The procedure is obtained by making some varia­tions to the algorithm designed by Resnik (1995) for disambiguating noun groups. Given a set of nouns W = {w1,w2,...,wn}, obtained from document d, with each wi having an associated sense inven­tory Si = {si1,si2,...,sik} of possible senses, the goal is assigning each wi with the most appropri­ate sense sih G Si, according to the similarity of wi with the other words in W (the context for wi). The idea is to define a function ^(wi,sij), wi G W, sij G Si, that computes a value in [0,1] representing the confidence with which word wi can be assigned with sense sij. The intuition behind this algorithm is essentially the same exploited by Lesk (1986) and other authors: The most plausible assignment of senses to multiple co-occurring words is the one that maximizes relatedness of meanings among the chosen senses. JIGSAWnouns differs from the original algorithm by Resnik (1995) in the similarity mea­sure used to compute relatedness of two senses. We adopted the Leacock-Chodorow measure (Leacock and Chodorow, 1998), which is based on the length of the path between concepts in an IS-A hierarchy. The idea behind this measure is that similarity be­tween two synsets, s1 and s2, is inversely propor­tional to their distance in the WordNet IS-A hierar­chy. The distance is computed by finding the most specific subsumer (MSS) between si and s2 (each ancestor of both s1 and s2 in the WordNet hierar­chy is a subsumer, the MSS is the one at the lowest level) and counting the number of nodes in the path between s1 and s2 that traverse their MSS. We ex­tended this measure by introducing a parameter k that limits the search for the MSS to k ancestors (i.e. that climbs the WordNet IS-A hierarchy until either it finds the MSS or k + 1 ancestors of both s1 and s2 have been explored). This guarantees that "too abstract" (i.e. "less informative") MSSs will be ig­nored. In addition to the semantic similarity func­tion, JIGSAWnouns differs from the Resnik algo­rithm in the use of:

1. a Gaussian factor G, which takes into account the dis­tance between the words in the text to be disambiguated;

2. a factor R, which gives more importance to the synsets that are more common than others, according to the fre­quency score in WordNet;

3. a parametrized search for the MSS between two concepts (the search is limited to a certain number of ancestors).

Algorithm 1 describes the complete procedure for the disambiguation of nouns. This algorithm consid­ers the words in W pairwise. For each pair (wi,wj), the most specific subsumer MSSj is identified, by reducing the search to depthl ancestors at most. Then, the similarity sim(wi,Wj,depth2) between the two words is computed, by reducing the search for the MSS to depth2 ancestors at most. MSSj is considered as supporting evidence for those synsets sik in Si and sjh in Sj that are descendants of MSSij. The MSS search is computed choosing the nearest MSS in all pairs of synsets sik,sjh. Like­wise, the similarity for (wi,wj) is the max similarity computed in all pairs of sik ,sjh and is weighted by a gaussian factor that takes into account the posi­tion of wi and wj in W (the shorter is the distance Algorithm 1 The procedure for disambiguating nouns derived from the algorithm by Resnik between the words, the higher is the weight). The value <p(i,k) assigned to each candidate synset sikfor the word wi is the sum of two elements. The first one is the proportion of support it received, out of the support possible, computed as supik/normiin Algorithm 1. The other element that contributes to <p(i,k) is a factor R(k) that takes into account the rank of sik in WordNet, i.e. how common is the sense sik for the word wi. R(k) is computed as:

where n is the cardinality of the sense inventory Si for wi, and k is the rank of sik in Si, starting from 0.

Finally, both elements are weighted by two pa­rameters: a, which controls the contribution given to p(i, k) by the normalized support, and ß, which controls the contribution given by the rank of sik. We set a = 0.7 and ß = 0.3. The synset assigned to each word in W is the one with the highest p value. Notice that we used two different parameters, depthl and depth2 for setting the maximum depth for the search of the MSS: depth1 limits the search for the MSS computed in the similarity function, while depth2 limits the computation of the MSS used for assigning support to candidate synsets. We set depth1 = 6 and depth2 = 3.

Before describing the JIGSAWverbs procedure, the description of a synset must be defined. It is the string obtained by concatenating the gloss and the sentences that WordNet uses to explain the usage of a synset. First, JIGSAWverbs includes, in the context C for the target verb wi, all the nouns in the window of 2n words surrounding wi. For each candidate synset sik of wi, the algorithm computes nouns(i, k), that is the set of nouns in the descrip­tion for sik.

maxjk = maxwlEnouns(i,k) {sim(wj,wi,depth) } (2)

where sim(wj,wt, depth) is defined as in JIGSAWnouns. In other words, maxjk is the highest similarity value for wj wrt the nouns related to the k-th sense for wi. Finally, an overall simi­larity score among sik and the whole context C is computed:

where R(k) is defined as in Equation 1 with a differ­ent constant factor (0.9) and G(pos(wi) ,pos(wj)) is the same Gaussian factor used in JIGSAWnouns, that gives a higher weight to words closer to the tar­get word. The synset assigned to wi is the one with the highest p value. Algorithm 2 provides a detailed description of the procedure.

This procedure is based on the WSD algorithm pro­posed by Banerjee and Pedersen (2002). The idea is to compare the glosses of each candidate sense for Algorithm 2 The procedure for the disambiguation of verbs

1: procedure JIGSAWverbs(wi,d, depth) > finds the proper synset of a polysemous verb wi in document d the context for wi. For example, C = {wi,W2,W4,w5}, if the sequence of words {w1,w2,w3,w4,w5} occurs in d, w3 being the target verb, wj being nouns, j = 3 is the sense inventory for wi, that is the set of all candidate

synsets for wi returned by WordNet 4: s — null > s is the synset to be returned 5: score —--MAXDOUBLE > score is the

similarity score assigned to s 6: p — 1 >p is the position of the synsets for wi

nouns(i, k) is the set of all nouns in the description of sik10: sumGauss — 0 12: for all wj e C do > computation of the similarity

between C and sik13: maxjk — 0 >maxjk is the highest similarity

value for wj, wrt the nouns related to the k-th sense for wi. 14: sumGauss — G(pos(wi) ,pos(wj )) >

Gaussian function which takes into account the difference

between the positions of the nouns in d 15: for all nouni e nouns(i, k) do 16: sim — sim(wj,nouni,depth) >simis the similarity between the j-th noun in C and l-th noun in

nouns(i, k) 17: if sim > maxjk then 22: for all wj e C do 25: sumTot — sumTot/sumGauss JIGSAWnouns

the target word to the glosses of all the words in its context. Let Wi be the sense inventory for the tar­get word wi. For each sik G Wi, JIGSAWotherscomputes the string targetGlossik that contains the words in the gloss of sik. Then, the procedure computes the string contextGlossi, which contains the words in the glosses of all the synsets corresponding to each word in the context for wi. Fi­nally, the procedure computes the overlap between contextGlossi and targetGlossik, and assigns the synset with the highest overlap score to wi. This score is computed by counting the words that occur both in targetGlossik and in contextGlossi. If ties occur, the most common synset in WordNet is cho­sen.