Concurrent Reasoning with Inference Graphs

Since at least the early 1980s there has been an effort to utilize multiple processors for logical reasoning. Prior to the rise of the multi-core desktop computer, this often meant parallel algorithms on specialized hardware. Parallel logic programming systems designed during that same period were less attached to a particular parallel architecture, but parallelizing Prolog is a very complex problem (Shapiro 1989). Parallelizing Datalog has been more successful, but it is a less expressive subset of Prolog. Recent work in statistical inference has returned to large scale parallelism using GPUs, but while GPUs are good at statistical calculations, they do not do logical inference well (Yan, Xu, and Qi 2009). We present inference graphs, a graph-based natural deduction inference system which lives within a KR system and is capable of taking advantage of multiple cores and/or processors using concurrrent processing techniques rather than parallelism. Inference graphs extend propositional graphs so that the representation of knowledge is also the inference system, something we believe is unique among logical inference systems. We chose to use natural deduction inference, despite the existence of very well performing refutation based theorem provers, because our system is designed to be able to perform forward, bi-directional (Shapiro, Martins, and McKay 1982), and focused reasoning in addition to the backwards inference used in resolution. Natural deduction also allows formulas generated during inference to be retained in the KB for later re-use, whereas refutation techniques always reason about the negation of the formula to be derived, making intermediate derivations invalid. In addition, our system is designed to allow formulas to be disbelieved, and to propogate that disbelief to dependent formulas. We believe inference graphs are the only concurrent inference system with all these capabilities.