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 tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.
Deep reinforcement learning (DRL) has achieved significant breakthroughs in various tasks. However, most DRL algorithms suffer a problem of generalizing the learned policy which makes the learning performance largely affected even by minor modifications of the training environment. Except that, the use of deep neural networks makes the learned policies hard to be interpretable. To address these two challenges, we propose a novel algorithm named Neural Logic Reinforcement Learning (NLRL) to represent the policies in reinforcement learning by first-order logic. NLRL is based on policy gradient methods and differentiable inductive logic programming that have demonstrated significant advantages in terms of interpretability and generalisability in supervised tasks. Extensive experiments conducted on cliff-walking and blocks manipulation tasks demonstrate that NLRL can induce interpretable policies achieving near-optimal performance while demonstrating good generalisability to environments of different initial states and problem sizes.
Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of tasks and initial background knowledge. Before solving the tasks, the learner enters an unsupervised playing stage where it creates its own tasks to solve, tries to solve them, and saves any solutions (programs) to the background knowledge. After the playing stage is finished, the learner enters the supervised building stage where it tries to solve the user-supplied tasks and can reuse solutions learnt whilst playing. The idea is that playing allows the learner to discover reusable general programs on its own which can then help solve the user-supplied tasks. We claim that playing can improve learning performance. We show that playing can reduce the textual complexity of target concepts which in turn reduces the sample complexity of a learner. We implement our idea in Playgol, a new inductive logic programming system. We experimentally test our claim on two domains: robot planning and real-world string transformations. Our experimental results suggest that playing can substantially improve learning performance. We think that the idea of playing (or, more verbosely, unsupervised bootstrapping for supervised program induction) is an important contribution to the problem of developing program induction approaches that self-discover BK.
We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these elementary operators can be combined in a simple and meaningful way to form Neural Logic Networks (NLNs). We examine the effectiveness of the proposed NLN framework in learning Boolean functions and discrete-algorithmic tasks. We demonstrate that, in contrast to the implicit learning in MLP approach, the proposed neural logic networks can learn the logical functions explicitly that can be verified and interpreted by human. In particular, we propose a new framework for learning the inductive logic programming (ILP) problems by exploiting the explicit representational power of NLN. We show the proposed neural ILP solver is capable of feats such as predicate invention and recursion and can outperform the current state of the art neural ILP solvers using a variety of benchmark tasks such as decimal addition and multiplication, and sorting on ordered list.
Transportation systems serve the people in essence, in this study we focus in traffic information related to violation events to respond to safety requirements of the cities. Traffic violation events have an important role in city safety awareness and secure travel. In this work, we describe the use of knowledge discovery from traffic violation reports in combination with demographics approach using inductive logic programming to automatically extract knowledge about traffic violation behavior and their impact on the environment.
In recent years, non-monotonic Inductive Logic Programming has received growing interest. Specifically, several new learning frameworks and algorithms have been introduced for learning under the answer set semantics, allowing the learning of common-sense knowledge involving defaults and exceptions, which are essential aspects of human reasoning. In this paper, we present a noise-tolerant generalisation of the learning from answer sets framework. We evaluate our ILASP3 system, both on synthetic and on real datasets, represented in the new framework. In particular, we show that on many of the datasets ILASP3 achieves a higher accuracy than other ILP systems that have previously been applied to the datasets, including a recently proposed differentiable learning framework.
We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the model's global behavior, we propose the LIME-FOLD algorithm ---a heuristic-based inductive logic programming (ILP) algorithm capable of learning non-monotonic logic programs---that we apply to a transformed dataset produced by LIME. Our proposed approach is agnostic to the choice of the ILP algorithm. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics. Meanwhile, the number of induced rules dramatically decreases compared to ALEPH, a state-of-the-art ILP system.
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives in logic programming, which is now increasingly seen to provide a declarative background to complex machine learning applications. While many systems offer inference capabilities, the more significant challenge is that of learning meaningful and interpretable symbolic representations from data. In that regard, inductive logic programming and related techniques have paved much of the way for the last few decades. Unfortunately, a major limitation of this exciting landscape is that much of the work is limited to finite-domain discrete probability distributions. Recently, a handful of systems have been extended to represent and perform inference with continuous distributions. The problem, of course, is that classical solutions for inference are either restricted to well-known parametric families (e.g., Gaussians) or resort to sampling strategies that provide correct answers only in the limit. When it comes to learning, moreover, inducing representations remains entirely open, other than "data-fitting" solutions that force-fit points to aforementioned parametric families. In this paper, we take the first steps towards inducing probabilistic logic programs for continuous and mixed discrete-continuous data, without being pigeon-holed to a fixed set of distribution families. Our key insight is to leverage techniques from piecewise polynomial function approximation theory, yielding a principled way to learn and compositionally construct density functions. We test the framework and discuss the learned representations.
Our interest in this paper is in the construction of symbolic explanations for predictions made by a deep neural network. We will focus attention on deep relational machines (DRMs, first proposed by H. Lodhi). A DRM is a deep network in which the input layer consists of Boolean-valued functions (features) that are defined in terms of relations provided as domain, or background, knowledge. Our DRMs differ from those proposed by Lodhi, which use an Inductive Logic Programming (ILP) engine to first select features (we use random selections from a space of features that satisfies some approximate constraints on logical relevance and non-redundancy). But why do the DRMs predict what they do? One way of answering this is the LIME setting, in which readable proxies for a black-box predictor. The proxies are intended only to model the predictions of the black-box in local regions of the instance-space. But readability alone may not enough: to be understandable, the local models must use relevant concepts in an meaningful manner. We investigate the use of a Bayes-like approach to identify logical proxies for local predictions of a DRM. We show: (a) DRM's with our randomised propositionalization method achieve state-of-the-art predictive performance; (b) Models in first-order logic can approximate the DRM's prediction closely in a small local region; and (c) Expert-provided relevance information can play the role of a prior to distinguish between logical explanations that perform equivalently on prediction alone.
Knowledge Representation and Reasoning and Machine Learning are two important fields in AI. Nonmonotonic logic programming (NMLP) and Answer Set Programming (ASP) provide formal languages for representing and reasoning with commonsense knowledge and realize declarative problem solving in AI. On the other side, Inductive Logic Programming (ILP) realizes Machine Learning in logic programming, which provides a formal background to inductive learning and the techniques have been applied to the fields of relational learning and data mining. Generally speaking, NMLP and ASP realize nonmonotonic reasoning while lack the ability of learning. By contrast, ILP realizes inductive learning while most techniques have been developed under the classical monotonic logic. With this background, some researchers attempt to combine techniques in the context of nonmonotonic ILP. Such combination will introduce a learning mechanism to programs and would exploit new applications on the NMLP side, while on the ILP side it will extend the representation language and enable us to use existing solvers. Cross-fertilization between learning and nonmonotonic reasoning can also occur in such as the use of answer set solvers for ILP, speed-up learning while running answer set solvers, learning action theories, learning transition rules in dynamical systems, abductive learning, learning biological networks with inhibition, and applications involving default and negation. This workshop is the first attempt to provide an open forum for the identification of problems and discussion of possible collaborations among researchers with complementary expertise. The workshop was held on September 15th of 2013 in Corunna, Spain. This post-proceedings contains five technical papers (out of six accepted papers) and the abstract of the invited talk by Luc De Raedt.
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 probability by representing clause as graphical model and literals as vertices in it. This model is still too complicate and only can be approximate by pseudo-likelihood. We propose Inductive Logic Boosting framework to transform the relational dataset into a feature-based dataset, induces logic rules by boosting Problog Rule Trees and relaxes the independence constraint of pseudo-likelihood. Experimental evaluation on benchmark datasets demonstrates that the AUC-PR and AUC-ROC value of ILP learned rules are higher than current state-of-the-art SRL methods.
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 computed answer sets. Our approach is prototypically implemented. Examples illustrate the introduced concepts and point at issues and topics for future research.
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 $T$.
We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials.
A particularly successful role for Inductive Logic Programming (ILP) is as a tool for discovering useful relational features for subsequent use in a predictive model. Conceptually, the case for using ILP to construct relational features rests on treating these features as functions, the automated discovery of which necessarily requires some form of first-order learning. Practically, there are now several reports in the literature that suggest that augmenting any existing features with ILP-discovered relational features can substantially improve the predictive power of a model. While the approach is straightforward enough, much still needs to be done to scale it up to explore more fully the space of possible features that can be constructed by an ILP system. This is in principle, infinite and in practice, extremely large. Applications have been confined to heuristic or random selections from this space. In this paper, we address this computational difficulty by allowing features to be constructed in a distributed manner. That is, there is a network of computational units, each of which employs an ILP engine to construct some small number of features and then builds a (local) model. We then employ a consensus-based algorithm, in which neighboring nodes share information to update local models. For a category of models (those with convex loss functions), it can be shown that the algorithm will result in all nodes converging to a consensus model. In practice, it may be slow to achieve this convergence. Nevertheless, our results on synthetic and real datasets that suggests that in relatively short time the "best" node in the network reaches a model whose predictive accuracy is comparable to that obtained using more computational effort in a non-distributed setting (the best node is identified as the one whose weights converge first).
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 cannot fully undertake. In addition, event-based data is usually massive and collected at different times and under various circumstances. Ideally, systems that learn from temporal data should be able to operate in an incremental mode, that is, revise prior constructed knowledge in the face of new evidence. Most ILP systems are batch learners, in the sense that in order to account for new evidence they have no alternative but to forget past knowledge and learn from scratch. Given the increased inherent complexity of ILP and the volumes of real-life temporal data, this results to algorithms that scale poorly. In this work we present an incremental method for learning and revising event-based knowledge, in the form of Event Calculus programs. The proposed algorithm relies on abductive-inductive learning and comprises a scalable clause refinement methodology, based on a compressive summarization of clause coverage in a stream of examples. We present an empirical evaluation of our approach on real and synthetic data from activity recognition and city transport applications.
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 addresses efficiency issues by introducing a novel, efficient and effective search strategy to guide the search in PILP environments. The capabilities of SkILL are demonstrated in three dif- ferent datasets: (i) a synthetic toy example used to validate the system, (ii) a probabilistic adaptation of a well-known biological metabolism ap- plication, and (iii) a real world medical dataset in the breast cancer domain. Results show that SkILL can perform as well as a deterministic ILP learner, while also being able to incorporate probabilistic knowledge that would otherwise not be considered.
This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, called Learning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples as ordered pairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) are preferred to others. In this new learning task inductive solutions are searched within a hypothesis space of normal rules, choice rules, and hard and weak constraints. We propose a new algorithm, ILASP2, which is sound and complete with respect to our new learning framework. We investigate its applicability to learning preferences in an interview scheduling problem and also demonstrate that when restricted to the task of learning ASP programs without weak constraints, ILASP2 can be much more efficient than our previously proposed system.
Systems for symbolic event recognition 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). We present an ILP system for online learning of Event Calculus theories. To allow for a single-pass learning strategy, we use the Hoeffding bound for evaluating clauses on a subset of the input stream. We employ a decoupling scheme of the Event Calculus axioms during the learning process, that allows to learn each clause in isolation. Moreover, we use abductive-inductive logic programming techniques to handle unobserved target predicates. We evaluate our approach on an activity recognition application and compare it to a number of batch learning techniques. We obtain results of comparable predicative accuracy with significant speed-ups in training time. We also outperform hand-crafted rules and match the performance of a sound incremental learner that can only operate on noise-free datasets. This paper is under consideration for acceptance in TPLP.
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.