Statistical Relational Learning with Soft Quantifiers

Abstract. Quantification in statistical relational learning (SRL) is either existen-tial or universal, however humans might be more inclined to express knowledge using soft quantifiers, such as “most ” and “a few”. In this paper, we define the syntax and semantics of PSLQ, a new SRL framework that supports reasoning with soft quantifiers, and present its most probable explanation (MPE) inference algorithm. To the best of our knowledge, PSLQ is the first SRL framework that combines soft quantifiers with first-order logic rules for modeling uncertain rela-tional data. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and in-tuitive formulation of domain knowledge, but also improves the accuracy of in-ferred results.