| Popis: |
This thesis presents two novel inductive logic programming (ILP) approaches, based on the notion of a connected theory. A connected theory contains clauses that depend on one another, either directly or via clauses in the background knowledge. Generalisation of such a theory is proved to be a sound and complete method for learning definite ILP hypotheses. The Induction on Failure (IOF) proof procedure, based on the connected theory generalisation method, adds secondary examples into the hypothesis, and generates auxiliary clauses to explain them. These concepts, novel to IOF, address the issues of incompleteness present in previous definite ILP methods. The concept of the connected theory is also applied to the non-monotonic, normal program setting. Thus, the method of generalisation of a normal connected theory is presented. Fundamental to this is the assertion that a partial non-monotonic hypothesis must include both positive and negative information, which the general hypothesis should preserve. This has resulted in, as far as the author is aware, the most complete semantic characterisation available of non-monotonic ILP using a bridge formula. It is proved that generalisation of such a formula to a set of completed definitions is a sound method of generating normal program hypotheses. In the course of establishing a completeness result for this latter approach, the semantics of the supported consequences of a normal program are defined, and the support tree method is presented and shown to be a sound and complete proof procedure for supported consequences. Using these results, it is shown that, for function-free programs, any correct hypothesis for which the examples are supported consequences of the learned program can be derived via a normal connected theory. |
