This paper is mainly concerned with the relation-algebraical aspects of the well-known Region Connection Calculus (RCC). We show that the contact relation algebra (CRA) of certain RCC model is not atomic complete and hence infinite. So in general an extensional composition table for the RCC cannot be obtained by simply refining the RCC8 relations. After having shown that each RCC model is a consistent model of the RCC11 CT, we give an exhaustive investigation about extensional interpretation of the RCC11 CT. More important, we show the complemented closed disk algebra is a representation for the relation algebra determined by the RCC11 table. The domain of this algebra contains two classes of regions, the closed disks and closures of their complements in the real plane.
The logic of nulls in databases has been subject of investigation since their introduction in Codd's Relational Model, which is the foundation of the SQL standard. We show a logical characterisation of a first-order fragment of SQL with null values, by first focussing on a simple extension with null values of standard relational algebra, which captures exactly the SQL fragment, and then proposing two different domain relational calculi, in which the null value is a term of the language but it does not appear as an element of the semantic interpretation domain of the logics. In one calculus, a …
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules, provided the considered consequences are built on a given finite set of ground terms, represented by constant symbols. In contrast to other approaches, most existing results about the termination of the superposition calculus can be carried over to our procedure. This ensures in particular that the calculus is terminating for many theories of interest to the SMT c…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present…
CETINIA Universidad Rey Juan Carlos（胡安卡洛斯国王大学CETINIA）；IMDEA Software Institute（IMDEA软件研究所）；Universidad Politécnica de Madrid（马德里理工大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
Automated commonsense reasoning is essential for building human-like AI systems featuring, for example, explainable AI. Event Calculus (EC) is a family of formalisms that model commonsense reasoning with a sound, logical basis. Previous attempts to mechanize reasoning using EC faced difficulties in the treatment of the continuous change in dense domains (e.g., time and other physical quantities), constraints among variables, default negation, and the uniform application of different inference methods, among others. We propose the use of s(CASP), a query-driven, top-down execution model for Pre…
Institute of Information Systems, University of Lübeck（吕贝克大学信息系统研究所）
Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (TAMe), which incorporates (i) clustering for grouping submodels as well as (ii) statistical significance checks to test the fitness of the clustering outcome. In exchange for faster runtimes, TAMe introduces a bounded error that becomes negligible over time. Empirical results show that TAMe significantly improves the runtime performance of in…
Reinforcement learning (RL) agents are often designed specifically for a particular problem and they generally have uninterpretable working processes. Statistical methods-based agent algorithms can be improved in terms of generalizability and interpretability using symbolic Artificial Intelligence (AI) tools such as logic programming. In this study, we present a model-free RL architecture that is supported with explicit relational representations of the environmental objects. For the first time, we use the PrediNet network architecture in a dynamic decision-making problem rather than image-bas…
We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard transformations, our calculus extends to SROIQ, which covers all of OWL 2 DL except for datatypes. A key feature of our calculus is its pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the full logic.
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an instantiation of a relational causal model; however, causal reasoning over such instantiation requires additional templating assumptions that capture feedback loops of influence. Previous research has developed lifted representations to address the relational nature of such dynamics but has strictly required that the representation has no cycles. To facilitate cycles…
Technical University of Denmark（丹麦技术大学）；Tradeshift；DeepMind
This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational network, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]'s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the a…
University of Alberta（阿尔伯塔大学）；Université de Montréal（蒙特利尔大学）；Mila（米拉人工智能研究所）；Huawei Kirin Solution（华为麒麟解决方案部门）
Systematicity, i.e., the ability to recombine known parts and rules to form new sequences while reasoning over relational data, is critical to machine intelligence. A model with strong systematicity is able to train on small-scale tasks and generalize to large-scale tasks. In this paper, we propose R5, a relational reasoning framework based on reinforcement learning that reasons over relational graph data and explicitly mines underlying compositional logical rules from observations. R5 has strong systematicity and being robust to noisy data. It consists of a policy value network equipped with …
Reasoning-Oriented and Analogy-Based Methods for Locating and Editing in Zero-Shot Event-Relational Reasoning
School of Computer Science and Technology, Dalian University of Technology（大连理工大学计算机科学与技术学院）；School of Computer Science and Technology, Beijing Institute of Technology（北京理工大学计算机科学与技术学院）；School of Computer Science and Artificial Intelligence, Liaoning Normal University（辽宁师范大学计算机与人工智能学院）
本文提出 ROLE 和 ABLE 两种定位与编辑方法，分别通过定位语言模型关键模块和利用任务间类比关系，高效提升零样本事件关系推理的可解释性与性能。
Mila（米拉研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）；Facebook AI Research (FAIR)（脸书人工智能研究院）；Samsung Advanced Institute of Technology (SAIT)（三星综合技术院）
Neural networks for natural language reasoning have largely focused on extractive, fact-based question-answering (QA) and common-sense inference. However, it is also crucial to understand the extent to which neural networks can perform relational reasoning and combinatorial generalization from natural language---abilities that are often obscured by annotation artifacts and the dominance of language modeling in standard QA benchmarks. In this work, we present a novel benchmark dataset for language understanding that isolates performance on relational reasoning. We also present a neural message-…
Reasoning on the knowledge graph (KG) aims to infer new facts from existing ones. Methods based on the relational path have shown strong, interpretable, and transferable reasoning ability. However, paths are naturally limited in capturing local evidence in graphs. In this paper, we introduce a novel relational structure, i.e., relational directed graph (r-digraph), which is composed of overlapped relational paths, to capture the KG's local evidence. Since the r- digraphs are more complex than paths, how to efficiently construct and effectively learn from them are challenging. Directly encoding…
We investigate the composability of soft-rules learned by relational neural architectures when operating over object-centric (slot-based) representations, under a variety of sparsity-inducing constraints. We find that increasing sparsity, especially on features, improves the performance of some models and leads to simpler relations. Additionally, we observe that object-centric representations can be detrimental when not all objects are fully captured; a failure mode to which CNNs are less prone. These findings demonstrate the trade-offs between interpretability and performance, even for models…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence of our proposal is to lift Codd's relational algebra from operations on relational tables to operations on classes of structures (with recursion), and to add a direction of information propagation. We observe the presence of information propagation in several formalisms for efficient reasoning and use it to express unary negation and operations used in grap…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a probabilistic logic with truth functional connectives. We propose an alternative mechanism, Incidence Calculus, which is based on a representation of uncertainty using sets of points, which might represent situations, models or possible worlds. Incidence Calculus does provide a probabilistic logic with truth functional connectives.
KU Leuven（鲁汶大学）；ETH Zurich（苏黎世联邦理工学院）；Cardiff University（卡迪夫大学）
We consider the problem of predicting plausible missing facts in relational data, given a set of imperfect logical rules. In particular, our aim is to provide bounds on the (expected) number of incorrect inferences that are made in this way. Since for classical inference it is in general impossible to bound this number in a non-trivial way, we consider two inference relations that weaken, but remain close in spirit to classical inference.
Are Large Language Models Capable of Deep Relational Reasoning? Insights from DeepSeek-R1 and Benchmark Comparisons
School of Professional Education and Executive Development（专业教育与执行发展学院）；The Hong Kong Polytechnic University（香港理工大学）；School of Mathematics and Statistics（数学与统计学学院）；Beijing Institute of Technology（北京理工大学）；Department of Mathematics（数学系）；The University of Hong Kong（香港大学）
Institute for Artificial Intelligence（人工智能研究所）；University of Bremen（不来梅大学）
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the reasons for this explosion is that so far the approaches do not sufficiently exploit the structure and similarity of possible worlds in order to encode the models more compactly. We propose fuzzy inference in Markov logic networks, which enables the use of taxonomic knowledge as a source of imposing structure onto possible worlds. We show that by exploiting this…
Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding
Australian Artificial Intelligence Institute (AAII)（澳大利亚人工智能研究所）；University of Technology Sydney（悉尼科技大学）；Centre for Frontier AI Research, A*STAR（新加坡科技研究局前沿人工智能研究中心）
Method for the semantic indexing of concept hierarchies, uniform representation, use of relational database systems and generic and case-based reasoning
TU Dresden（德累斯顿工业大学）；Frauenhofer Institut für Intelligente Analyse und Informationssysteme IAIS（弗劳恩霍夫智能分析与信息系统研究所IAIS）
Temporal Fact Reasoning over Hyper-Relational Knowledge Graphs
LMU Munich（慕尼黑大学）；University of Cambridge（剑桥大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Stuttgart（斯图加特大学）；Technical University of Munich（慕尼黑工业大学）
The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We f…
LLM-Guided Semantic Relational Reasoning for Multimodal Intent Recognition
Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；School of Information Science and Engineering, Hebei University of Science and Technology（河北科技大学信息科学与工程学院）
Artificial Intelligence Research Laboratory（人工智能研究实验室）；College of Information Sciences and Technology（信息科学与技术学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Maier et al. (2010) introduced the relational causal model (RCM) for representing and inferring causal relationships in relational data. A lifted representation, called abstract ground graph (AGG), plays a central role in reasoning with and learning of RCM. The correctness of the algorithm proposed by Maier et al. (2013a) for learning RCM from data relies on the soundness and completeness of AGG for relational d-separation to reduce the learning of an RCM to learning of an AGG. We revisit the definition of AGG and show that AGG, as defined in Maier et al. (2013b), does not correctly abstract a…
University of Florence（佛罗伦萨大学）；University of Siena（锡耶纳大学）
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these rea…
University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and probability allows us to further quantify the weight and ratio of the worlds that must satisfy a property. To that end, numerous developments have been undertaken, culminating in proposals such as probabilistic relational models. While this progress has been notable, a general-purpose first-order knowledge representation language to reason about probabilities and dyna…
University of Cambridge（剑桥大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Multihop Question Answering is a complex Natural Language Processing task that requires multiple steps of reasoning to find the correct answer to a given question. Previous research has explored the use of models based on Graph Neural Networks for tackling this task. Various architectures have been proposed, including Relational Graph Convolutional Networks (RGCN). For these many node types and relations between them have been introduced, such as simple entity co-occurrences, modelling coreferences, or "reasoning paths" from questions to answers via intermediary entities. Nevertheless, a thoug…
Institute of Computer Science FO.R.T.H.（希腊研究与技术基金会计算机科学研究所）；Lissi Laboratory Paris-Est Créteil Val-de-Marne University (UPEC)（巴黎东大克雷泰伊马恩河谷大学Lissi实验室）
Action languages have emerged as an important field of Knowledge Representation for reasoning about change and causality in dynamic domains. This article presents Cerbere, a production system designed to perform online causal, temporal and epistemic reasoning based on the Event Calculus. The framework implements the declarative semantics of the underlying logic theories in a forward-chaining rule-based reasoning system, coupling the high expressiveness of its formalisms with the efficiency of rule-based systems. To illustrate its applicability, we present both the modeling of benchmark problem…
Analogical reasoning has been a principal focus of various waves of AI research. Analogy is particularly challenging for machines because it requires relational structures to be represented such that they can be flexibly applied across diverse domains of experience. Here, we study how analogical reasoning can be induced in neural networks that learn to perceive and reason about raw visual data. We find that the critical factor for inducing such a capacity is not an elaborate architecture, but rather, careful attention to the choice of data and the manner in which it is presented to the model. …
UCLA Center for Vision, Cognition, Learning and Autonomy（加州大学洛杉矶分校视觉、认知、学习与自主性中心）；International Center for AI and Robot Autonomy (CARA)（人工智能与机器人自主性国际中心（CARA））
Dramatic progress has been witnessed in basic vision tasks involving low-level perception, such as object recognition, detection, and tracking. Unfortunately, there is still an enormous performance gap between artificial vision systems and human intelligence in terms of higher-level vision problems, especially ones involving reasoning. Earlier attempts in equipping machines with high-level reasoning have hovered around Visual Question Answering (VQA), one typical task associating vision and language understanding. In this work, we propose a new dataset, built in the context of Raven's Progress…
Binding operation is fundamental to many cognitive processes, such as cognitive map formation, relational reasoning, and language comprehension. In these processes, two different modalities, such as location and objects, events and their contextual cues, and words and their roles, need to be bound together, but little is known about the underlying neural mechanisms. Previous works introduced a binding model based on quadratic functions of bound pairs, followed by vector summation of multiple pairs. Based on this framework, we address following questions: Which classes of quadratic matrices are…
Stanford University（斯坦福大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；University of California, Berkeley（加州大学伯克利分校）
While the modeling of pair-wise relations has been widely studied in multi-agent interacting systems, its ability to capture higher-level and larger-scale group-wise activities is limited. In this paper, we propose a group-aware relational reasoning approach (named EvolveHypergraph) with explicit inference of the underlying dynamically evolving relational structures, and we demonstrate its effectiveness for multi-agent trajectory prediction. In addition to the edges between a pair of nodes (i.e., agents), we propose to infer hyperedges that adaptively connect multiple nodes to enable group-awa…
Generalization of CNNs on Relational Reasoning with Bar Charts
School of Computer Science and Technology, Shandong University（山东大学计算机科学与技术学院）；State Key Lab of CAD&CG, Zhejiang University（浙江大学CAD&CG国家重点实验室）；School of Information, Renmin University of China（中国人民大学信息学院）；College of Science and Mathematics, University of Massachusetts Boston（马萨诸塞大学波士顿分校科学与数学学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）
UCLA（加州大学洛杉矶分校）；Stanford University（斯坦福大学）；MIT BCS, CBMM, CSAIL（麻省理工学院脑与认知科学系、心智/大脑/机器研究中心、计算机科学与人工智能实验室）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
A critical aspect of human visual perception is the ability to parse visual scenes into individual objects and further into object parts, forming part-whole hierarchies. Such composite structures could induce a rich set of semantic concepts and relations, thus playing an important role in the interpretation and organization of visual signals as well as for the generalization of visual perception and reasoning. However, existing visual reasoning benchmarks mostly focus on objects rather than parts. Visual reasoning based on the full part-whole hierarchy is much more challenging than object-cent…
Neural Structural Reasoner: A Brain-inspired Architecture for Reasoning over Structured Knowledge
Chinese Institute for Brain Research, Beijing（北京脑科学与类脑研究中心）；Beijing Key Laboratory of Brain Science and Brain-Machine Interface（北京脑科学与脑机接口重点实验室）；Sun Yat-sen University（中山大学）
Institute of Informatics, UFRGS（UFRGS信息学院）；City, University of London（伦敦大学城市学院）
The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of the key challenges in this direction, as neural learning and symbolic reasoning offer complementary characteristics that can benefit the development of AI systems. Relational labelling or link prediction on knowledge graphs has become one of the main problems in deep learning-based natural language processing research. Moreover, other fields which make use of …
Transfer learning has become the de facto standard in computer vision and natural language processing, especially where labeled data is scarce. Accuracy can be significantly improved by using pre-trained models and subsequent fine-tuning. In visual reasoning tasks, such as image question answering, transfer learning is more complex. In addition to transferring the capability to recognize visual features, we also expect to transfer the system's ability to reason. Moreover, for video data, temporal reasoning adds another dimension. In this work, we formalize these unique aspects of transfer lear…
Reasoning about visual relationships is central to how humans interpret the visual world. This task remains challenging for current deep learning algorithms since it requires addressing three key technical problems jointly: 1) identifying object entities and their properties, 2) inferring semantic relations between pairs of entities, and 3) generalizing to novel object-relation combinations, i.e., systematic generalization. In this work, we use vision transformers (ViTs) as our base model for visual reasoning and make better use of concepts defined as object entities and their relations to imp…
Applied AI Lab, University of Oxford（牛津大学应用人工智能实验室）
The majority of contemporary object-tracking approaches do not model interactions between objects. This contrasts with the fact that objects' paths are not independent: a cyclist might abruptly deviate from a previously planned trajectory in order to avoid colliding with a car. Building upon HART, a neural class-agnostic single-object tracker, we introduce a multi-object tracking method MOHART capable of relational reasoning. Importantly, the entire system, including the understanding of interactions and relations between objects, is class-agnostic and learned simultaneously in an end-to-end f…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization …
