Efficiently inducing high-level interpretable regularities from knowledge graphs (KGs) is an essential yet challenging task that benefits many downstream applications. In this work, we present GPFL, a probabilistic rule learner optimized to mine instantiated first-order logic rules from KGs. Instantiated rules contain constants extracted from KGs. Compared to abstract rules that contain no constants, instantiated rules are capable of explaining and expressing concepts in more details. GPFL utilizes a novel two-stage rule generation mechanism that first generalizes extracted paths into templates that are acyclic abstract rules until a certain degree of template saturation is achieved, then specializes the generated templates into instantiated rules. Unlike existing works that ground every mined instantiated rule for evaluation, GPFL shares groundings between structurally similar rules for collective evaluation. Moreover, we reveal the presence of overfitting rules, their impact on the predictive performance, and the effectiveness of a simple validation method filtering out overfitting rules. Through extensive experiments on public benchmark datasets, we show that GPFL 1.) significantly reduces the runtime on evaluating instantiated rules; 2.) discovers much more quality instantiated rules than existing works; 3.) improves the predictive performance of learned rules by removing overfitting rules via validation; 4.) is competitive on knowledge graph completion task compared to state-of-the-art baselines.
Harbin Institute of Technology at Weihai（哈尔滨工业大学（威海））
Large-scale knowledge graphs provide structured representations of human knowledge. However, as it is impossible to collect all knowledge, knowledge graphs are usually incomplete. Reasoning based on existing facts paves a way to discover missing facts. In this paper, we study the problem of learning logical rules for reasoning on knowledge graphs for completing missing factual triplets. Learning logical rules equips a model with strong interpretability as well as the ability to generalize to similar tasks. We propose a model able to fully use training data which also considers multi-target sce…
University of Bonn（波恩大学）；Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）
Knowledge graph embedding models have gained significant attention in AI research. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine learning tasks. However, so far, most existing models do not allow the inclusion of rules. We address the challenge of including rules and present a new neural based embedding model (LogicENN). We prove that LogicENN can learn every ground truth of encoded rules in a knowledge graph. To the best of our knowledge, this has not been proved so far for the neural …
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG they are brittle and mining ones that infer facts beyond the known KG is challenging. Probabilistic embedding methods are effective in capturing global soft statistical tendencies and reasoning with them is computationally efficient. While embedding representations learned from rich training data are expressive, incompleteness and sparsity in real-world KGs can impact their…
Many systems have been developed in recent years to mine logical rules from large-scale Knowledge Graphs (KGs), on the grounds that representing regularities as rules enables both the interpretable inference of new facts, and the explanation of known facts. Among these systems, the walk-based methods that generate the instantiated rules containing constants by abstracting sampled paths in KGs demonstrate strong predictive performance and expressivity. However, due to the large volume of possible rules, these systems do not scale well where computational resources are often wasted on generating…
We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a discrete space. We propose a framework, Neural Logic Programming, that combines the parameter and structure learning of first-order logical rules in an end-to-end differentiable model. This approach is inspired by a recently-developed differentiable logic called TensorLog, where inference tasks can be compiled into sequences of differentiable operations. We design…
RulE: Knowledge Graph Reasoning with Rule Embedding
Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）；National Key Laboratory of General Artificial Intelligence, BIGAI（北京智源人工智能研究院通用人工智能全国重点实验室）；Tsinghua University（清华大学）
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…
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University College London（伦敦大学学院）
A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of observed facts and learns to extract from them a set of logical rules and a small set of core facts which together entail the observations. Our approach is neuro-symbolic in the sense that the rule pred- icates and core facts are given dense vector representations. The rules are applied to the core facts using a soft unification procedure to infer additional fa…
Siemens AG（西门子股份公司）；Ludwig Maximilian University of Munich（慕尼黑大学）
Conventional static knowledge graphs model entities in relational data as nodes, connected by edges of specific relation types. However, information and knowledge evolve continuously, and temporal dynamics emerge, which are expected to influence future situations. In temporal knowledge graphs, time information is integrated into the graph by equipping each edge with a timestamp or a time range. Embedding-based methods have been introduced for link prediction on temporal knowledge graphs, but they mostly lack explainability and comprehensible reasoning chains. Particularly, they are usually not…
Learning logical rules is critical to improving reasoning in KGs. This is due to their ability to provide logical and interpretable explanations when used for predictions, as well as their ability to generalize to other tasks, domains, and data. While recent methods have been proposed to learn logical rules, the majority of these methods are either restricted by their computational complexity and can not handle the large search space of large-scale KGs, or show poor generalization when exposed to data outside the training set. In this paper, we propose an end-to-end neural model for learning c…
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）
Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models
Laboratory for Big Data and Decision（大数据与决策实验室）；National University of Defense Technology（国防科技大学）；National Key Laboratory of Information Systems Engineering（信息系统工程国家重点实验室）；Microsoft Corporation（微软公司）；College of Computer Science and Technology（计算机科学与技术学院）
Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-tra…
Honey, I shrunk the hypothesis space (through logical preprocessing)
ELLIS Institute（ELLIS研究所）；University of Helsinki（赫尔辛基大学）；Czech Academy of Sciences Institute of Computer Science（捷克科学院计算机科学研究所）；Dynatrace Research（Dynatrace研究）
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an open problem. In this paper, we explore how symbolic logic, defined as logic programs at a character level, is learned to be represented in a high-dimensional vector space using RNN-based iterative neural networks to perform reasoning. We create a new dataset that defines 12 classes of logic programs exemplifying increased level of complexity of logical rea…
This paper presents inference rules for Resource Description Framework (RDF), RDF Schema (RDFS) and Web Ontology Language (OWL). Our formalization is based on Notation 3 Logic, which extended RDF by logical symbols and created Semantic Web logic for deductive RDF graph stores. We also propose OWL-P that is a lightweight formalism of OWL and supports soft inferences by omitting complex language constructs.
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning ability in arithmetic tasks is limited, which we reproduce experimentally. Here, we recast this limitation as not unique to mathematics but common to tasks that require logical operations. We then propose a new set of tasks, termed logical tasks, which will be the next challenge to address. This higher point of view helps the development of inductive biases that…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta-constraints, supports the use of uncertain information in the form of either undefined values or possible combinations of val…
University of California San Diego（加州大学圣地亚哥分校）；Bosch Research North America（博世北美研究院）；Bosch Research（博世研究院）
We study the problem of building entity tagging systems by using a few rules as weak supervision. Previous methods mostly focus on disambiguation entity types based on contexts and expert-provided rules, while assuming entity spans are given. In this work, we propose a novel method TALLOR that bootstraps high-quality logical rules to train a neural tagger in a fully automated manner. Specifically, we introduce compound rules that are composed from simple rules to increase the precision of boundary detection and generate more diverse pseudo labels. We further design a dynamic label selection st…
This paper investigates the relationship between the Logical Algorithms language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHR-rp: CHR with rule priorities, and show that the meta-complexity theorem for LA can be applied to a subset of CHR-rp via inverse translation. Inspired by the high-level implementation proposal for Logical Algorithm by Ganzinger and McAllester and based on a new scheduling algorithm, we propose an alternative implementation for CHR-rp that gives strong complexity guarantees and results in a new and ac…
Siemens AG（西门子股份公司）；Ludwig Maximilian University of Munich（慕尼黑大学）
The graph structure of biomedical data differs from those in typical knowledge graph benchmark tasks. A particular property of biomedical data is the presence of long-range dependencies, which can be captured by patterns described as logical rules. We propose a novel method that combines these rules with a neural multi-hop reasoning approach that uses reinforcement learning. We conduct an empirical study based on the real-world task of drug repurposing by formulating this task as a link prediction problem. We apply our method to the biomedical knowledge graph Hetionet and show that our approac…
Charles University, Faculty of Mathematics and Physics（查理大学数学与物理学院）；Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
In this paper, we focus on exploiting neural networks for the analysis and planning stage in self-adaptive architectures. The studied motivating cases in the paper involve existing (legacy) self-adaptive architectures and their adaptation logic, which has been specified by logical rules. We further assume that there is a need to endow these systems with the ability to learn based on examples of inputs and expected outputs. One simple option to address such a need is to replace the reasoning based on logical rules with a neural network. However, this step brings several problems that often crea…
TU Kaiserslautern（凯泽斯劳滕工业大学）；University of Mainz（美因茨大学）；Johannes Gutenberg University of Mainz（约翰内斯·古腾堡大学美因茨分校）；TU Darmstadt（达姆施塔特工业大学）
Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural language instead of distributed representations. However, for high-dimensional input data such as images, the individual symbols, i.e. pixels, are not easily interpretable. We introduce the concept of first-order convolutional rules, which are logical rules that can be extracted using a convolutional neural network (CNN), and whose complexity depends on the s…
University of Southern California（南加州大学）；Indian Institute of Technology, Delhi（印度理工学院德里分校）
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in natural language. Recent works show that such models can also produce the reasoning steps (i.e., the proof graph) that emulate the model's logical reasoning process. Currently, these black-box models generate both the proof graph and intermediate inferences within the same model and thus may be unfaithful. In this work, we frame the deductive logical reasoning task by defining three modular components: rule selection, fact selection, and knowledge composition.…
We present a straightforward source-to-source transformation that introduces justifications for user-defined constraints into the CHR programming language. Then a scheme of two rules suffices to allow for logical retraction (deletion, removal) of constraints during computation. Without the need to recompute from scratch, these rules remove not only the constraint but also undo all consequences of the rule applications that involved the constraint. We prove a confluence result concerning the rule scheme and show its correctness. When algorithms are written in CHR, constraints represent both dat…
Eurecom（欧洲通信系统工程师学校与微电子中心）；Qatar Computing Research Institute, HBKU（哈马德·本·哈利法大学卡塔尔计算研究所）
While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction …
Universidad de Buenos Aires（布宜诺斯艾利斯大学）；CONICET-UBA（阿根廷科学与技术研究委员会-布宜诺斯艾利斯大学联合机构）；SRI International（SRI国际公司）
In this work, we present a framework for incorporating descriptive logical rules in state-of-the-art neural networks, enabling them to learn how to handle unseen labels without the introduction of any new training data. The rules are integrated into existing networks without modifying their architecture, through an additional term in the network's loss function that penalizes states of the network that do not obey the designed rules. As a case of study, the framework is applied to an existing neural-based Dialog State Tracker. Our experiments demonstrate that the inclusion of logical rules all…
KAIST（韩国科学技术院）；Institute for Basic Science (IBS)（基础科学研究院）
SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We prese…
Logical inference, an integral feature of the Semantic Web, is the process of deriving new triples by applying entailment rules on knowledge bases. The entailment rules are determined by the model-theoretic semantics. Incorporating context of an RDF triple (e.g., provenance, time, and location) into the inferencing process requires the formal semantics to be capable of describing the context of RDF triples also in the form of triples, or in other words, RDF contextual triples about triples. The formal semantics should also provide the rules that could entail new contextual triples about triple…
In Search of the Long-Tail: Systematic Generation of Long-Tail Inferential Knowledge via Logical Rule Guided Search
University of Southern California（南加州大学）；Ohio State University（俄亥俄州立大学）；Fudan University（复旦大学）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；University of Pittsburgh（匹兹堡大学）；University of Washington（华盛顿大学）；Cornell University（康奈尔大学）
Université de Toulouse（图卢兹大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）
The goal of this paper is to propose a framework for representing and reasoning about the rules governing a combinatorial exchange. Such a framework is at first interest as long as we want to build up digital marketplaces based on auction, a widely used mechanism for automated transactions. Combinatorial exchange is the most general case of auctions, mixing the double and combinatorial variants: agents bid to trade bundles of goods. Hence the framework should fulfill two requirements: (i) it should enable bidders to express their bids on combinations of goods and (ii) it should allow describin…
