The first three algorithms produce similarity scores by matching words in the two phrases and the fourth is an edit distance.

The algorithm is essentially bottom-up agglomerative clustering of word senses using a similarity score derived from P(Y|X1, X2).

The similarity score for two senses is defined as:

Third, we compared to the entailment classifier with no transitivity constraints (clsf) to see if combining distributional similarity scores improves performance over single measures.

similarity score estimating whether p1 entails p2.

We compute 11 distributional similarity scores for each pair of predicates based on the arguments appearing in the extracted arguments.