Symbolic Rules Research Articles

A small team as an effective group and center of leadership

Building an ideal small team capable of solving problems that are beyond the capacity of an ordinary group of specialists is a long and exhausting process. This article presents the ability to work in a small team as the most valuable personality trait. Describing the small team philosophy as highly effective, the author of the article presents it as a reference model of gifted and talented individuals, a well-coordinated combat unit, a special centre of leadership, flexibility and psychological compatibility. Revealing the effectiveness of a small team in the symbolic range of two images of “Simplicity”-“Complexity”, the author derives the symbolic rule of “Simplicity”: the effectiveness of success is rooted in the ability to work only with small teams of smart people. It is proved that as soon as the number of people in a team increases, “Complexity” is automatically introduced. The article also describes the philosophy of a two-person team. It is proved how much more effective, constructive and motivated it can be compared to a large team. It is highlighted that the key to the success of a two-person team is the holistic dominance of five components: 1) psychological safety; 2) reliability; 3) structure and clarity; 4) awareness; 5) influence. It is found out that a small team is a homogeneous combat unit, since it is designed to promote the origination of a new, emergent mind, the need for which increases significantly in the conditions of high danger, constant change and uncertainty. The author emphasises that the coordinated work of a small team in a dangerous environment requires rapid adaptability, constant reassessment of the situation, discussion and coordination. In such a team, its members, sending signals to each other every minute, decoding the responses, should understand every step and intention of their partner, as this is the key to life and victory.

From explanation to intervention: Interactive knowledge extraction from Convolutional Neural Networks used in radiology.

Deep Learning models such as Convolutional Neural Networks (CNNs) are very effective at extracting complex image features from medical X-rays. However, the limited interpretability of CNNs has hampered their deployment in medical settings as they failed to gain trust among clinicians. In this work, we propose an interactive framework to allow clinicians to ask what-if questions and intervene in the decisions of a CNN, with the aim of increasing trust in the system. The framework translates a layer of a trained CNN into a measurable and compact set of symbolic rules. Expert interactions with visualizations of the rules promote the use of clinically-relevant CNN kernels and attach meaning to the rules. The definition and relevance of the kernels are supported by radiomics analyses and permutation evaluations, respectively. CNN kernels that do not have a clinically-meaningful interpretation are removed without affecting model performance. By allowing clinicians to evaluate the impact of adding or removing kernels from the rule set, our approach produces an interpretable refinement of the data-driven CNN in alignment with medical best practice.

Learning distributed representations of knowledge that preserve deductive reasoning

Deep neural networks have shown promise in various fields including image processing, natural language processing and speech processing. Despite their proven usefulness in both theory and empirical studies, significant difficulties in their application still persist. More specifically, enabling deep neural networks to reason over data for knowledge acquisition is arguably challenging. Neural networks have the ability to learn patterns and generalize over data but often lack model interpretability, i.e., it is not always clear how they reason over data. Enabling neural networks to symbolically reason is one way to bring explainability and improve knowledge acquisition. In this paper, we introduce a Deduction-Preserved Embedding (DPE) model designed to learn a distributed representation that integrates symbolic deductive reasoning. Our approach effectively incorporates symbolic rules, resulting in enhanced link prediction performance for knowledge graph completion. Our experimental results highlight that the proposed model consistently outperforms baseline methods, demonstrating superior overall performance despite having a relatively small number of parameters. Notably, the version of the model that incorporates symbolic rules surpasses the majority of compared models, particularly in scenarios characterized by data sparsity.

The right superior temporal gyrus plays a role in semantic-rule learning: Evidence supporting a reinforcement learning model

In real-life communication, individuals use language that carries evident rewarding and punishing elements, such as praise and criticism. A common trend is to seek more praise while avoiding criticism. Furthermore, semantics is crucial for conveying information, but such semantic access to native and foreign languages is subtly distinct. To investigate how rule learning occurs in different languages and to highlight the importance of semantics in this process, we investigated both verbal and non-verbal rule learning in first (L1) and second (L2) languages using a reinforcement learning framework, including a semantic rule and a color rule. Our computational modeling on behavioral and brain imaging data revealed that individuals may be more motivated to learn and adhere to rules in an L1 compared to L2, with greater striatum activation during the outcome phase in the L1. Additionally, results on the learning rates and inverse temperature in the two rule learning tasks showed that individuals tend to be conservative and are reluctant to change their judgments regarding rule learning of semantic information. Moreover, the greater the prediction errors, the greater activation of the right superior temporal gyrus in the semantic-rule learning condition, demonstrating that such learning has differential neural correlates than symbolic rule learning. Overall, the findings provide insight into the neural mechanisms underlying rule learning in different languages, and indicate that rule learning involving verbal semantics is not a general symbolic learning that resembles a conditioned stimulus-response, but rather has its own specific characteristics.

The Iconic-Symbolic Spectrum

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures.

Cornet: Learning Spreadsheet Formatting Rules by Example

Data management and analysis tasks are often carried out using spreadsheet software. A popular feature in most spreadsheet platforms is the ability to define data-dependent formatting rules. These rules can express actions such as "color red all entries in a column that are negative" or "bold all rows not containing error or failure". Unfortunately, users who want to exercise this functionality need to manually write these conditional formatting (CF) rules. We introduce Cornet, a system that automatically learns such conditional formatting rules from user examples. Cornet takes inspiration from inductive program synthesis and combines symbolic rule enumeration, based on semi-supervised clustering and iterative decision tree learning, with a neural ranker to produce accurate conditional formatting rules. In this demonstration, we show Cornet in action as a simple add-in to Microsoft's Excel. After the user provides one or two formatted cells as examples, Cornet generates formatting rule suggestions for the user to apply to the spreadsheet.

Cornet: Learning Table Formatting Rules By Example

Spreadsheets are widely used for table manipulation and presentation. Stylistic formatting of these tables is an important property for presentation and analysis. As a result, popular spreadsheet software, such as Excel, supports automatically formatting tables based on rules. Unfortunately, writing such formatting rules can be challenging for users as it requires knowledge of the underlying rule language and data logic. We present Cornet, a system that tackles the novel problem of automatically learning such formatting rules from user-provided formatted cells. Cornet takes inspiration from advances in inductive programming and combines symbolic rule enumeration with a neural ranker to learn conditional formatting rules. To motivate and evaluate our approach, we extracted tables with over 450K unique formatting rules from a corpus of over 1.8M real worksheets. Since we are the first to introduce the task of automatically learning conditional formatting rules, we compare Cornet to a wide range of symbolic and neural baselines adapted from related domains. Our results show that Cornet accurately learns rules across varying setups. Additionally, we show that in some cases Cornet can find rules that are shorter than those written by users and can also discover rules in spreadsheets that users have manually formatted. Furthermore, we present two case studies investigating the generality of our approach by extending Cornet to related data tasks (e.g., filtering) and generalizing to conditional formatting over multiple columns.

Relating relational networks: An initial experimental analysis.

Studying relating of relational networks is a complex and challenging task. The main objective of the present study was to demonstrate relating within and across relational networks based on same/opposite and bigger/smaller contextual cues and establish antecedent control. After nonarbitrary pretraining of the contextual cues, two nonsense stimulus classes were established based on comparative relations. Participants were trained to select stimuli from an array of options based on a symbolic rule that established a relation between two stimuli: one of Network 1 and one of Network 2. Training involved relating Network 1 to Network 2, and testing assessed relating Network 2 to Network 1. Seven of eight participants reached the mastery criterion in training and responded accordingly in test. In a final stage, reinforcing and punishing consequences were varied systematically in the presence of two novel stimuli and antecedent control was observed for all 7 participants. Experiment 2 replicated the results of Experiment 1 but using contextual cues taken from natural language, and Experiment 3 sought to understand the effects of pretraining relational responding using natural language. The mastery criteria were reached by four of seven participants in Experiment 2 and by all eight participants in Experiment 3. Future studies could develop and refine the methods employed here in analyzing the relating of relational networks, thus allowing for an increasingly sophisticated behavior-analytic account of human language and cognition.

Symbolic knowledge extraction for explainable nutritional recommenders

Background and objective:This paper focuses on nutritional recommendation systems (RS), i.e. AI-powered automatic systems providing users with suggestions about what to eat to pursue their weight/body shape goals. A trade-off among (potentially) conflictual requirements must be taken into account when designing these kinds of systems, there including: (i) adherence to experts’ prescriptions, (ii) adherence to users’ tastes and preferences, (iii) explainability of the whole recommendation process. Accordingly, in this paper we propose a novel approach to the engineering of nutritional RS, combining machine learning and symbolic knowledge extraction to profile users—hence harmonising the aforementioned requirements.MethodsOur contribution focuses on the data processing workflow. Stemming from neural networks (NN) trained to predict user preferences, we use CART Breiman et al.(1984) to extract symbolic rules in Prolog Körner et al.(2022) form, and we combine them with expert prescriptions brought in similar form. We can then query the resulting symbolic knowledge base via logic solvers, to draw explainable recommendations.ResultsExperiments are performed involving a publicly available dataset of 45,723 recipes, plus 12 synthetic datasets about as many imaginary users, and 6 experts’ prescriptions. Fully-connected 4-layered NN are trained on those datasets, reaching ∼86% test-set accuracy, on average. Extracted rules, in turn, have ∼80% fidelity w.r.t. those NN. The resulting recommendation system has a test-set precision of ∼74%. The symbolic approach makes it possible to devise how the system draws recommendations.ConclusionsThanks to our approach, intelligent agents may learn users’ preferences from data, convert them into symbolic form, and extend them with experts’ goal-directed prescriptions. The resulting recommendations are then simultaneously acceptable for the end user and adequate under a nutritional perspective, while the whole process of recommendation generation is made explainable.

An End-to-End Natural Language Processing System for Automatically Extracting Radiation Therapy Events From Clinical Texts

Real-world evidence for radiation therapy (RT) is limited because it is often documented only in the clinical narrative. We developed a natural language processing system for automated extraction of detailed RT events from text to support clinical phenotyping. A multi-institutional data set of 96 clinician notes, 129 North American Association of Central Cancer Registries cancer abstracts, and 270 RT prescriptions from HemOnc.org was used and divided into train, development, and test sets. Documents were annotated for RT events and associated properties: dose, fraction frequency, fraction number, date, treatment site, and boost. Named entity recognition models for properties were developed by fine-tuning BioClinicalBERT and RoBERTa transformer models. A multiclass RoBERTa-based relation extraction model was developed to link each dose mention with each property in the same event. Models were combined with symbolic rules to create a hybrid end-to-end pipeline for comprehensive RT event extraction. Named entity recognition models were evaluated on the held-out test set with F1 results of 0.96, 0.88, 0.94, 0.88, 0.67, and 0.94 for dose, fraction frequency, fraction number, date, treatment site, and boost, respectively. The relation model achieved an average F1 of 0.86 when the input was gold-labeled entities. The end-to-end system F1 result was 0.81. The end-to-end system performed best on North American Association of Central Cancer Registries abstracts (average F1 0.90), which are mostly copy-paste content from clinician notes. We developed methods and a hybrid end-to-end system for RT event extraction, which is the first natural language processing system for this task. This system provides proof-of-concept for real-world RT data collection for research and is promising for the potential of natural language processing methods to support clinical care.

Low PAPR channel estimation for OTFS with scattered superimposed pilots

Orthogonal time frequency space (OTFS) modulation has been proven to be superior to traditional orthogonal frequency division multiplexing (OFDM) systems in high-speed communication scenarios. However, the existing channel estimation schemes may results in poor peak to average power ratio (PAPR) performance of OTFS system or low spectrum efficiency. Hence, in this paper, we propose a low PAPR channel estimation scheme with high spectrum efficiency. Specifically, we design a multiple scattered pilot pattern, where multiple low power pilot symbols are superimposed with data symbols in delay-Doppler domain. Furthermore, we propose the placement rules for pilot symbols, which can guarantee the low PAPR. Moreover, the data aided iterative channel estimation was invoked, where joint channel estimation is proposed by exploiting multiple independent received signals instead of only one received signal in the existing scheme, which can mitigate the interference imposed by data symbols for channel estimation. Simulation results shows that the proposed multiple scattered pilot aided channel estimation scheme can significantly reduce the PAPR while keeping the high spectrum efficiency.

Curiously exploring affordance spaces of a pouring task

AbstractHuman beings and other biological agents appear driven by curiosity to explore the affordances of their environments. Such exploration is its own reward – children have fun when playing – but it probably also serves the practical purpose of learning theories with which to predict outcomes of actions. Cognitive robots however have yet to match the performance of human beings at learning and reusing manipulation skills. In this paper, we implement a method that emulates the curiosity drive and uses it as a heuristic to guide (simulated) exploration of a particular task – pouring liquids. The result of this exploration is a collection of symbolic rules linking qualitative descriptions of object arrangements and the pouring action with qualitative descriptions of likely outcomes. The manner in which qualitative descriptions of object arrangements and actions are converted to numerical descriptions for the purpose of simulation parametrization is via probability distributions, which themselves are adjusted in the process of simulated exploration. This allows the grounding of the symbolic descriptions to attempt to adapt itself to the task. The resulting symbolic rules form a theory that, together with the probability distributions that ground it in numerical parametrizations, is intended to be used to predict qualitative outcomes or select manners of pouring towards achieving a goal.

Algorithms of adaptation in inductive inference

We investigate the idea that human concept inference utilizes local adaptive search within a compositional mental theory space. To explore this, we study human judgments in a challenging task that involves actively gathering evidence about a symbolic rule governing the behavior of a simulated environment. Participants learn by performing mini-experiments before making generalizations and explicit guesses about a hidden rule. They then collect additional evidence themselves (Experiment 1) or observe evidence gathered by someone else (Experiment 2) before revising their own generalizations and guesses. In each case, we focus on the relationship between participants’ initial and revised guesses about the hidden rule concept. We find an order effect whereby revised guesses are anchored to idiosyncratic elements of the earlier guess. To explain this pattern, we develop a family of process accounts that combine program induction ideas with local (MCMC-like) adaptation mechanisms. A particularly local variant of this adaptive account captures participants’ hypothesis revisions better than a range of alternative explanations. We take this as suggestive that people deal with the inherent complexity of concept inference partly through use of local adaptive search in a latent compositional theory space.

Investigating the Reconfiguration of Internationalization Strategies under Digitalization

Digitalization can induce the structural changes of multinational enterprises (MNEs), therefore, it is important to reconsider their internal organization. In this paper, the changes in the roles of the subsidiaries of MNEs due to digitalization was investigated. By adopting the internalization theory perspective, the local organizations, including the market demand, the digital technology, infrastructure platform, the institutional systems of the host country, including the legitimacy, substantial institutions, and symbolic rules, in contributing to the changes in the role of subsidiaries was also illustrate in this paper. Additionally, the implications of the framework on entry mode, knowledge transfer and other research issues was also discussed in this paper.

A Danish case study of a sociomaterial construction of a new nomos and purpose of higher education

This article combines Bourdieusian practice with narrative sociomaterial theory to investigate what story of higher education and its purpose is being conveyed to students. Our case study revolves around a Danish university. We conduct a sociomaterial analysis of three university sites: an information day for prospective students, a video of a campus tour, and on-campus signage. We subject photographs of these data and the transcribed video to a sociomaterial analysis of how material objects and human subjects are socially positioned. We find that sociomateriality constructs two conflicting narratives about the purpose of higher education. High school graduates are courted with a narrative of an educational, person-centric, and knowledge-centric journey that will safely lead to favorable professional positions. Upon enrollment a changed, market-centered narrative envisions students as soon-to-be business assets who must self-optimize to forge a career. Both narratives remain at the stage of ante-narrative as they do not provide an ending: while the person-centric narrative is replaced upon enrollment, the business-centric narrative reduces university experiences to the “start” of the students’ career. On a sociopolitical level, our case is indicative of the trend of higher education adjusting its symbolic rules to business parameters and thus handing over relative autonomy to the economic field. Moreover, our study entails implications for theory in that it brings together Bourdieusian and Bojean (ante)narrative theory and conceptualizes dominant narratives as nomos. The paper further offers ideas on how to document and analyze data for researchers taking a sociomaterial approach.

Hybrid Knowledge Extraction Framework Using Modified Adaptive Genetic Algorithm and BPNN

Fault diagnosis based on the expert system (ES) is still a research topic of manufacturing in the Industry 4.0 because of the stronger interpretability. As the core component of the ES, fault diagnosis accuracy is positively correlated to the precise of the knowledge base. But it is difficult for users to understand the knowledge obtained from the original dataset utilizing the existing knowledge extraction method. Therefore, it is of great significance to extract easy-to-understand and exact rules from the NN framework. This paper proposes a hybrid extraction framework to perform the rule extraction for overcoming this drawback. First, an improved adaptive genetic algorithm (GA) using a logistic function, namely LAGA, is proposed to solve the traditional GA’s insufficient prediction performance issue. Compared with the other three mainstream adaptive GAs, the experiment results of optimizing six selected test functions by these GA variants show that the LAGA algorithm’s convergence accuracy and speed have been greatly improved, especially for high latitude functions. On this basis, a rule extraction method based on symbol rule and NN, namely the LAGA-BP framework, is discussed in this manuscript to classify the real-valued attributes. This framework obtains hidden knowledge (knowledge refinement process) by NN and further transforms the acquired hidden knowledge into more easy-to-understand rule knowledge (rule extraction process). The execution of the LAGA-BP framework could be separated into two phases. The first phase is to optimize a back propagation NN (BPNN) using the LAGA and refine prediction classification knowledge over the optimized BPNN. In the second phase, an attribute reduction algorithm using multi-layered NN (SD algorithm) based on two different superposed networks is used on this framework to reduce data-set attributes and then uses the K-means clustering algorithm to extract the if-then rule from the simplified attributes. the Wisconsin breast cancer data-set is used as a case study to reveal the correctness and robustness of the proposed LAGA-BP method. Consulting relevant medical personnel and referencing relevant data shows that the rules extracted using this method help verify the diagnosis results, thus verifying the proposed framework’s feasibility and practicality.

Nessy: A Neuro-Symbolic System for Label Noise Reduction

Noisy labels represent one of the key issues in supervised machine learning. Existing work for label noise reduction mainly takes a probabilistic approach that infers true labels from data distributions in low-level feature spaces. Such an approach is not only limited by its capability to learn high-quality data representations, but also by the low predictive power of data distributions in inferring true classes. To address those problems, we introduce Nessy, a neuro-symbolic system that integrates deep probabilistic modeling and symbolic knowledge for label noise reduction. Our deep probabilistic model infers the true classes of data instances with noisy labels by exploiting data distributions in an underlying latent feature representation space. For data instances where inference is not reliable enough, Nessy extracts symbolic rules and ranks them according to several utility metrics. Top-ranking rules are injected into the deep probabilistic model via expectation regularization, i.e., via a posterior regularization term constraining the class distribution in the objective function. In a real deployment over multiple relation extraction tasks, we demonstrate that Nessy is able to significantly improve the state of the art, by 7% accuracy and 10.7% AUC on average.

Symbolic dynamical scales: modes, orbitals, and transversals

We study classes of musical scales obtained from shift spaces in symbolic dynamics through the first symbol rule, which yields scales in any n-TET tuning system. The modes are thought as elements of orbit equivalence classes of cyclic shift actions on languages, and we study their orbitals and transversals. We present explicit formulations of the generating functions that allow us to deduce the orbital and transversal dimensions of classes of musical scales generated by vertex shifts, for all n, in particular for the 12-TET tuning system.

Neural Sequence-to-grid Module for Learning Symbolic Rules

Logical reasoning tasks over symbols, such as learning arithmetic operations and computer program evaluations, have become challenges to deep learning. In particular, even state-of-the-art neural networks fail to achieve \textit{out-of-distribution} (OOD) generalization of symbolic reasoning tasks, whereas humans can easily extend learned symbolic rules. To resolve this difficulty, we propose a neural sequence-to-grid (seq2grid) module, an input preprocessor that automatically segments and aligns an input sequence into a grid. As our module outputs a grid via a novel differentiable mapping, any neural network structure taking a grid input, such as ResNet or TextCNN, can be jointly trained with our module in an end-to-end fashion. Extensive experiments show that neural networks having our module as an input preprocessor achieve OOD generalization on various arithmetic and algorithmic problems including number sequence prediction problems, algebraic word problems, and computer program evaluation problems while other state-of-the-art sequence transduction models cannot. Moreover, we verify that our module enhances TextCNN to solve the bAbI QA tasks without external memory.

New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions

We present new sum rules for 3jm coefficients, which involve, in addition to the usual weighting factor (2j + 1) where j is an angular momentum, the quantity [j(j + 1)] k with k ⩾ 1. The sum rules appear for instance in the statistical modeling of rotational spectra within the theory of moments, and enable one to deduce the expectation values of r k (used in the theory of Stark effect for hydrogenic ions) in parabolic coordinates from the expectation values of r k in spherical coordinates.