Inductive Logic Programming as Abductive Search

We present a novel approach to non-monotonic ILP and its implementation called TAL (Top-directed Abductive Learning). TAL overcomes some of the completeness problems of ILP systems based on Inverse Entailment and is the first top-down ILP system that allows background theories and hypotheses to be normal logic programs. The approach relies on mapping an ILP problem into an equivalent ALP one. This enables the use of established ALP proof procedures and the specification of richer language bias with integrity constraints. The mapping provides a principled search space for an ILP problem, over which an abductive search is used to compute inductive solutions

Learning programs by learning from failures

We describe an inductive logic programming (ILP) approach called learning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the generate stage, the learner generates a hypothesis (a logic program) that satisfies a set of hypothesis constraints (constraints on the syntactic form of hypotheses). In the test stage, the learner tests the hypothesis against training examples. A hypothesis fails when it does not entail all the positive examples or entails a negative example. If a hypothesis fails, then, in the constrain stage, the learner learns constraints from the failed hypothesis to prune the hypothesis space, i.e. to constrain subsequent hypothesis generation. For instance, if a hypothesis is too general (entails a negative example), the constraints prune generalisations of the hypothesis. If a hypothesis is too specific (does not entail all the positive examples), the constraints prune specialisations of the hypothesis. This loop repeats until either (i) the learner finds a hypothesis that entails all the positive and none of the negative examples, or (ii) there are no more hypotheses to test. We introduce Popper, an ILP system that implements this approach by combining answer set programming and Prolog. Popper supports infinite problem domains, reasoning about lists and numbers, learning textually minimal programs, and learning recursive programs. Our experimental results on three domains (toy game problems, robot strategies, and list transformations) show that (i) constraints drastically improve learning performance, and (ii) Popper can outperform existing ILP systems, both in terms of predictive accuracies and learning times.Comment: Accepted for the machine learning journa

Inductive logic programming at 30

Inductive logic programming (ILP) is a form of logic-based machine learning. The goal of ILP is to induce a hypothesis (a logic program) that generalises given training examples and background knowledge. As ILP turns 30, we survey recent work in the field. In this survey, we focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs that generalise from few examples, (iii) new approaches for predicate invention, and (iv) the use of different technologies, notably answer set programming and neural networks. We conclude by discussing some of the current limitations of ILP and discuss directions for future research.Comment: Extension of IJCAI20 survey paper. arXiv admin note: substantial text overlap with arXiv:2002.11002, arXiv:2008.0791

Inductive logic programming at 30: a new introduction

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.Comment: Paper under revie

Logic Programs as Declarative and Procedural Bias in Inductive Logic Programming

Machine Learning is necessary for the development of Artificial Intelligence, as pointed out by Turing in his 1950 article ``Computing Machinery and Intelligence''. It is in the same article that Turing suggested the use of computational logic and background knowledge for learning. This thesis follows a logic-based machine learning approach called Inductive Logic Programming (ILP), which is advantageous over other machine learning approaches in terms of relational learning and utilising background knowledge. ILP uses logic programs as a uniform representation for hypothesis, background knowledge and examples, but its declarative bias is usually encoded using metalogical statements. This thesis advocates the use of logic programs to represent declarative and procedural bias, which results in a framework of single-language representation. We show in this thesis that using a logic program called the top theory as declarative bias leads to a sound and complete multi-clause learning system MC-TopLog. It overcomes the entailment-incompleteness of Progol, thus outperforms Progol in terms of predictive accuracies on learning grammars and strategies for playing Nim game. MC-TopLog has been applied to two real-world applications funded by Syngenta, which is an agriculture company. A higher-order extension on top theories results in meta-interpreters, which allow the introduction of new predicate symbols. Thus the resulting ILP system Metagol can do predicate invention, which is an intrinsically higher-order logic operation. Metagol also leverages the procedural semantic of Prolog to encode procedural bias, so that it can outperform both its ASP version and ILP systems without an equivalent procedural bias in terms of efficiency and accuracy. This is demonstrated by the experiments on learning Regular, Context-free and Natural grammars. Metagol is also applied to non-grammar learning tasks involving recursion and predicate invention, such as learning a definition of staircases and robot strategy learning. Both MC-TopLog and Metagol are based on a $\top$-directed framework, which is different from other multi-clause learning systems based on Inverse Entailment, such as CF-Induction, XHAIL and IMPARO. Compared to another $\top$-directed multi-clause learning system TAL, Metagol allows the explicit form of higher-order assumption to be encoded in the form of meta-rules.Open Acces

Inductive logic programming as satisfiability modulo theories

At the intersection of machine learning, program synthesis and automated reasoning lies the field of Inductive Logic Programming (ILP). The aim of ILP is to automatically learn relational programs from input/output examples, typically through logic-based techniques. Inspired by Karl Popper’s falsification perspective on science, this dissertation sets out a new approach to ILP: Learning From Failures (LFF). In science, starting from a huge set of a priori viable hypotheses, we select a hypothesis to test. This hypothesis typically gets falsified due to failing in some specific way. By examining the failure we learn that an entire space of related hypotheses is now ruled out. Having thus reduced our set of viable hypotheses, we subsequently select from just those that remain. LFF applies this methodology to program induction, codifying it as a three-stage loop. The generate stage maintains a formula whose satisfying assignments correspond to the set of viable hypotheses. The test stage takes a satisfying assignment, interprets it as a logic program and tests it against training examples – imperfect fit is considered a failure. The constrain stage turns a failure into constraints to add to the generate stage’s formula, thereby eliminating a class of hypotheses which will fail for the same reason. The thesis of this dissertation is three-fold. The first claim is that LFF frames the ILP problem as one of Satisfiability Modulo Theories (SMT). With the search for viable hypotheses handed-off to a SAT-solver, the test stage can be regarded as a theory solver collaborating with the SAT-solver, effectively making ILP’s notion of background knowledge into a (Horn) background theory. The second claim is that LFF’s three-stage loop is an effective basis for falsification-based program induction. Chapter 4 develops the above correspondence into a feature-rich and flexible three-stage ILP system. Experimental evidence is provided for this system going beyond the state-of-the-art in ILP, e.g., by supporting large hypothesis spaces and large domains. The third claim is that the LFF-as-SMT-perspective helps apply satisfiability solving techniques to ILP, in particular to reduce hypothesis space exploration. In Chapter 5, we show that SMT-based techniques for explaining conflicts have a natural analog in terms of explaining which parts of a hypothesis are responsible for its failure. In Chapter 6, we incorporate other theory solvers alongside the test stage to reason about the (satisfiability of) over-approximating properties of hypotheses. We show that both of these techniques can significantly reduce the number of iterations of the three-stage loop

Inductive learning of answer set programs

The goal of Inductive Logic Programming (ILP) is to find a hypothesis that explains a set of examples in the context of some pre-existing background knowledge. Until recently, most research on ILP targeted learning definite logic programs. This thesis constitutes the first comprehensive work on learning answer set programs, introducing new learning frameworks, theoretical results on the complexity and generality of these frameworks, algorithms for learning ASP programs, and an extensive evaluation of these algorithms. Although there is previous work on learning ASP programs, existing learning frameworks are either brave -- where examples should be explained by at least one answer set -- or cautious where examples should be explained by all answer sets. There are cases where brave induction is too weak and cautious induction is too strong. Our proposed frameworks combine brave and cautious learning and can learn ASP programs containing choice rules and constraints. Many applications of ASP use weak constraints to express a preference ordering over the answer sets of a program. Learning weak constraints corresponds to preference learning, which we achieve by introducing ordering examples. We then explore the generality of our frameworks, investigating what it means for a framework to be general enough to distinguish one hypothesis from another. We show that our frameworks are more general than both brave and cautious induction. We also present a new family of algorithms, called ILASP (Inductive Learning of Answer Set Programs), which we prove to be sound and complete. This work concerns learning from both non-noisy and noisy examples. In the latter case, ILASP returns a hypothesis that maximises the coverage of examples while minimising the length of the hypothesis. In our evaluation, we show that ILASP scales to tasks with large numbers of examples finding accurate hypotheses even in the presence of high proportions of noisy examples.Open Acces

Inductive logic programming using bounded hypothesis space

Inductive Logic Programming (ILP) systems apply inductive learning to an inductive learning task by deriving a hypothesis which explains the given examples. Applying ILP systems to real applications poses many challenges as they require large search space, noise is present in the learning task, and in domains such as software engineering hypotheses are required to satisfy domain specific syntactic constraints. ILP systems use language biases to define the hypothesis space, and learning can be seen as a search within the defined hypothesis space. Past systems apply search heuristics to traverse across a large hypothesis space. This is unsuitable for systems implemented using Answer Set Programming (ASP), for which scalability is a constraint as the hypothesis space will need to be grounded by the ASP solver prior to solving the learning task, making them unable to solve large learning tasks. This work explores how to learn using bounded hypothesis spaces and iterative refinement. Hypotheses that explain all examples are learnt by refining smaller partial hypotheses. This improves the scalability of ASP based systems as the learning task is split into multiple smaller manageable refinement tasks. The thesis presents how syntactic integrity constraints on the hypothesis space can be used to strengthen hypothesis selection criteria, removing hypotheses with undesirable structure. The notion of constraint-driven bias is introduced, where hypotheses are required to be acceptable with respect to the given meta-level integrity constraints. Building upon the ILP system ASPAL, the system RASPAL which learns through iterative hypothesis refinement is implemented. RASPAL's algorithm is proven, under certain assumptions, to be complete and consistent. Both systems have been applied to a case study in learning user's behaviours from data collected from their mobile usage. This demonstrates their capability for learning with noise, and the difference in their efficiency. Constraint-driven bias has been implemented for both systems, and applied to a task in specification revision, and in learning stratified programs.Open Acces