In this paper we explore a topic which is at the intersection of two areas of Machine Learning: namely Support Vector Machines (SVMs) and Inductive Logic Programming (ILP). We propose a general method for constructing kernels for Support Vector Inductive Logic Programming (SVILP). The kernel not only captures the semantic and syntactic relational information contained in the data but also provides the flexibility of using arbitrary forms of structured and non-structured data coded in a relational way. While specialised kernels have been developed for strings, trees and graphs our approach uses declarative background knowledge to provide the learning bias. The use of explicitly encoded background knowledge distinguishes SVILP from existing relational kernels which in ILP-terms work purely at the atomic generalisation level. The SVILP approach is a form of generalisation relative to background knowledge, though the final combining function for the ILP-learned clauses is an SVM rather than a logical conjunction. We evaluate SVILP empirically against related approaches, including an industry-standard toxin predictor called TOPKAT. Evaluation is conducted on a new broad-ranging toxicity dataset (DSSTox). The experimental results demonstrate that our approach significantly outperforms all other approaches in the study.