The path ranking algorithm (PRA) has been recently proposed to address relational classification and retrieval tasks at large scale. We describe Cor-PRA, an enhanced system that can model a larger space of relational rules, including longer relational rules and a class of first order rules with constants, while maintaining scalability. We describe and test faster algorithms for searching for these features. A key contribution is to leverage backward random walks to efficiently discover these types of rules. An empirical study is conducted on the tasks of graph-based knowledge base inference, and person named entity extraction from parsed text. Our results show that learning paths with constants improves performance on both tasks, and that modeling longer paths dramatically improves performance for the named entity extraction task.