Lack of sensitivity to lexical information Lack of sensitivity to structural frequencies Another Case of PP Attachment Ambiguity a)S NP NNS workersworkers VP VBD dumped NP NNSinto sacks PP IN NP DT abin NN b)S NP NNS workersworkers VP VBD dumped NP NNS sacks PP IN into NP DTNN abin A Case of Coordination Ambiguity a)NP NNS dogs PP IN inNNS NP houses CC and NP NNS cats b)NP NNS dogs PP IN in NP NNSandNNS houses CC NP cats