Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine learning that induces logic programs from data, which has shown promise at addressing these limitations. We focus on new methods for learning recursive programs that generalise from few examples, a shift from using hand-crafted background knowledge to \emph{learning} background knowledge, and the use of different technologies, notably answer set programming and neural networks. As ILP approaches 30, we also discuss directions for future research.
The limit behavior of inductive logic programs has not been explored, but when considering incremental or online inductive learning algorithms which usually run ongoingly, such behavior of the programs should be taken into account. An example is given to show that some inductive learning algorithm may not be correct in the long run if the limit behavior is not considered. An inductive logic program is convergent if given an increasing sequence of example sets, the program produces a corresponding sequence of the Horn logic programs which has the set-theoretic limit, and is limit-correct if the…
University of Oxford（牛津大学）；University of Cambridge（剑桥大学）
Multi-core machines are ubiquitous. However, most inductive logic programming (ILP) approaches use only a single core, which severely limits their scalability. To address this limitation, we introduce parallel techniques based on constraint-driven ILP where the goal is to accumulate constraints to restrict the hypothesis space. Our experiments on two domains (program synthesis and inductive general game playing) show that (i) parallelisation can substantially reduce learning times, and (ii) worker communication (i.e. sharing constraints) is important for good performance.
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.
University of Oxford（牛津大学）；KU Leuven（鲁汶大学）；Imperial College London（伦敦帝国理工学院）
Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs, (iii) new approaches for predicate invention, and (iv) the use of different technologies. We conclude by discussing current limitations of ILP and directions for future research.
Recent years have seen a surge of interest in Probabilistic Logic Programming (PLP) and Statistical Relational Learning (SRL) models that combine logic with probabilities. Structure learning of these systems is an intersection area of Inductive Logic Programming (ILP) and statistical learning (SL). However, ILP cannot deal with probabilities, SL cannot model relational hypothesis. The biggest challenge of integrating these two machine learning frameworks is how to estimate the probability of a logic clause only from the observation of grounded logic atoms. Many current methods models a joint p…
Mila（米拉研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）；Stanford University（斯坦福大学）；HEC Montréal（蒙特利尔高等商学院）
Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and complex query answering tasks by learning representations of entities, relations, and queries. Still, most existing query answering methods rely on transductive entity embeddings and cannot generalize to KGs containing new entities without retraining the entity embeddings. In this work, we study the inductive query answering task where inference is performed on a …
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the method…
The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain problem in the scope of inductive logic programming (ILP). We propose Neural Logic Inductive Learning (NLIL), an efficient differentiable ILP framework that learns first-order logic rules that can explain the patterns in the data. In experiments, compared with the state-of-the-art methods, we find NLIL can search for rules that are x10 times longer while remaining x3 times faster. We also show that NLIL can scale …
Inductive logic programming is a type of machine learning in which logic programs are learned from examples. This learning typically occurs relative to some background knowledge provided as a logic program. This dissertation introduces bottom preprocessing, a method for generating initial constraints on the programs an ILP system must consider. Bottom preprocessing applies ideas from inverse entailment to modern ILP systems. Inverse entailment is an influential early ILP approach introduced with Progol. This dissertation also presents $\bot$-Popper, an implementation of bottom preprocessing fo…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.
We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate invention. Our experiments on three domains (classification, inductive general game playing, and program synthesis) show that our approach can increase predictive accuracies and reduce learning times.
National Center for Scientific Research “Demokritos”（“德谟克利特”国家科学研究中心）；National University of Athens（雅典国立大学）；University of Piraeus（比雷埃夫斯大学）
Event recognition systems rely on properly engineered knowledge bases of event definitions to infer occurrences of events in time. The manual development of such knowledge is a tedious and error-prone task, thus event-based applications may benefit from automated knowledge construction techniques, such as Inductive Logic Programming (ILP), which combines machine learning with the declarative and formal semantics of First-Order Logic. However, learning temporal logical formalisms, which are typically utilized by logic-based Event Recognition systems is a challenging task, which most ILP systems…
Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned "rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer strong connection to classica…
Kyoto University（京都大学）；NTT Communication Science Laboratories（NTT通信科学实验室）
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire reasonable solutions from noisy datasets. However, this framework severely limits expressions for solutions, e.g., no function symbols are allowed, and the shapes of clauses are fixed. As a result, the framework cannot deal with structured examples. Therefore we propose a new framework to learn logic programs from noisy and structured examples, including th…
CRACS & INESC TEC（CRACS与INESC TEC）；Faculty of Sciences, University of Porto（波尔图大学理学院）
Probabilistic Inductive Logic Programming (PILP) is a rel- atively unexplored area of Statistical Relational Learning which extends classic Inductive Logic Programming (ILP). This work introduces SkILL, a Stochastic Inductive Logic Learner, which takes probabilistic annotated data and produces First Order Logic theories. Data in several domains such as medicine and bioinformatics have an inherent degree of uncer- tainty, that can be used to produce models closer to reality. SkILL can not only use this type of probabilistic data to extract non-trivial knowl- edge from databases, but it also add…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. The goal of this paper is to study a deductive inference method for PC(ID), which is the propositional fragment of FO(ID). We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical pr…
Rules complement and extend ontologies on the Semantic Web. We refer to these rules as onto-relational since they combine DL-based ontology languages and Knowledge Representation formalisms supporting the relational data model within the tradition of Logic Programming and Deductive Databases. Rule authoring is a very demanding Knowledge Engineering task which can be automated though partially by applying Machine Learning algorithms. In this chapter we show how Inductive Logic Programming (ILP), born at the intersection of Machine Learning and Logic Programming and considered as a major approac…
In recent research, human-understandable explanations of machine learning models have received a lot of attention. Often explanations are given in form of model simplifications or visualizations. However, as shown in cognitive science as well as in early AI research, concept understanding can also be improved by the alignment of a given instance for a concept with a similar counterexample. Contrasting a given instance with a structurally similar example which does not belong to the concept highlights what characteristics are necessary for concept membership. Such near misses have been proposed…
We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In contrast to the majority of past methods, instead of searching through the space of possible first-order logic rules by using some restrictive rule templates, we directly learn the symbolic logical predicate rules by introducing a novel differentiable Neural Logic (dNL) network. The proposed dNL network is able to learn and represent Boolean functions efficient…
Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporat…
In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems a…
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing induction over well-founded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for Non-Monotone Inductive Definitions (ID-logic). The semantics…
Explaining Neural Networks in Preference Learning: a Post-hoc Inductive Logic Programming Approach
Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy（意大利拉奎拉大学信息工程、计算机科学与数学系）；Department of Life, Health and Environmental Sciences, University of L'Aquila, Italy（意大利拉奎拉大学生命、健康与环境科学系）；Department of Electrical Engineering and Information Technologies, University of Naples, Italy（意大利那不勒斯大学电气工程与信息技术系）；Ethos Group, Department of Human Sciences, University of Verona, Italy（意大利维罗纳大学人文科学系Ethos研究组）
University of Klagenfurt（克拉根福大学）；Graz University of Technology（格拉茨工业大学）
Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic since the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. As a result, a time-consuming recomputation of SBCs must be done before every in…
From Circuit Evidence to Mechanistic Theory: An Inductive Logic Approach
Department of Computer Science, University of Manchester（曼彻斯特大学计算机科学系）；Idiap Research Institute（Idiap研究机构）；CRUK National Biomarker Centre, University of Manchester（曼彻斯特大学癌症研究联盟国家生物标志物中心）
ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming
Dept. of Mechanical and Aerospace Engineering, George Washington University, USA（机械与航空航天工程系，乔治华盛顿大学）；Dept. of Mechanical Engineering Sciences, University of Surrey, UK（机械工程科学系，萨里大学）
Inductive Learning for Possibilistic Logic Programs Under Stable Models
Multi-dimensional data perception and intelligent recognition Chongqing Engineering Research Center, Chongqing University of Arts and Sciences, Chongqing, 402160, China（重庆艺术科技大学智能识别多维数据感知工程研究中心）；College of Computer Science and Technology, Guizhou University, Guiyang, 550025, China（贵州大学计算机科学与技术学院）；State Key Laboratory of Public Big Data（公共大数据国家重点实验室）；Key Laboratory of Advanced Medical Imaging（先进医学影像重点实验室）；Institute for Artificial Intelligence, Guizhou University, Guiyang, 550025, China（贵州大学人工智能研究所）；School of Information and Communication Technology, Griffith University, QLD 4111, Australia（格里菲斯大学信息与通信技术学院）
The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples. Until recently, most research on ILP targeted learning Prolog programs. The ILASP system instead learns Answer Set Programs (ASP). Learning such expressive programs widens the applicability of ILP considerably; for example, enabling preference learning, learning common-sense knowledge, including defaults and exceptions, and learning non-deterministic theories. Early versions of ILASP can be considered meta-level ILP approaches, which encode a learning task as a logic program and delegate the se…
National University of Ireland, Galway（爱尔兰国立大学戈尔韦）
We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and for learning of such weights from data (parameter estimation). Weighted formulas are given a semantics in terms of soft and hard constraints which determine a probability distribution over answer sets. In contrast to related approaches, we approach inference by optionally utilizing so-called streamlining XOR constraints, in order to reduce the number of comp…
Technische Universität Wien（维也纳技术大学）；Marmara University（马尔马拉大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Sabanci University（萨班哲大学）
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 approa…
Humans constantly restructure knowledge to use it more efficiently. Our goal is to give a machine learning system similar abilities so that it can learn more efficiently. We introduce the \textit{knowledge refactoring} problem, where the goal is to restructure a learner's knowledge base to reduce its size and to minimise redundancy in it. We focus on inductive logic programming, where the knowledge base is a logic program. We introduce Knorf, a system which solves the refactoring problem using constraint optimisation. We evaluate our approach on two program induction domains: real-world string…
Sun Yat-sen University（中山大学）；Tencent AI Lab（腾讯人工智能实验室）；Wuhan University（武汉大学）
Knowledge graph embedding aims at modeling entities and relations with low-dimensional vectors. Most previous methods require that all entities should be seen during training, which is unpractical for real-world knowledge graphs with new entities emerging on a daily basis. Recent efforts on this issue suggest training a neighborhood aggregator in conjunction with the conventional entity and relation embeddings, which may help embed new entities inductively via their existing neighbors. However, their neighborhood aggregators neglect the unordered and unequal natures of an entity's neighbors. T…
Spatial Reasoning（空间推理）；The DesignSpace Group（设计空间集团）；University of Bremen（不来梅大学）；University of Münster（明斯特大学）
We present an inductive spatio-temporal learning framework rooted in inductive logic programming. With an emphasis on visuo-spatial language, logic, and cognition, the framework supports learning with relational spatio-temporal features identifiable in a range of domains involving the processing and interpretation of dynamic visuo-spatial imagery. We present a prototypical system, and an example application in the domain of computing for visual arts and computational cognitive science.
Motivated by the needs of resource constrained dialog policy learning, we introduce dialog policy via differentiable inductive logic (DILOG). We explore the tasks of one-shot learning and zero-shot domain transfer with DILOG on SimDial and MultiWoZ. Using a single representative dialog from the restaurant domain, we train DILOG on the SimDial dataset and obtain 99+% in-domain test accuracy. We also show that the trained DILOG zero-shot transfers to all other domains with 99+% accuracy, proving the suitability of DILOG to slot-filling dialogs. We further extend our study to the MultiWoZ dataset…
The ability to recognise and make analogies is often used as a measure or test of human intelligence. The ability to solve Bongard problems is an example of such a test. It has also been postulated that the ability to rapidly construct novel abstractions is critical to being able to solve analogical problems. Given an image, the ability to construct a program that would generate that image is one form of abstraction, as exemplified in the Dreamcoder project. In this paper, we present a preliminary examination of whether programs constructed by Dreamcoder can be used for analogical reasoning to…
We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning …
Universidad Autonoma de Madrid（马德里自治大学）；Laboratoire des Sciences du Numérique de Nantes（南特数字科学实验室）；National Institute of Informatics（国立信息学研究所）
Machine learning methods are growing in relevance for biometrics and personal information processing in domains such as forensics, e-health, recruitment, and e-learning. In these domains, white-box (human-readable) explanations of systems built on machine learning methods can become crucial. Inductive Logic Programming (ILP) is a subfield of symbolic AI aimed to automatically learn declarative theories about the process of data. Learning from Interpretation Transition (LFIT) is an ILP technique that can learn a propositional logic theory equivalent to a given black-box system (under certain co…
By their nature, the composition of black box models is opaque. This makes the ability to generate explanations for the response to stimuli challenging. The importance of explaining black box models has become increasingly important given the prevalence of AI and ML systems and the need to build legal and regulatory frameworks around them. Such explanations can also increase trust in these uncertain systems. In our paper we present RICE, a method for generating explanations of the behaviour of black box models by (1) probing a model to extract model output examples using sensitivity analysis; …
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…
We present a clustering- and demotion-based algorithm called Kmeans-FOLD to induce nonmonotonic logic programs from positive and negative examples. Our algorithm improves upon-and is inspired by-the FOLD algorithm. The FOLD algorithm itself is an improvement over the FOIL algorithm. Our algorithm generates a more concise logic program compared to the FOLD algorithm. Our algorithm uses the K-means based clustering method to cluster the input positive samples before applying the FOLD algorithm. Positive examples that are covered by the partially learned program in intermediate steps are not disc…
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 probabiliti…
In Inverse subsumption for complete explanatory induction Yamamoto et al. investigate which inductive logic programming systems can learn a correct hypothesis $H$ by using the inverse subsumption instead of inverse entailment. We prove that inductive logic programming system Imparo is complete by inverse subsumption for learning a correct definite hypothesis $H$ wrt the definite background theory $B$ and ground atomic examples $E$, by establishing that there exists a connected theory $T$ for $B$ and $E$ such that $H$ subsumes $T$.
Federal University of Amazonas（亚马逊联邦大学）；City, University of London（伦敦城市大学）
Amao is a cognitive agent framework that tackles the invention of predicates with a different strategy as compared to recent advances in Inductive Logic Programming (ILP) approaches like Meta-Intepretive Learning (MIL) technique. It uses a Neural Multi-Space (NeMuS) graph structure to anti-unify atoms from the Herbrand base, which passes in the inductive momentum check. Inductive Clause Learning (ICL), as it is called, is extended here by using the weights of logical components, already present in NeMuS, to support inductive learning by expanding clause candidates with anti-unified atoms. An e…
Imperial College London（伦敦帝国理工学院）；University of Bath（巴斯大学）；National Institute of Informatics（国立信息学研究所）
In this paper we propose a use-case-driven iterative design methodology for normative frameworks, also called virtual institutions, which are used to govern open systems. Our computational model represents the normative framework as a logic program under answer set semantics (ASP). By means of an inductive logic programming approach, implemented using ASP, it is possible to synthesise new rules and revise the existing ones. The learning mechanism is guided by the designer who describes the desired properties of the framework through use cases, comprising (i) event traces that capture possible …
The SLDNFA-system results from the LP+ project at the K.U.Leuven, which investigates logics and proof procedures for these logics for declarative knowledge representation. Within this project inductive definition logic (ID-logic) is used as representation logic. Different solvers are being developed for this logic and one of these is SLDNFA. A prototype of the system is available and used for investigating how to solve efficiently problems represented in ID-logic.
