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Visual reasoning is essential for building intelligent agents that understand the world and perform problem-solving beyond perception. Differentiable forward reasoning has been developed to integrate reasoning with gradient-based machine learning paradigms. However, due to the memory intensity, most existing approaches do not bring the best of the expressivity of first-order logic, excluding a crucial ability to solve abstract visual reasoning, where agents need to perform reasoning by using analogies on abstract concepts in different scenarios. To overcome this problem, we propose NEUro-symbolic Message-pAssiNg reasoNer (NEUMANN), which is a graph-based differentiable forward reasoner, passing messages in a memory-efficient manner and handling structured programs with functors. Moreover, we propose a computationally-efficient structure learning algorithm to perform explanatory program induction on complex visual scenes. To evaluate, in addition to conventional visual reasoning tasks, we propose a new task, visual reasoning behind-the-scenes, where agents need to learn abstract programs and then answer queries by imagining scenes that are not observed. We empirically demonstrate that NEUMANN solves visual reasoning tasks efficiently, outperforming neural, symbolic, and neuro-symbolic baselines. [ABSTRACT FROM AUTHOR]

One of the foundational subjects in both artificial intelligence (AI) and database technologies is natural language interfaces for databases (NLIDB). The primary goal of NLIDB is to enable users to interact with databases using natural languages such as English, Arabic, and French. While many existing NLIDBs rely on linguistic operations to meet the challenges of user's ambiguity existing in natural language queries (NLQ), there is currently a growing emphasis on utilizing inductive logic programming (ILP) to develop natural language processing (NLP) applications. This is because ILP reduces the requirement for linguistic expertise in building NLP systems. This paper outlines a methodology for automating the construction of NLIDB. This method utilizes ILP to derive transfer rules that directly translate NLQ into a clear and unambiguous logical query, which subsequently translatable into database query languages (DQL). To acquire these rules, our system was trained within a corpus consisting of parallel examples of NLQs and their logical interpretations. The experimental results demonstrate the promise of this approach, as it enables the direct translation of all NLQs with grammatical structures similar to those already present in the trained corpus into a logical query. [ABSTRACT FROM AUTHOR]

In multi-task learning, a learner adds the learned programs into background knowledge (BK) and reuses them to learn other programs. Continually acquiring BK can lead to the problem of excessive BK, which overwhelms a learning system. Hence, it is necessary to forget irrelevant BK. However, existing forgetting approaches rarely consider the relevance between BK and learning tasks, commonly providing the same BK for different induction tasks. To address this issue, this paper proposes a relevance identification approach based on counterfactual thinking, termed counterfactual acquisition. This approach first measures each hypothesis' s contribution to the learning task using a relevance function. Then, it retains only those hypotheses whose relevance function values exceed a predefined threshold. Moreover, this approach is applied to inductive logic programming (ILP) through the introduction of a multi- task ILP learner named Countergol. Theoretical analysis demonstrates that Countergol can reduce the hypothesis space and sample complexity size. Experimental comparisons against other forgetting approaches show that Countergol outperforms similar methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a modular methodology that combines state-of-the-art methods in (stochastic) machine learning with well-established methods in inductive logic programming (ILP) and rule induction to provide efficient and scalable algorithms for the classification of vast data sets. By construction, these classifications are based on the synthesis of simple rules, thus providing direct explanations of the obtained classifications. Apart from evaluating our approach on the common large scale data sets MNIST, Fashion-MNIST and IMDB, we present novel results on explainable classifications of dental bills. The latter case study stems from an industrial collaboration with Allianz Private Krankenversicherung which is an insurance company offering diverse services in Germany. [ABSTRACT FROM AUTHOR]

The employment of Machine Learning (ML) techniques in embedded systems has seen constant growth in recent years, especially for black-box ML techniques (such as Artificial Neural Networks (ANNs)). However, despite the successful employment of ML techniques in embedded environments, their performance potential is constrained by the limited computing resources of their embedded computers. Several hardware-based approaches were developed (e.g., using FPGAs and ASICs) to address the constraints of limited computing resources. The scope of this work focuses on improving the performance for Inductive Logic Programming (ILP) on embedded environments. ILP is a powerful logic-based ML technique that uses logic programming to construct human-interpretable ML models, where those logic-based ML models are capable of describing complex and multi-relational concepts. In this work, we present a hardware-based approach that accelerates the hypothesis evaluation task for ILPs in embedded environments that use Description Logic (DL) languages as their logic-based representation. In particular, we target the \(\mathcal {ALCQ}^{\mathcal {(D)}}\) language. According to experimental results (through an FPGA implementation), our presented approach has achieved speedups up to 48.7-fold for a disjunction of 32 concepts on 100 M individuals, where the baseline performance is the sequential CPU performance of the Raspberry Pi 4. For role and concrete role restrictions, the FPGA implementation achieved speedups up to 2.4-fold (for MIN cardinality role restriction on 1M role assertions); all FPGA implemented role and concrete role restrictions have achieved similar speedups. In the worst-case scenario, the FPGA implementation achieved either a similar or slightly better performance than the baseline (for all DL operations); the worst-case scenario resulted from using small datasets such as: using conjunction and disjunction on < 100 individuals, and using role and concrete (float/string) role restrictions on < 100,000 assertions. [ABSTRACT FROM AUTHOR]

Many inductive logic programming (ILP) methods are incapable of learning programs from probabilistic background knowledge, for example, coming from sensory data or neural networks with probabilities. We propose Propper, which handles flawed and probabilistic background knowledge by extending ILP with a combination of neurosymbolic inference, a continuous criterion for hypothesis selection (binary cross-entropy) and a relaxation of the hypothesis constrainer (NoisyCombo). For relational patterns in noisy images, Propper can learn programs from as few as 8 examples. It outperforms binary ILP and statistical models such as a graph neural network. [ABSTRACT FROM AUTHOR]

Deep neural networks, despite their capabilities, are constrained by the need for large-scale training data, and often fall short in generalisation and interpretability. Inductive logic programming (ILP) presents an intriguing solution with its data-efficient learning of first-order logic rules. However, ILP grapples with challenges, notably the handling of non-linearity in continuous domains. With the ascent of neuro-symbolic ILP, there's a drive to mitigate these challenges, synergising deep learning with relational ILP models to enhance interpretability and create logical decision boundaries. In this research, we introduce a neuro-symbolic ILP framework, grounded on differentiable Neural Logic networks, tailored for non-linear rule extraction in mixed discrete-continuous spaces. Our methodology consists of a neuro-symbolic approach, emphasising the extraction of non-linear functions from mixed domain data. Our preliminary findings showcase our architecture's capability to identify non-linear functions from continuous data, offering a new perspective in neural-symbolic research and underlining the adaptability of ILP-based frameworks for regression challenges in continuous scenarios. [ABSTRACT FROM AUTHOR]

Augmented reality (AR) has become a popular platform in education, providing an interactive and engaging way to learn through manipulatable communication. AR technology can increase motivation and retention of vocabulary. This study explores the efficacy of an AR-based flashcard application to teach basic Tamil words to primary school students in Madurai District, Tamil Nadu. The target sample included students in classes three, four, and five, who had minimal residual knowledge due to disrupted classroom learning from the pandemic period. The current study aimed to compare the level of learning achieved through traditional flashcards and AR-based flashcards. A total of 67 students (35 boys, 32 girls) were randomly divided into an experimental group (N = 31; 46.27%) and a control group (N = 36; 53.73%). Pre-tests followed by intervention and post-test design were adopted to establish the benefits of AR statistically and explained following the theoretical supplement of Piaget (1964). The results indicated that learning through AR-based flashcards enhanced primary students' learning of basic Tamil and increased their interest in learning. This study might help learners move from the cognitive to the affective domain, leading to desirable changes in learning behaviour. AR technology provides diverse learning opportunities, and the flexibility of schema formation in this age group and enhanced through inductive logic. Further research may complement and induce the desire among educators to implement this technology in enhancing the power of flashcards and complementary diagrams. [ABSTRACT FROM AUTHOR]

We present MP-HTHEDL, a massively parallel hypothesis evaluation engine for inductive learning in description logic (DL). MP-HTHEDL is an extension on our previous work HT-HEDL, which also targets improving hypothesis evaluation performance for inductive logic programming (ILP) algorithms, that uses DL as their representation language. Unlike our previous work (HT-HEDL), MP-HTHEDL is a massively parallel approach that improves hypothesis evaluation performance through horizontal scaling, by exploiting the computing capabilities of all CPUs and GPUs from networked machines in Hadoop clusters. Many modern CPUs, have extended instruction sets for accelerating specific types of computations – especially for data parallel or vector computations. For CPU-based hypothesis evaluation, MP-HTHEDL employs vectorized multiprocessing as opposed to HT-HEDL’s vectorized multithreading; though, both MP-HTHEDL and HT-HEDL combine the classical scalar processing of multi-core CPUs with the extended vector instructions of each CPU core. This combination of CPUs’ scalar and vector processing, resulted in more extracted performance from CPUs. According to experimental results through Apache Spark implementation, on a Hadoop cluster of 3 worker nodes that have a total of 36 CPU cores and 7 GPUs; the performance improvement achieved using the pure scalar processing power of multi-core CPUs, has yielded a speedup of up to ~25.4 folds. When combining the scalar-processing and the extended vector instructions of those multi-core CPUs, the performance gains increased from ~25.4 folds to ~67 folds, on the same cluster of 3 worker nodes – these large speedups are achieved using only CPU-based processing. In terms of GPU-based evaluation, MP-HTHEDL achieved a speedup of up to ~161 folds, using the GPUs from the same 3 worker nodes.

This article presents MP-SPILDL, a massively parallel inductive logic learner in Description Logic (DL). MP-SPILDL is a scalable inductive Logic Programming (ILP) algorithm that exploits existing Big Data infrastructure to perform large-scale inductive logic learning in DL (the $\mathcal {ALCQI}^{\mathcal {(D)}}$ DL language in particular). MP-SPILDL targets accelerating both hypothesis search and hypothesis evaluation by aggregating the computing power of multi-core CPUs with their vector/SIMD instructions and multi-GPUs in a Hadoop cluster. In terms of hypothesis search, MP-SPILDL employs a novel MapReduce-based algorithm that performs distributed parallel hypothesis search. MP-SPILDL also employs a novel MapReduce-based procedure that eliminates all redundant hypotheses generated after each learning iteration. Moreover, MP-SPILDL utilizes deterministic ordering of hypotheses’ operands to avoid exploring redundant areas of the search space, similar to the DL-Learner, the state of the art in DL-based ILP literature. In terms of hypothesis evaluation, MP-SPILDL performs parallel hypothesis evaluation, which uses all CPU cores combined with their vector instructions and all multi-GPUs of all machines in the Hadoop cluster. According to the experimental results using an Apache Spark implementation on a Hadoop cluster of three worker machines (36 total CPU cores, 7 total GPUs), MP-SPILDL achieved speedups of up to 13.3 folds using parallel beam search with $beamWidth = 32$ and CPU-based vectorized hypothesis evaluation – the best-case scenario. On small datasets such as Michalski’s trains, MP-SPILDL achieved a slower performance than the baseline, representing the worst-case scenario.

Cyber attacking is easier than cyber defending—attackers only need to find one breach, while the defenders must successfully repel all attacks. This research demonstrates how cyber defenders can increase their capabilities by joining forces with eXplainable-AI (XAI) utilizing interactive human-machine collaboration. With a global shortfall of cyber defenders there is a need to amplify their skills using AI. Cyber asymmetries make propositional machine learning techniques impractical. Human reasoning and skill is a key ingredient in defense and must be embedded in the AI framework. For Human-Machine collaboration to work requires that the AI is an ultra-strong machine learner and can explain its models. Unlike Deep Learning, Inductive Logic Programming can communicate what it learns to a human. An empirical study was undertaken using six months of eavesdropped network traffic from an organization generating up-to 562K network events daily. Easier-to-defend devices were identified using a form of the Good-Turing Frequency estimator which is a promising form of volatility measure. A behavioral cloning grammar in explicit symbolic form was then produced from a single device's network activity using the compression algorithm SEQUITUR. A novel visualization was generated to allow defenders to identify network sequences they wish to explain. Interactive Inductive Logic Programming (the XAI) is supplied the network traffic meta data, sophisticated pre-existing cyber security background knowledge, and one recurring sequence of events from a single device to explain. A co-inductive process between the human cyber defender and the XAI where the human is able to understand, then refute and shape the XAI's developing model, to produce a model that conforms with the data as well as the original device designers programming. The acceptable model is in a form that can be deployed as an ongoing active cyber defense.

Inductive Logic Programming (ILP) is a research field at the intersection between machine learning and logic programming, focusing on developing a formal framework for inductively learning relational descriptions in the form of logic programs from examples and background knowledge. As an emerging method of ILP, Meta-Interpretive Learning (MIL) leverages the specialization of a set of higher-order metarules to learn logic programs. In MIL, the input includes a set of examples, background knowledge, and a set of metarules, while the output is a logic program. MIL executes a depth-first traversal search, where its program search space expands polynomially with the number of predicates in the provided background knowledge and exponentially with the number of clauses in the program, sometimes even leading to search collapse. To address this challenge, this study introduces a strategy that employs the concept of reuse, specifically through the integration of auxiliary predicates, to reduce the number of clauses in programs and improve the learning efficiency. This approach focuses on the proactive identification and reuse of common program patterns. To operationalize this strategy, we introduce MILER, a novel method integrating a predicate generator, program learner, and program evaluator. MILER leverages frequent subgraph mining techniques to detect common patterns from a limited dataset of training samples, subsequently embedding these patterns as auxiliary predicates into the background knowledge. In our experiments involving two Visual Question Answering (VQA) tasks and one program synthesis task, we assessed MILER's approach to utilizing reusable program patterns as auxiliary predicates. The results indicate that, by incorporating these patterns, MILER identifies reusable program patterns, reduces program clauses, and directly decreases the likelihood of timeouts compared to traditional MIL. This leads to improved learning success rates by optimizing computational efforts. [ABSTRACT FROM AUTHOR]

Humans are experiencing the inclusion of artificial agents in their lives, such as unmanned vehicles, service robots, voice assistants, and intelligent medical care. If the artificial agents cannot align with social values or make ethical decisions, they may not meet the expectations of humans. Traditionally, an ethical decision-making framework is constructed by rule-based or statistical approaches. In this paper, we propose an ethical decision-making framework based on incremental ILP (Inductive Logic Programming), which can overcome the brittleness of rule-based approaches and little interpretability of statistical approaches. As the current incremental ILP makes it difficult to solve conflicts, we propose a novel ethical decision-making framework considering conflicts in this paper, which adopts our proposed incremental ILP system. The framework consists of two processes: the learning process and the deduction process. The first process records bottom clauses with their score functions and learns rules guided by the entailment and the score function. The second process obtains an ethical decision based on the rules. In an ethical scenario about chatbots for teenagers' mental health, we verify that our framework can learn ethical rules and make ethical decisions. Besides, we extract incremental ILP from the framework and compare it with the state-of-the-art ILP systems based on ASP (Answer Set Programming) focusing on conflict resolution. The results of comparisons show that our proposed system can generate better-quality rules than most other systems. [ABSTRACT FROM AUTHOR]

Three key strengths of relational machine learning programs like those developed in Inductive Logic Programming (ILP) are: (1) The use of an expressive subset of first-order logic that allows models that capture complex relationships amongst data instances; (2) The use of domain-specific relations to guide the construction of models; and (3) The models constructed are human-readable, which is often one step closer to being human-understandable. The price for these advantages is that ILP-like methods have not been able to capitalise fully on the rapid hardware, software and algorithmic developments fuelling current developments in deep neural networks. In this paper, we treat relational features as functions and use the notion of generalised composition of functions to derive complex functions from simpler ones. Motivated by the work of McCreath and Sharma, we formulate the notion of a set of M -simple features in a mode language M and identify two composition operators ( ρ 1 and ρ 2 ) from which all possible complex features can be derived. We use these results to implement a form of "explainable neural network" called Compositional Relational Machines, or CRMs. CRMs are labelled directed-acyclic graphs. The vertex-label for any vertex j in the CRM contains a feature-function f j and an continuous activation function g j . If j is a "non-input" vertex, then f j is the composition of features associated with vertices in the direct predecessors of j. Our focus is on CRMs in which input vertices (those without any direct predecessors) all have M -simple features in their vertex-labels. We provide a randomised procedure for constructing the structure of such CRMs, and a procedure for estimating the parameters (the w ij 's) using back-propagation and stochastic gradient descent. Using a notion of explanations based on the compositional structure of features in a CRM, we provide empirical evidence on synthetic data of the ability to identify appropriate explanations; and demonstrate the use of CRMs as 'explanation machines' for black-box models that do not provide explanations for their predictions. [ABSTRACT FROM AUTHOR]

With its powerful expressive capability and intuitive presentation, the knowledge graph has emerged as one of the primary forms of knowledge representation and management. However, the presence of biases in our cognitive and construction processes often leads to varying degrees of incompleteness and errors within knowledge graphs. To address this, reasoning becomes essential for supplementing and rectifying these shortcomings. Logical rule-based knowledge graph reasoning methods excel at performing inference by uncovering underlying logical rules, showcasing remarkable generalization ability and interpretability. Moreover, the flexibility of logical rules allows for seamless integration with diverse neural network models, thereby offering promising prospects for research and application. Despite the growing number of logical rule-based knowledge graph reasoning methods, a systematic classification and analysis of these approaches is lacking. In this review, we delve into the relevant research on logical rule-based knowledge graph reasoning, classifying them into four categories: methods based on inductive logic programming (ILP), methods that unify probabilistic graphical models and logical rules, methods that unify embedding techniques and logical rules, and methods that jointly use neural networks (NNs) and logical rules. We introduce and analyze the core concepts and key techniques, as well as the advantages and disadvantages associated with these methods, while also providing a comparative evaluation of their performance. Furthermore, we summarize the main problems and challenges, and offer insights into potential directions for future research. [ABSTRACT FROM AUTHOR]

The topic of comprehensibility of machine-learned theories has recently drawn increasing attention. Inductive logic programming uses logic programming to derive logic theories from small data based on abduction and induction techniques. Learned theories are represented in the form of rules as declarative descriptions of obtained knowledge. In earlier work, the authors provided the first evidence of a measurable increase in human comprehension based on machine-learned logic rules for simple classification tasks. In a later study, it was found that the presentation of machine-learned explanations to humans can produce both beneficial and harmful effects in the context of game learning. We continue our investigation of comprehensibility by examining the effects of the ordering of concept presentations on human comprehension. In this work, we examine the explanatory effects of curriculum order and the presence of machine-learned explanations for sequential problem-solving. We show that (1) there exist tasks A and B such that learning A before learning B results in better comprehension for humans in comparison to learning B before learning A and (2) there exist tasks A and B such that the presence of explanations when learning A contributes to improved human comprehension when subsequently learning B. We propose a framework for the effects of sequential teaching on comprehension based on an existing definition of comprehensibility and provide evidence for support from data collected in human trials. Our empirical study involves curricula that teach novices the merge sort algorithm. Our results show that sequential teaching of concepts with increasing complexity (a) has a beneficial effect on human comprehension and (b) leads to human re-discovery of divide-and-conquer problem-solving strategies, and (c) allows adaptations of human problem-solving strategy with better performance when machine-learned explanations are also presented. [ABSTRACT FROM AUTHOR]

Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated. Thus inspired, we introduce failure explanation techniques for inductive logic programming. Given a hypothesis represented as a logic program, we test it on examples. If a hypothesis fails, we explain the failure in terms of failing sub-programs. In case a positive example fails, we identify failing sub-programs at the granularity of literals. We introduce a failure explanation algorithm based on analysing branches of SLD-trees. We integrate a meta-interpreter based implementation of this algorithm with the test-stage of the Popper ILP system. We show that fine-grained failure analysis allows for learning fine-grained constraints on the hypothesis space. Our experimental results show that explaining failures can drastically reduce hypothesis space exploration and learning times. [ABSTRACT FROM AUTHOR]

Autonomous robots start to be integrated in human environments where explicit and implicit social norms guide the behavior of all agents. To assure safety and predictability, these artificial agents should act in accordance with the applicable social norms. However, it is not straightforward to define these rules and incorporate them in an agent's policy. Particularly because social norms are often implicit and environment specific. In this paper, we propose a novel iterative approach to extract a set of rules from observed human trajectories. This hybrid method combines the strengths of inverse reinforcement learning and inductive logic programming. We experimentally show how our method successfully induces a compact logic program which represents the behavioral constraints applicable in a Tower of Hanoi and a traffic simulator environment. The induced program is adopted as prior knowledge by a model-free reinforcement learning agent to speed up training and prevent any social norm violation during exploration and deployment. Moreover, expressing norms as a logic program provides improved interpretability, which is an important pillar in the design of safe artificial agents, as well as transferability to similar environments. [ABSTRACT FROM AUTHOR]

Reasoning about graphs, and learning from graph data is a field of artificial intelligence that has recently received much attention in the machine learning areas of graph representation learning and graph neural networks. Graphs are also the underlying structures of interest in a wide range of more traditional fields ranging from logic-oriented knowledge representation and reasoning to graph kernels and statistical relational learning. In this review we outline a broad map and inventory of the field of learning and reasoning with graphs that spans the spectrum from reasoning in the form of logical deduction to learning node embeddings. To obtain a unified perspective on such a diverse landscape we introduce a simple and general semantic concept of a model that covers logic knowledge bases, graph neural networks, kernel support vector machines, and many other types of frameworks. Still at a high semantic level, we survey common strategies for model specification using probabilistic factorization and standard feature construction techniques. Based on this semantic foundation we introduce a taxonomy of reasoning tasks that casts problems ranging from transductive link prediction to asymptotic analysis of random graph models as queries of different complexities for a given model. Similarly, we express learning in different frameworks and settings in terms of a common statistical maximum likelihood principle. Overall, this review aims to provide a coherent conceptual framework that provides a basis for further theoretical analyses of respective strengths and limitations of different approaches to handling graph data, and that facilitates combination and integration of different modeling paradigms.

Deep neural learning has shown remarkable performance at learning representations for visual object categorization. However, deep neural networks such as CNNs do not explicitly encode objects and relations among them. This limits their success on tasks that require a deep logical understanding of visual scenes, such as Kandinsky patterns and Bongard problems. To overcome these limitations, we introduce α ILP , a novel differentiable inductive logic programming framework that learns to represent scenes as logic programs—intuitively, logical atoms correspond to objects, attributes, and relations, and clauses encode high-level scene information. α ILP has an end-to-end reasoning architecture from visual inputs. Using it, α ILP performs differentiable inductive logic programming on complex visual scenes, i.e., the logical rules are learned by gradient descent. Our extensive experiments on Kandinsky patterns and CLEVR-Hans benchmarks demonstrate the accuracy and efficiency of α ILP in learning complex visual-logical concepts. [ABSTRACT FROM AUTHOR]

A magic value in a program is a constant symbol that is essential for the execution of the program but has no clear explanation for its choice. Learning programs with magic values is difficult for existing program synthesis approaches. To overcome this limitation, we introduce an inductive logic programming approach to efficiently learn programs with magic values. Our experiments on diverse domains, including program synthesis, drug design, and game playing, show that our approach can (1) outperform existing approaches in terms of predictive accuracies and learning times, (2) learn magic values from infinite domains, such as the value of pi, and (3) scale to domains with millions of constant symbols. [ABSTRACT FROM AUTHOR]

Building rules on ontology is the main task of mining the logical layer of the Semantic Web. A major effort has been made to develop algorithms capable of efficiently processing relational data and complex background knowledge. One of the promising technologies used in this effort is inductive logic programming (ILP). Steam boilers are an important equipment in power plants, and boiler trips can lead to a complete shutdown of the plant. Thus, it is essential to detect possible boiler trips in critical times to maintain normal and safe operating conditions. To address this challenge, the automatic rule-learning approach is used in this study to diagnose rule extraction. The learning examples are event sequences obtained by simulating an industrial steam boiler model. The ontology is considered as prior conceptual knowledge in ILP to induce supervision rules. The latter are eventually introduced into a scenario recognition system capable of continuously analyzing the event flow arriving at the supervisory center and alerting the operator when a fault situation is detected. [ABSTRACT FROM AUTHOR]

Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified in a structured logical form. To address this limitation, we propose a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FFNSL), that integrates a logic-based machine learning system capable of learning from noisy examples, with neural networks, in order to learn interpretable knowledge from labelled unstructured data. We demonstrate the generality of FFNSL on four neural-symbolic classification problems, where different pre-trained neural network models and logic-based machine learning systems are integrated to learn interpretable knowledge from sequences of images. We evaluate the robustness of our framework by using images subject to distributional shifts, for which the pre-trained neural networks may predict incorrectly and with high confidence. We analyse the impact that these shifts have on the accuracy of the learned knowledge and run-time performance, comparing FFNSL to tree-based and pure neural approaches. Our experimental results show that FFNSL outperforms the baselines by learning more accurate and interpretable knowledge with fewer examples. [ABSTRACT FROM AUTHOR]

In Meta-interpretive learning (MIL) the metarules, second-order datalog clauses acting as inductive bias, are manually defined by the user. In this work we show that second-order metarules for MIL can be learned by MIL. We define a generality ordering of metarules by θ -subsumption and show that user-defined sort metarules are derivable by specialisation of the most-general matrix metarules in a language class; and that these matrix metarules are in turn derivable by specialisation of third-order punch metarules with variables quantified over the set of atoms and for which only an upper bound on their number of literals need be user-defined. We show that the cardinality of a metarule language is polynomial in the number of literals in punch metarules. We re-frame MIL as metarule specialisation by resolution. We modify the MIL metarule specialisation operator to return new metarules rather than first-order clauses and prove the correctness of the new operator. We implement the new operator as TOIL, a sub-system of the MIL system Louise. Our experiments show that as user-defined sort metarules are progressively replaced by sort metarules learned by TOIL, Louise's predictive accuracy and training times are maintained. We conclude that automatically derived metarules can replace user-defined metarules. [ABSTRACT FROM AUTHOR]

Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far the systems that LFIT handled were mainly restricted to synchronous deterministic dynamics. However, other dynamics exist in the field of logical modeling, in particular the asynchronous semantics which is widely used to model biological systems. In this paper, we propose a modeling of discrete memory-less multi-valued dynamic systems as logic programs in which a rule represents what can occur rather than what will occur. This modeling allows us to represent non-determinism and to propose an extension of LFIT to learn regardless of the update schemes, allowing to capture a large range of semantics. We also propose a second algorithm which is able to learn a whole system dynamics, including its semantics, in the form of a single propositional logic program with constraints. We show through theoretical results the correctness of our approaches. Practical evaluation is performed on benchmarks from biological literature. [ABSTRACT FROM AUTHOR]