In recent years, several frameworks and systems have been proposed that extend Inductive Logic Programming (ILP) to the Answer Set Programming (ASP) paradigm. In ILP, examples must all be explained by a hypothesis together with a given background knowledge. In existing systems, the background knowledge is the same for all examples; however, examples may be context-dependent. This means that some examples should be explained in the context of some information, whereas others should be explained in different contexts. In this paper, we capture this notion and present a context-dependent extension of the Learning from Ordered Answer Sets framework. In this extension, contexts can be used to further structure the background knowledge. We then propose a new iterative algorithm, ILASP2i, which exploits this feature to scale up the existing ILASP2 system to learning tasks with large numbers of examples. We demonstrate the gain in scalability by applying both algorithms to various learning tasks. Our results show that, compared to ILASP2, the newly proposed ILASP2i system can be two orders of magnitude faster and use two orders of magnitude less memory, whilst preserving the same average accuracy. This paper is under consideration for acceptance in TPLP.
Our interest in this paper is in optimisation problems that are intractable to solve by direct numerical optimisation, but nevertheless have significant amounts of relevant domain-specific knowledge. The category of heuristic search techniques known as estimation of distribution algorithms (EDAs) seek to incrementally sample from probability distributions in which optimal (or near-optimal) solutions have increasingly higher probabilities. Can we use domain knowledge to assist the estimation of these distributions? To answer this in the affirmative, we need: (a)a general-purpose technique for the incorporation of domain knowledge when constructing models for optimal values; and (b)a way of using these models to generate new data samples. Here we investigate a combination of the use of Inductive Logic Programming (ILP) for (a), and standard logic-programming machinery to generate new samples for (b). Specifically, on each iteration of distribution estimation, an ILP engine is used to construct a model for good solutions. The resulting theory is then used to guide the generation of new data instances, which are now restricted to those derivable using the ILP model in conjunction with the background knowledge). We demonstrate the approach on two optimisation problems (predicting optimal depth-of-win for the KRK endgame, and job-shop scheduling). Our results are promising: (a)On each iteration of distribution estimation, samples obtained with an ILP theory have a substantially greater proportion of good solutions than samples without a theory; and (b)On termination of distribution estimation, samples obtained with an ILP theory contain more near-optimal samples than samples without a theory. Taken together, these results suggest that the use of ILP-constructed theories could be a useful technique for incorporating complex domain-knowledge into estimation distribution procedures.
We investigate solving discrete optimisation problems using the estimation of distribution (EDA) approach via a novel combination of deep belief networks(DBN) and inductive logic programming (ILP).While DBNs are used to learn the structure of successively better feasible solutions,ILP enables the incorporation of domain-based background knowledge related to the goodness of solutions.Recent work showed that ILP could be an effective way to use domain knowledge in an EDA scenario.However,in a purely ILP-based EDA,sampling successive populations is either inefficient or not straightforward.In our Neuro-symbolic EDA,an ILP engine is used to construct a model for good solutions using domain-based background knowledge.These rules are introduced as Boolean features in the last hidden layer of DBNs used for EDA-based optimization.This incorporation of logical ILP features requires some changes while training and sampling from DBNs: (a)our DBNs need to be trained with data for units at the input layer as well as some units in an otherwise hidden layer, and (b)we would like the samples generated to be drawn from instances entailed by the logical model.We demonstrate the viability of our approach on instances of two optimisation problems: predicting optimal depth-of-win for the KRK endgame,and jobshop scheduling.Our results are promising: (i)On each iteration of distribution estimation,samples obtained with an ILP-assisted DBN have a substantially greater proportion of good solutions than samples generated using a DBN without ILP features, and (ii)On termination of distribution estimation,samples obtained using an ILP-assisted DBN contain more near-optimal samples than samples from a DBN without ILP features.These results suggest that the use of ILP-constructed theories could be useful for incorporating complex domain-knowledge into deep models for estimation of distribution based procedures.
This technical report describes the usage, syntax, semantics and core algorithms of the probabilistic inductive logic programming framework PrASP. PrASP is a research software which integrates non-monotonic reasoning based on Answer Set Programming (ASP), probabilistic inference and parameter learning. In contrast to traditional approaches to Probabilistic (Inductive) Logic Programming, our framework imposes only little restrictions on probabilistic logic programs. In particular, PrASP allows for ASP as well as First-Order Logic syntax, and for the annotation of formulas with point probabilities as well as interval probabilities. A range of widely configurable inference algorithms can be combined in a pipeline-like fashion, in order to cover a variety of use cases.
We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic Programming and E-generalization that includes an extension of Plotkin's lgg theorem to the equational case. We demonstrate the potential power of E-generalization by three example applications: computation of suggestions for auxiliary lemmas in equational inductive proofs, computation of construction laws for given term sequences, and learning of screen editor command sequences.
Logic-based event recognition systems infer occurrences of events in time using a set of event definitions in the form of first-order rules. The Event Calculus is a temporal logic that has been used as a basis in event recognition applications, providing among others, direct connections to machine learning, via Inductive Logic Programming (ILP). OLED is a recently proposed ILP system that learns event definitions in the form of Event Calculus theories, in a single pass over a data stream. In this work we present a version of OLED that allows for distributed, online learning. We evaluate our approach on a benchmark activity recognition dataset and show that we can significantly reduce training times, exchanging minimal information between processing nodes.
Inductive Logic Programming (ILP) combines rule-based and statistical artificial intelligence methods, by learning a hypothesis comprising a set of rules given background knowledge and constraints for the search space. We focus on extending the XHAIL algorithm for ILP which is based on Answer Set Programming and we evaluate our extensions using the Natural Language Processing application of sentence chunking. With respect to processing natural language, ILP can cater for the constant change in how we use language on a daily basis. At the same time, ILP does not require huge amounts of training examples such as other statistical methods and produces interpretable results, that means a set of rules, which can be analysed and tweaked if necessary. As contributions we extend XHAIL with (i) a pruning mechanism within the hypothesis generalisation algorithm which enables learning from larger datasets, (ii) a better usage of modern solver technology using recently developed optimisation methods, and (iii) a time budget that permits the usage of suboptimal results. We evaluate these improvements on the task of sentence chunking using three datasets from a recent SemEval competition. Results show that our improvements allow for learning on bigger datasets with results that are of similar quality to state-of-the-art systems on the same task. Moreover, we compare the hypotheses obtained on datasets to gain insights on the structure of each dataset.
Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model, yielding a nearly ubiquitous overfitting problem. Although mitigated by a variety of model regularisation methods, the common cure is to seek large amounts of training data---which is not necessarily easily obtained---that sufficiently approximates the data distribution of the domain we wish to test on. In contrast, logic programming methods such as Inductive Logic Programming offer an extremely data-efficient process by which models can be trained to reason on symbolic domains. However, these methods are unable to deal with the variety of domains neural networks can be applied to: they are not robust to noise in or mislabelling of inputs, and perhaps more importantly, cannot be applied to non-symbolic domains where the data is ambiguous, such as operating on raw pixels. In this paper, we propose a Differentiable Inductive Logic framework, which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with. Furthermore, as it is trained by backpropagation against a likelihood objective, it can be hybridised by connecting it with neural networks over ambiguous data in order to be applied to domains which ILP cannot address, while providing data efficiency and generalisation beyond what neural networks on their own can achieve.
We describe the Inspire system which participated in the first competition on Inductive Logic Programming (ILP). Inspire is based on Answer Set Programming (ASP). The distinguishing feature of Inspire is an ASP encoding for hypothesis space generation: given a set of facts representing the mode bias, and a set of cost configuration parameters, each answer set of this encoding represents a single rule that is considered for finding a hypothesis that entails the given examples. Compared with state-of-the-art methods that use the length of the rule body as a metric for rule complexity, our approach permits a much more fine-grained specification of the shape of hypothesis candidate rules. The Inspire system iteratively increases the rule cost limit and thereby increases the search space until it finds a suitable hypothesis. The system searches for a hypothesis that entails a single example at a time, utilizing an ASP encoding derived from the encoding used in XHAIL. We perform experiments with the development and test set of the ILP competition. For comparison we also adapted the ILASP system to process competition instances. Experimental results show that the cost parameters for the hypothesis search space are an important factor for finding hypotheses to competition instances within tight resource bounds.
Over the years the Artificial Intelligence (AI) community has produced several datasets which have given the machine learning algorithms the opportunity to learn various skills across various domains. However, a subclass of these machine learning algorithms that aimed at learning logic programs, namely the Inductive Logic Programming algorithms, have often failed at the task due to the vastness of these datasets. This has impacted the usability of knowledge representation and reasoning techniques in the development of AI systems. In this research, we try to address this scalability issue for the algorithms that learn answer set programs. We present a sound and complete algorithm which takes the input in a slightly different manner and performs an efficient and more user controlled search for a solution. We show via experiments that our algorithm can learn from two popular datasets from machine learning community, namely bAbl (a question answering dataset) and MNIST (a dataset for handwritten digit recognition), which to the best of our knowledge was not previously possible. The system is publicly available at https://goo.gl/KdWAcV. This paper is under consideration for acceptance in TPLP.