Similarity-Guided Clause Generalization

Abstract

Abstract. Few works are available in the literature to define similarity criteria between First-Order Logic formulae, where the presence of relations causes various portions of one description to be possibly mapped in different ways onto another description, which poses serious computational problems. Hence, the need for a set of general criteria that are able to support the comparison between formulae. This could have many applications; this paper tackles the case of two descriptions (e.g., a definition and an observation) to be generalized, where the similarity criteria could help in focussing on the subparts of the descriptions that are more similar and hence more likely to correspond to each other, based only on their syntactic structure. Experiments on real-world datasets prove the effectiveness of the proposal, and the efficiency of the corresponding implementation in a generalization procedure.

FOL Learning for Knowledge Discovery in Documents

“…This means that no class was initially known and all classes in the final theory result from incremental revisions. Two versions of INTHELEX were run and compared to each other: the classical one (I), and a new one endowed with the similarityguided generalization (SF) of (Ferilli, 2007). It is interesting to note that, on the document dataset, the similaritydriven generalization was very effective, preserving on average more than 90% atoms of the shortest clause, with a maximum of 99.48% and just 0.006 variance.…”

“…To find such an approximation, the similarity between clause paths, as defined in previous sections, can be exploited, in order to quickly locate subcomponents of the clauses to be generalized that best match to each other. The algorithm, presented in (Ferilli, 2007) and reported below, works as follows: generalizations of all couples of paths in the original clauses to be generalized are scanned by decreasing similarity and added to the current partial generalization if compatible with it, or ignored otherwise. When all path generalizations have been considered, a generalization is obtained.…”

Generalization-Based Similarity for Conceptual Clustering

“…The path intersections are considered by decreasing similarity, adding to the partial generalization generated thus far the common literals of each pair whenever they are compatible [7]. The question arises whether the proposed similarity framework is actually able to lead towards the identification of the proper sub-parts to be put in correspondence in the two descriptions under comparison.…”

k-Nearest Neighbor Classification on First-Order Logic Descriptions

“…For this reason, most ILP learners require the generalization to be a subset of the clauses to be generalized, in which case the θ OI subsumption generalization model [6], based on the Object Identity assumption, represents a supporting framework with solid theoretical foundations to be exploited. The work in [7] shows that the similarity techniques shown so far are also able to guide the generalization procedure in obtaining quickly an accurate approximation of the least general generalization. Under θ OI subsumption, the least general generalization is not unique, but each minimal generalization is already reduced, and hence all of the atoms that make it up are mapped onto different atoms in the generalized clauses, which reduces computation of the common atoms to counting the length of the generalization, and computation of the different ones to subtracting the length of the generalization from that of either clause.…”