Markov Logic Research Articles

Quantified neural Markov logic networks

Markov Logic Networks (MLNs) are discrete generative models in the exponential family. However, specifying these rules requires considerable expertise and can pose a significant challenge. To overcome this limitation, Neural MLNs (NMLNs) have been introduced, enabling the specification of potential functions as neural networks. Thanks to the compact representation of their neural potential functions, NMLNs have shown impressive performance in modeling complex domains like molecular data. Despite the superior performance of NMLNs, their theoretical expressiveness is still equivalent to that of MLNs without quantifiers. In this paper, we propose a new class of NMLN, called Quantified NMLN, that extends the expressivity of NMLNs to the quantified setting. Furthermore, we demonstrate how to leverage the neural nature of NMLNs to employ learnable aggregation functions as quantifiers, increasing expressivity even further. We demonstrate the competitiveness of Quantified NMLNs over original NMLNs and state-of-the-art diffusion models in molecule generation experiments.

Integration Strategies of Information Technology in Mathematics Education and Student Motivation Enhancement

Abstract Integrating information technology with the curriculum has been closely watched by the educational community, and how well the two are integrated determines the effectiveness of mathematics education. This paper proposes an implementation scheme for mapping mathematical knowledge. Firstly, the Word2vec word vector model is used to acquire data from the original mathematical text, and then the Conditional Random Field model is used to extract the knowledge entities, and the Markov Logic Nets are used to extract the relationships between the knowledge entities. Then, the Path Ranking algorithm is utilized on the basis of entity alignment to realize the knowledge inference of the subject knowledge graph and mine the learning paths in the knowledge graph. Through the experimental and questionnaire methods, it was found that the math scores of the experimental class before the comparison experiment increased by 9.4337 points, which was significantly ahead of the control class. The average number of students who thought knowledge mapping teaching greatly improved their interest in math learning was 46.81%, while 31.29% believed that the new method had a relatively positive impact on their motivation to learn. It shows that knowledge mapping can be an effective method of teaching information technology.

Improving smart deals system to secure human-centric consumer applications: Internet of things and Markov logic network approaches

Considering the increasing inclination of modern consumers to frequent large retail chains capable of promptly fulfilling their diverse needs, there is a noticeable surge in the prevalence of contemporary shopping complexes. Subscription services, customer-focused strategies, and efficient supply management are driving the progression of intelligent commerce within these expansive retail platforms. The Internet of Things (IoT) presents the foundation for “smart” retailers that can monitor inventory levels, diminish equipment failures, and provide better customer experience. Many models, as one of the widely used methods in this domain, Markov Logic Network (MLN), can simultaneously use activity knowledge and data by unifying probability and logic. In this research, we determine a smart deals system (SDS), consider the improved machine learning algorithms to meet performance, and develop secure human-centric consumer applications to render the system workable. From the results, and based on the percentage of efficiency, around 10% of clients are connected randomly, which has a minor impact on the outcomes from LR (logistic regression). Similar outcomes are delivered when the number of customers in the scope of 30–40% is connected for NB (Naive Bayes). Hence, prospective shopping sales will increase along with the efficiency and speed at which it operates.

Wavelet-based temporal models of human activity for anomaly detection in smart robot-assisted environments1

Detecting anomalies in patterns of sensor data is important in many practical applications, including domestic activity monitoring for Active Assisted Living (AAL). How to represent and analyse these patterns, however, remains a challenging task, especially when data is relatively scarce and an explicit model is required to be fine-tuned for specific scenarios. This paper, therefore, presents a new approach for temporal modelling of long-term human activities with smart-home sensors, which is used to detect anomalous situations in a robot-assisted environment. The model is based on wavelet transforms and used to forecast smart sensor data, providing a temporal prior to detect unexpected events in human environments. To this end, a new extension of Hybrid Markov Logic Networks has been developed that merges different anomaly indicators, including activities detected by binary sensors, expert logic rules, and wavelet-based temporal models. The latter in particular allows the inference system to discover deviations from long-term activity patterns, which cannot be detected by simpler frequency-based models. Two new publicly available datasets were collected using several smart-sensors to evaluate the approach in office and domestic scenarios. The experimental results demonstrate the effectiveness of the proposed solutions and their successful deployment in complex human environments, showing their potential for future smart-home and robot integrated services.

Generating Markov Logic Networks Rulebase Based on Probabilistic Latent Semantics Analysis

Human Activity Recognition (HAR) has become a subject of concern and plays an important role in daily life. HAR uses sensor devices to collect user behavior data, obtain human activity information and identify them. Markov Logic Networks (MLN) are widely used in HAR as an effective combination of knowledge and data. MLN can solve the problems of complexity and uncertainty, and has good knowledge expression ability. However, MLN structure learning is relatively weak and requires a lot of computing and storage resources. Essentially, the MLN structure is derived from sensor data in the current scene. Assuming that the sensor data can be effectively sliced and the sliced data can be converted into semantic rules, MLN structure can be obtained. To this end, we propose a rulebase building scheme based on probabilistic latent semantic analysis to provide a semantic rulebase for MLN learning. Such a rulebase can reduce the time required for MLN structure learning. We apply the rulebase building scheme to single-person indoor activity recognition and prove that the scheme can effectively reduce the MLN learning time. In addition, we evaluate the parameters of the rulebase building scheme to check its stability.

Qualitative spatial reasoning with uncertain evidence using Markov logic networks

Probabilistic logics combine the ability to reason about complex scenes, with a rigorous approach to uncertainty. This paper explores the construction of probabilistic spatial logics through the combination of established qualitative spatial calculi together with Markov logic networks (MLNs). Qualitative spatial calculi provide the basis for automated representation and reasoning with complex spatial scenes; MLNs provide a rigorous basis for handling uncertainty and driving probabilistic inference. Our approach focuses specifically on the combination of an uncertain knowledge base with a certain spatial reasoning rule-base. The experiments explore how uncertain knowledge propagates through certain qualitative spatial inferences, using the specific example of reasoning with cardinal directions. The results provide a template for probabilistic qualitative spatial reasoning more generally, with applications to a wide range of common scenarios for situational awareness and automated reasoning under uncertainty.

Operation state-based adaptive control in response to production disturbances of energy-efficient serial production lines

The energy-efficient control has emerged as one of the most promising measures to reduce the unproductive energy consumption of machines during production disruptions. Diverse production disturbances (PDs) are the fundamental cause of production interruptions that result in unproductive energy consumption. In this scenario, the diversity and randomness of PDs necessitate elaborative consideration in energy-efficient controls. This consideration is crucial to the effectiveness of energy-efficient controls, yet it has been generally overlooked. To this end, this paper presents an adaptive energy-efficient control (AEC) methodology to generate adaptive control decisions when machines encounter diverse PDs in serial production lines. As a first step towards AEC, a PD identification method driven by Markov Logic Network is introduced to identify ongoing PDs. To then estimate the system performances in terms of energy savings and throughputs, a system dynamics model for serial production lines is established based on max-plus algebra. Finally, an AEC policy is formulated to optimize unproductive energy consumption on a nearly global scale while maintaining throughputs. A case study was performed on a die-casting production line in order to validate the effectiveness of the methodology. The results indicated a 96.1% F1 score for PD identifications. Based on this, the AEC policy resulted in a 61.12% reduction in unproductive energy consumption, with a corresponding decrease in throughputs of only 0.65%. It was confirmed that the AEC methodology achieved greater energy savings while minimizing throughput losses compared to conventional energy-efficient control methods.

Semantic ontology enabled modeling, retrieval and inference for incomplete mobile trajectory data

Prevalence of vehicular terminals enables more and more mobile trajectory data to be collected. To promote the intelligent urban planning, traffic management and service in smart city applications, how to analyze and reasoning the inherent patterns in mobile trajectory has grabbed considerable research attentions from academia and industry. Current widely used popular methods are subject to the check-in dataset, and the pattern inference results greatly suffer from the sparsity and incompleteness in mobile trajectory data. To address this issue, a method of semantic ontology enabled modeling, retrieval and inference for incomplete mobile trajectory is investigated in this paper. To enhance the interpretability of mobile trajectory data, the latitude and longitude coordinates in spatio-temporal sequence are converted into semantic locations, and an ontology model with constraints then is constructed for vehicle movement through defining the corresponding semantic rules with the considerations of the location relationships both between road intersections and between vehicle movements. On the basis, by taking the constructed ontology model as the knowledge base and taking the semantic query results as the training set, an ontology based markov logic network is investigated for the mobile trajectory inference problem with incomplete data. Through comprehensive comparison and analysis, the experimental results achieved on real-world data finally have been shown to demonstrate the efficiency of the investigations, and verify the influence of weight configurations on the inference performance achieved by the proposed ontology based markov logic network.

A Hybrid Driving Decision-Making System Integrating Markov Logic Networks and Connectionist AI

Connectionist artificial intelligence (AI) can power many critical tasks for connected and autonomous vehicles (CAVs). However, connectionist AI lacks interpretability and usually needs large amount of data for learning. A Markov logic network (MLN), which combines first-order logic (FOL) with statistical learning, learns weighted FOL formulas for inference. MLNs can incorporate domain expert knowledge in the form of FOL formulas to achieve data-efficient learning and transparent decision process. In this paper, we propose a hybrid driving decision-making system, which integrates a MLN module and a deep Q-network (DQN) for enhanced driving safety. The MLN module evaluates the safety of ranked actions from DQN to reduce potential collisions. A collective MLN (Co-MLN) learning algorithm is proposed and it enables CAVs collectively learn a global MLN model for safe state transitions, given distributed small amount of noisy data. A hybrid DQN-MLN learning algorithm is also developed for CAVs to collectively learn to drive in new driving environments. Simulations performed using a highway driving simulator show that the proposed Co-MLN algorithm is highly data-efficient and the learned hybrid driving system can effectively reduce collisions. In addition, the learned MLN module provides transparency for safety-critical driving decisions.

A PSL-based Approach to Human Activity Recognition in Smart Home Environments

Human activity recognition is widely used in smart cities, public safety and other fields, especially in smart home systems where it has a pivotal role. The study addresses the shortcomings of Markov logic networks for human activity recognition and proposes a human activity recognition method in smart home scenarios - an activity recognition framework based on Probabilistic Soft Logic (PSL). The framework is able to deal with logical uncertainty problems and provides expression and inference mechanisms for data uncertainty problems on this basis. The framework utilizes Deng entropy evidence theory to provide an evaluation method for sensor event uncertainty, and combines event calculus for activity modeling. Comparing the PSL method with three other common recognition methods, Ontology, Hidden Markov Model (HMM), and Markov logic network, on a public dataset, it was found that the PSL method has a much better ability to handle data uncertainty than the other three algorithms. The average recognition rates on the ADL and ADL-E sub datasets were 82.87% and 80.33%, respectively. In experiments to verify the ability of PSL to handle temporal complexity, PSL showed the least significant decrease in the average recognition rate and maintained an average recognition rate of 81.02% in the presence of concurrent and alternating activities. The human activity recognition method based on PSL has a better performance in handling both data uncertainty and temporal complexity.

Limits of multi-relational graphs

Graphons are limits of large graphs. Motivated by a theoretical problem from statistical relational learning, we develop a generalization of basic results from graphon theory into the “multi-relational” setting. We show that their multi-relational counterparts, which we call multi-relational graphons, are analogically limits of large multi-relational graphs. We extend the cut-distance topology for graphons to multi-relational graphons and prove its compactness and the density of multi-relational graphs in this topology. In turn, compactness enables to prove the large deviation principle for Multi-Relational Graphs (LDP) which enables to prove the most typical random graphs constrained by marginal statistics converge asymptotically to constrained multi-relational graphons with maximum entropy. We show the equivalence between a restricted version of Markov Logic Network and Multi-Relational Graphons with maximum entropy.

Discussion on Redundant Processing Algorithm of Association Rules Based on Hypergraph in Data Mining

With the rapid advancement of big data, it is becoming a great problem for people to find objective information in the database. The relevance data processing rule for digging the information can be the way. Relevance data processing rule for digging the information is mainly studied in three aspects: data dimension, data abstraction level, and processing variable type. In the aspect of rules, the research mainly focuses on three aspects: active relationships, passive rules, and uncommon relationship rules. Association rules of digging the data can be the most well-employed investigation goal and aim for the data digging. Along with the advancement of the information scale, the time rate of traditional relationship rules exploration of counting ways is too low. How to increase the time rate for the way of counting is the main research content of relevance data processing rules for digging the information. Current relevance data processing rules for digging the information have two limitations: (1) metrics such as support, confidence, and lift rely too much on expert knowledge or complex adjustment processes in value selection; (2) it is often difficult to explain rare association rules. Based on the existing research, this paper proposes a Markov logic network framework model of association rules to address the above shortcomings. The theory of a hypergraph and system is proposed, and the method of a hypergraph in 3D matrix modeling is studied. Aiming at the new characteristics of big data analysis, a new super edge definition method is introduced according to the definition of the system, which greatly enhances the ability to solve problems. In the cluster analysis and calculation of hypergraph, this paper will use the hypergraph segmentation operator hMETIS to carry out the cluster analysis method in order to achieve higher accuracy in cluster analysis and calculation. As for the test of cycle ones, which is in line with the relevance of the hypergraph with clear directions, the thesis will offer a brand-new way to make an analysis and turn the rule of relevance into the hypergraph with clear directions with a new definition of the near linking matrix, and it will change the dealing way from the test of the cycle and more ones into the linking f bricks and circles, which is a new way to explore. This paper uses two datasets of different sizes to conduct rule prediction accuracy experiments on the Markov logic network framework model algorithm of association rules and the traditional association rule algorithm. The results show that compared with the traditional association rule algorithm, the rules obtained by the Markov logic network framework model of association rules have a higher prediction accuracy.

Federated Markov Logic Network for indoor activity recognition in Internet of Things

Indoor activity recognition is essential in numerous Internet of Things (IoT) applications. As one of the widely used methods in this domain, Markov Logic Network (MLN) can simultaneously use activity knowledge and data by unifying probability and logic. The “cloud computing” model has recently been adopted to concentrate the activity data and activity knowledge in a central node for processing in indoor activity recognition by using MLN, which may lead to the data leakage of the clients. Therefore, to further alleviate client data privacy issues when building an indoor activity recognition model by training MLN, this paper proposes a Federated Markov Logic Network (FMLN) framework for indoor activity recognition. We designed different scenarios to investigate the FMLN framework, including statistical heterogeneity, the number ofvarious clients, and various network environments. The experimental results show that the FMLN framework effectively detects indoor activity.

Domain-Lifted Sampling for Universal Two-Variable Logic and Extensions

Given a first-order sentence ? and a domain size n, how can one sample a model of ? on the domain {1, . . . , n} efficiently as n scales? We consider two variants of this problem: the uniform sampling regime, in which the goal is to sample a model uniformly at random, and the symmetric weighted sampling regime, in which models are weighted according to the number of groundings of each predicate appearing in them. Solutions to this problem have applications to the scalable generation of combinatorial structures, as well as sampling in several statistical-relational models such as Markov logic networks and probabilistic logic programs. In this paper, we identify certain classes of sentences that are domain-liftable under sampling, in the sense that they admit a sampling algorithm that runs in time polynomial in n. In particular, we prove that every sentence of the form ∀x∀y: ?(x, y) for some quantifier-free formula ?(x,y) is domain-liftable under sampling. We then further show that this result continues to hold in the presence of one or more cardinality constraints as well as a single tree axiom constraint.

MCLA: Research on cumulative learning of Markov Logic Network

Compared with other probabilistic semantic learning algorithms, Markov Logic Network (MLN) learning can integrate existing knowledge fragments. However, the knowledge fragments increase as the MLN learning algorithm traverses candidate objects, making the execution time of the MLN learning algorithm long. To shorten the execution time, an MLN Cumulative Learning Algorithm (MCLA) that combines the MLN learning algorithm and cumulative learning is proposed. MCLA can unify the existing knowledge and the new–old knowledge, perform multi-task learning under appropriate circumstances, and directly call the existing knowledge to learn the new knowledge. This paper applies MCLA to single-resident indoor activity scenarios to verify the effectiveness of the learning algorithm. Experiments have proved that MCLA not only ensures the accuracy and improves the versatility of knowledge, but also dramatically decreases the learning time and effectively manages the knowledge memory of the MLN.

Relational attention-based Markov logic network for visual navigation

Relational attention-based Markov logic network for visual navigation

Few-shot activity learning by dual Markov logic networks

In Human activity recognition (HAR), a large amount of data may have no labels, so it is necessary to realize effective and credible data calibration under Few-shot learning (FSL). This paper proposes a new method for calibrating unlabeled data by using two models to improve the credibility of data labels further. Markov logic network (MLN) is used as the basic model. On the one hand, the construction of knowledge can reduce the dependence on the amount of data. On the other hand, the relationship between the actions can be effectively expressed. Specifically, we pre-train two MLN models using two unmatched training datasets. Then, these models are used to infer the possible labels of unlabeled data simultaneously. When labels are inconsistent, the most likely label will be selected and used to retrain the models. In order to ensure the credibility of the selected label, the selection process adopts a dual-model cross-validation method. This method uses the least square method to determine models’ weights according to the test results. Finally, it gives the possible probability of the labels under the common prediction of the models. Experimental results showed that the dual-model design method is better than the single model method in terms of time efficiency and better than the single model, TextCNN, TextLSTM, Transformer, and other models in terms of label credibility.

A taxonomy of weight learning methods for statistical relational learning

Statistical relational learning (SRL) frameworks are effective at defining probabilistic models over complex relational data. They often use weighted first-order logical rules where the weights of the rules govern probabilistic interactions and are usually learned from data. Existing weight learning approaches typically attempt to learn a set of weights that maximizes some function of data likelihood; however, this does not always translate to optimal performance on a desired domain metric, such as accuracy or F1 score. In this paper, we introduce a taxonomy of search-based weight learning approaches for SRL frameworks that directly optimize weights on a chosen domain performance metric. To effectively apply these search-based approaches, we introduce a novel projection, referred to as scaled space (SS), that is an accurate representation of the true weight space. We show that SS removes redundancies in the weight space and captures the semantic distance between the possible weight configurations. In order to improve the efficiency of search, we also introduce an approximation of SS which simplifies the process of sampling weight configurations. We demonstrate these approaches on two state-of-the-art SRL frameworks: Markov logic networks and probabilistic soft logic. We perform empirical evaluation on five real-world datasets and evaluate them each on two different metrics. We also compare them against four other weight learning approaches. Our experimental results show that our proposed search-based approaches outperform likelihood-based approaches and yield up to a 10% improvement across a variety of performance metrics. Further, we perform an extensive evaluation to measure the robustness of our approach to different initializations and hyperparameters. The results indicate that our approach is both accurate and robust.

Counting-MLNs: Learning Relational Structure for Decision Making

Many first-order probabilistic models can be represented much more compactly using aggregation operations such as counting. While traditional statistical relational representations share factors across sets of interchangeable random variables, representations that explicitly model aggregations also exploit interchangeability of random variables within factors. This is especially useful in decision making settings, where an agent might need to reason about counts of the different types of objects it interacts with. Previous work on counting formulas in statistical relational representations has mostly focused on the problem of exact inference on an existing model. The problem of learning such models is largely unexplored. In this paper, we introduce Counting Markov Logic Networks (C-MLNs), an extension of Markov logic networks that can compactly represent complex counting formulas. We present a structure learning algorithm for C-MLNs; we apply this algorithm to the novel problem of generalizing natural language instructions, and to relational reinforcement learning in the Crossblock domain, in which standard MLN learning algorithms fail to find any useful structure. The C-MLN policies learned from natural language instructions are compact and intuitive, and, despite requiring no instructions on test games, win 20% more Crossblock games than a state-of-the-art algorithm for following natural language instructions.

Goal Recognition with Markov Logic Networks for Player-Adaptive Games

Goal recognition in digital games involves inferring players’ goals from observed sequences of low-level player actions. Goal recognition models support player-adaptive digital games, which dynamically augment game events in response to player choices for a range of applications, including entertainment, training, and education. However, digital games pose significant challenges for goal recognition, such as exploratory actions and ill-defined goals. This paper presents a goal recognition framework based on Markov logic networks (MLNs). The model’s parameters are directly learned from a corpus that was collected from player interactions with a non-linear educational game. An empirical evaluation demonstrates that the MLN goal recognition framework accurately predicts players’ goals in a game environment with exploratory actions and ill-defined goals.