Combining symbolic human knowledge with neural networks provides a rule-based ante-hoc explanation of the output. In this paper, we propose feature extracting functions for integrating human knowledge abstracted as logic rules into the predictive behavior of a neural network. These functions are embodied as programming functions, which represent the applicable domain knowledge as a set of logical instructions and provide a modified distribution of independent features on input data. Unlike other existing neural logic approaches, the programmatic nature of these functions implies that they do not require any kind of special mathematical encoding, which makes our method very general and flexible in nature. We illustrate the performance of our approach for sentiment classification and compare our results to those obtained using two baselines.
Instituto Superior de Engenharia de Lisboa（里斯本高等工程学院）
This work describes a methodology that combines logic-based systems and connectionist systems. Our approach uses finite truth-valued Łukasiewicz logic, wherein every connective can be defined by a neuron in an artificial network. This allowed the injection of first-order formulas into a network architecture, and also simplified symbolic rule extraction. For that we trained a neural networks using the Levenderg-Marquardt algorithm, where we restricted the knowledge dissemination in the network structure. This procedure reduces neural network plasticity without drastically damaging the learning …
Université de Montréal（蒙特利尔大学）；Mila - Québec AI Institute（米拉 - 魁北克人工智能研究所）；Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院）；HEC Montréal（蒙特利尔高等商学院）；Tsinghua University（清华大学）
This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing methods either suffer from the problem of searching in a large search space (e.g., neural logic programming) or ineffective optimization due to sparse rewards (e.g., techniques based on reinforcement learning). To address these limitations, this paper proposes a probabilistic model called RNNLogic. RNNLogic treats logic rules as a latent variable, and simul…
Machine learning models on behavioral and textual data can result in highly accurate prediction models, but are often very difficult to interpret. Rule-extraction techniques have been proposed to combine the desired predictive accuracy of complex "black-box" models with global explainability. However, rule-extraction in the context of high-dimensional, sparse data, where many features are relevant to the predictions, can be challenging, as replacing the black-box model by many rules leaves the user again with an incomprehensible explanation. To address this problem, we develop and test a rule-…
In recent years, there has been significant work on increasing both interpretability and debuggability of a Deep Neural Network (DNN) by extracting a rule-based model that approximates its decision boundary. Nevertheless, current DNN rule extraction methods that consider a DNN's latent space when extracting rules, known as decompositional algorithms, are either restricted to single-layer DNNs or intractable as the size of the DNN or data grows. In this paper, we address these limitations by introducing ECLAIRE, a novel polynomial-time rule extraction algorithm capable of scaling to both large …
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…
Knowledge extraction is used to convert neural networks into symbolic descriptions with the objective of producing more comprehensible learning models. The central challenge is to find an explanation which is more comprehensible than the original model while still representing that model faithfully. The distributed nature of deep networks has led many to believe that the hidden features of a neural network cannot be explained by logical descriptions simple enough to be comprehensible. In this paper, we propose a novel layerwise knowledge extraction method using M-of-N rules which seeks to obta…
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…
TCS Research, Tata Consultancy Services（塔塔咨询服务公司TCS研究院）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；Indian Institute of Technology Patna（印度理工学院巴特那分校）
The task of end-to-end relation extraction consists of two sub-tasks: i) identifying entity mentions along with their types and ii) recognizing semantic relations among the entity mention pairs. %Identifying entity mentions along with their types and recognizing semantic relations among the entity mentions, are two very important problems in Information Extraction. It has been shown that for better performance, it is necessary to address these two sub-tasks jointly. We propose an approach for simultaneous extraction of entity mentions and relations in a sentence, by using inference in Markov L…
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…
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）
South Westfalia University of Applied Science（西南威斯特伐利亚应用科学大学）
Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian classifiers, DNN suffer from bad interpretability where we understand by interpretability, that a human can easily derive the relations modeled by the network. A reasonable way to provide interpretability for humans are logical rules. In this paper we propose neural logic rule layers (NLRL) which are able to represent arbitrary logic rules in terms of their …
China University of Petroleum (East China)（中国石油大学（华东））；Indian Statistical Institute（印度统计研究所）
A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are hardly any work dealing with datasets with dimensions more than hundred or so. Here, we propose a neuro-fuzzy framework that can handle datasets with dimensions even more than 7000! In this context, we propose an adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of ``numeric underflow" and ``fake minimum" that arise for existing fuzzy syste…
In this paper, we consider the problem of open information extraction (OIE) for extracting entity and relation level intermediate structures from sentences in open-domain. We focus on four types of valuable intermediate structures (Relation, Attribute, Description, and Concept), and propose a unified knowledge expression form, SAOKE, to express them. We publicly release a data set which contains more than forty thousand sentences and the corresponding facts in the SAOKE format labeled by crowd-sourcing. To our knowledge, this is the largest publicly available human labeled data set for open in…
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）
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…
This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use of the Dempster-Shafer Theory for representing a particular class of rules, Belief calculated being a lower probability given certain independence assumptions on an underlying space. It shows how a belief function framework can be generalised to other logics, including a general Monte-Carlo algorithm for calculating belief, and how a version of Reiter's Defa…
KAIST（韩国科学技术院）；IBS（基础科学研究院）；Microsoft Research Asia（微软亚洲研究院）
We present SELOR, a framework for integrating self-explaining capabilities into a given deep model to achieve both high prediction performance and human precision. By "human precision", we refer to the degree to which humans agree with the reasons models provide for their predictions. Human precision affects user trust and allows users to collaborate closely with the model. We demonstrate that logic rule explanations naturally satisfy human precision with the expressive power required for good predictive performance. We then illustrate how to enable a deep model to predict and explain with log…
Universidade Federal Rural de Pernambuco（伯南布哥州联邦农村大学）；Aix-Marseille Université（艾克斯-马赛大学）；Universidade Federal de Pernambuco（伯南布哥州联邦大学）
Relation Extraction (RE), the task of detecting and characterizing semantic relations between entities in text, has gained much importance in the last two decades, mainly in the biomedical domain. Many papers have been published on Relation Extraction using supervised machine learning techniques. Most of these techniques rely on statistical methods, such as feature-based and tree-kernels-based methods. Such statistical learning techniques are usually based on a propositional hypothesis space for representing examples, i.e., they employ an attribute-value representation of features. This kind o…
School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院）
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop an iterative distillation method that transfers the structured information of logic rules into the weights of neural networks. We deploy the framework on a CNN for sentiment analysis, and an RNN for named entity recognition. With a few highly intuitive rules, we obtain substanti…
Hong Kong University of Science and Technology（香港科技大学）；South China Normal University（华南师范大学）
In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two …
Instituto Superior de Engenharia de Lisboa（里斯本高等工程学院）
The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriate interface layer between deduction, abduction and induction. In this work we extend traditional algebraic specification methods in this direction. Here we assume that such interface for AI emerges from an adequate Neural-Symbolic integration. This integration is made for universe of discourse described on a Topos governed by a many-valued Łukasiewicz logic. Sentences are integrated in a symbolic knowledge base describing the problem domain, codified…
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…
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 …
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…
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 template…
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…
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…
Departamento de Matemática（数学系）；Instituto Superior de Engenharia de Lisboa（里斯本高等工程学院）
This work describes a methodology to combine logic-based systems and connectionist systems. Our approach uses finite truth valued Łukasiewicz logic, where we take advantage of fact what in this type of logics every connective can be define by a neuron in an artificial network having by activation function the identity truncated to zero and one. This allowed the injection of first-order formulas in a network architecture, and also simplified symbolic rule extraction. Our method trains a neural network using Levenderg-Marquardt algorithm, where we restrict the knowledge dissemination in the netw…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.
Representation learning of knowledge graphs encodes entities and relation types into a continuous low-dimensional vector space, learns embeddings of entities and relation types. Most existing methods only concentrate on knowledge triples, ignoring logic rules which contain rich background knowledge. Although there has been some work aiming at leveraging both knowledge triples and logic rules, they ignore the transitivity and antisymmetry of logic rules. In this paper, we propose a novel approach to learn knowledge representations with entities and ordered relations in knowledges and logic rule…
Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social attribute, its degrees being measured by the fraction of people who share a given opinion. Different known rules and some new ones are obtained depending on which particular constraints are assumed. These constraints allow to model different notions of choiceness. In particular, we give a new method to deal with approval-disapproval-preferential voting.
An important problem to be addressed within Event-Driven Architecture (EDA) is how to correctly and efficiently capture and process the event/action-based logic. This paper endeavors to bridge the gap between the Knowledge Representation (KR) approaches based on durable events/actions and such formalisms as event calculus, on one hand, and event-condition-action (ECA) reaction rules extending the approach of active databases that view events as instantaneous occurrences and/or sequences of events, on the other. We propose formalism based on reaction rules (ECA rules) and a novel interval-based…
Alibaba Group（阿里巴巴集团）；University of Oregon（俄勒冈大学）；Microsoft（微软）；South China University of Technology（华南理工大学）
Large scale knowledge graph embedding has attracted much attention from both academia and industry in the field of Artificial Intelligence. However, most existing methods concentrate solely on fact triples contained in the given knowledge graph. Inspired by the fact that logic rules can provide a flexible and declarative language for expressing rich background knowledge, it is natural to integrate logic rules into knowledge graph embedding, to transfer human knowledge to entity and relation embedding, and strengthen the learning process. In this paper, we propose a novel logic rule-enhanced me…
This paper introduces the independent choice logic, and in particular the "single agent with nature" instance of the independent choice logic, namely ICLdt. This is a logical framework for decision making uncertainty that extends both logic programming and stochastic models such as influence diagrams. This paper shows how the representation of a decision problem within the independent choice logic can be exploited to cut down the combinatorics of dynamic programming. One of the main problems with influence diagram evaluation techniques is the need to optimise a decision for all values of the '…
CP-logic is a probabilistic extension of the logic FO(ID). Unlike ASP, both of these logics adhere to a Tarskian informal semantics, in which interpretations represent objective states-of-affairs. In other words, these logics lack the epistemic component of ASP, in which interpretations represent the beliefs or knowledge of a rational agent. Consequently, neither CP-logic nor FO(ID) have the need for two kinds of negations: there is only one negation, and its meaning is that of objective falsehood. Nevertheless, the formal semantics of this objective negation is mathematically more similar to …
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…
American International University-Bangladesh（孟加拉国国际大学）
Artificial Neural Network is among the most popular algorithm for supervised learning. However, Neural Networks have a well-known drawback of being a "Black Box" learner that is not comprehensible to the Users. This lack of transparency makes it unsuitable for many high risk tasks such as medical diagnosis that requires a rational justification for making a decision. Rule Extraction methods attempt to curb this limitation by extracting comprehensible rules from a trained Network. Many such extraction algorithms have been developed over the years with their respective strengths and weaknesses. …
Griffith University（格里菲斯大学）；Singapore Management University（新加坡管理大学）；University of Verona（维罗纳大学）；University of Bologna（博洛尼亚大学）
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions of such theories were proposed in Olivieri et al (2021) This work extends such a logical framework by considering the deontic aspect. The resulting logic will not just be able to model policies but also tackle well-known aspects that occur in numerous legal systems. The use of Defeasible Logic (DL) to model meta-rules in the application area we just alluded…
RLJP: Legal Judgment Prediction via First-Order Logic Rule-enhanced with Large Language Models
College of Computer Science and Technology, National University of Defense and Technology（国防科技大学计算机科学与技术学院）；College of Electronic Engineering, National University of Defense Technology（国防科技大学电子工程学院）；School of Data and Computer Science, Shandong Women’s University（山东女子大学数据与计算机科学学院）；Institute for Artificial Intelligence, Tsinghua University（清华大学人工智能研究院）
Tacit Knowledge Extraction via Logic Augmented Generation and Active Inference
CNR - Institute of Cognitive Sciences and Technologies（CNR-认知科学与技术研究所）；University of Bologna（博洛尼亚大学）；MISTER Smart Innovation（MISTER智能创新）；Consorzio MUSP（MUSP协会）
This paper presents a method of computing a revision of a function-free normal logic program. If an added rule is inconsistent with a program, that is, if it leads to a situation such that no stable model exists for a new program, then deletion and addition of rules are performed to avoid inconsistency. We specify a revision by translating a normal logic program into an abductive logic program with abducibles to represent deletion and addition of rules. To compute such deletion and addition, we propose an adaptation of our top-down abductive proof procedure to compute a relevant abducibles to …
