Grammar learning using Inductive Logic Programming

This paper gives a brief introduction to a particular machine learning method known as inductive logic programming. It is argued that this method, unlike many current statistically based machine learning methods, implies a view of grammar learning that bears close affinity to the views linguists have of the ‘logical problem of language acquisition’. Two experiments in grammar learning using this technique are described, using a unification grammar formalism, and positive-only data. What is Inductive Logic Programming? Inductive Logic Programming [MDR94] is a machine learning technique that builds logical theories (here,(full) first order logic) to explain observations. ‘Explain’ here means that it is possible to deduce the evidence from the axioms of the theory (and not be able to deduce negative evidence). ILP is best introduced via the following schema, and a consequent derivation: 1. Background & Hypothesis |= Evidence We do not assume a tabula rasa: for reasons that every linguist will be familiar with, it is necessary to assume a fairly rich set of background assumptions to constrain the space of possible hypotheses. Given this background, and the evidence, the task is to come up with a hypothesis such that when it is conjoined with the background, the evidence can be deduced from it. Each of the components in the above schema is represented as a set of logical statements. Notice that schema 1 is logically equivalent to 2, since if P |= Q then P→ Q (the deduction theorem), and P → Q ≡ ¬Q → ¬P (contraposition): 2. Background & Evidence |= Hypothesis