In this paper we have explored how iterative refinement could be used with fix-point computation of ASP to improve a bottleneck computation of the ASPAL system. We have implemented our RASPAL approach and compared it against ASPAL. Our tests have demonstrated the impact of the additional mode decla-rations for learning change transactions: RASPAL performs worse than ASPAL when the learning task is small and the difference betweeniand the maximum size of a hypothesis clause is also small. On the other hand, when the search space for the hypothesis becomes extremely large and literals in the hypothesis are not strongly dependent on one another, our refinement approach is able to solve the task using a much smaller top theory.
In this paper we have concentrated on the comparison between ASPAL and RASPAL, but there are also other works that are similar to RASPAL and ASPAL. Past ILP algorithms have frequently used meta-level information to help with the search for the hypothesis, the language bias being the commonly used meta-level information for limiting the hypothesis search space. Systems such as ASPAL, RASPAL and Metagol [16] have taken a step further in this direc-tion by transforming the original learning task into a meta-level learning task.
This involves using transformations to abstract some or all of the inductive task into a corresponding meta-level representation. Unlike ASPAL and RASPAL, which only abstract their hypotheses and top theories, Metagol uses second order predicates to represent all of its learning task in meta-level form. By using meta-level representation of only the hypothesis space, ASPAL and RASPAL can still reason about the object level semantics and therefore allow more easily the learning of nonmonotonic hypotheses. Currently, Metagol does not extend to learning nonmonotonic hypotheses.
RASPAL also belongs to the subclass of ILP systems that use incremental learning. HYPER [2] is another example of an ILP system that learns through refinement. However, differently from our approach, it constructs the hypothesis by first finding an overly general partial hypothesis (i.e. one that covers all positive examples), which is then specialised until it covers no negative examples.
In addition to being unable to learn nonmonotonic tasks, HYPER’s refinement will only add at most a single body atom to each clause per each iteration.
Learning Through Hypothesis Refinement Using Answer Set Programming 45 This makes it unable to learn hypotheses where more than one body atom must be added to the same clause in the same iteration to impact the score of the refined hypothesis.
A recently proposed incremental learning system that is more related to RASPAL is ILED [9], an ILP system based on XHAIL [17], which is designed to address the scalability problem of learning from continuously collected real life temporal data. Like our work it uses hypothesis refinement and abductive reasoning for learning, and is capable of learning nonmonotonic clauses. However, unlike RASPAL, which uses refinement for learning a single learning task, ILED’s incremental learning is used for processing new knowledge and incorporating it into previous learnt concepts.
There are many future directions for our work. Our RASPAL approach has potentials for making further contributions in the area of Predicate Invention [21]. Initial attempts of using ASPAL for predicate invention have shown that the search space can grow very large as there are many possible formats new pred-icates could take. Iterative refinement in this case could be very beneficial. The implementation could also be further optimised to eliminate re-computations.
Acknowledgment. This work is partially funded by the 7th Framework EU-FET project 600792 ALLOW Ensembles and the EPSRC project P44745.
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