In this paper, we give an algorithm for computing the value of the kernel function K _TERM , which takes a pair of terms in first-order logic as its inputs, and facilitates Support Vector Machines classifying terms in a higher dimension space. The value of K _TERM (s,t) is given as the total number of terms which subsume both s and t. The algorithm presented in the paper computes K _TERM (s,t) without enumerating all such terms. We also implement the algorithm and present some experimental examples of classification of first-order terms with K _TERM . Furthermore, we also propose the concept of intentional kernels as a generalization of K _TERM .