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Journal articles on the topic 'Symbolic rules'

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Published: 3 June 2025

Last updated: 20 July 2025

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1

Cuyt, Annie, Brahim Benouahmane, Hamsapriye, and Irem Yaman. "Symbolic–numeric Gaussian cubature rules." Applied Numerical Mathematics 61, no. 8 (2011): 929–45. http://dx.doi.org/10.1016/j.apnum.2011.03.003.

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2

Hadley, Robert F. "Connectionism, explicit rules, and symbolic manipulation." Minds and Machines 3, no. 2 (1993): 183–200. http://dx.doi.org/10.1007/bf00975531.

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3

Kozaitis, S. P. "Higher-ordered rules for symbolic substitution." Optics Communications 65, no. 5 (1988): 339–42. http://dx.doi.org/10.1016/0030-4018(88)90098-3.

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4

Cleeremans, Axel, and Arnaud Destrebecqz. "Real rules are conscious." Behavioral and Brain Sciences 28, no. 1 (2005): 19–20. http://dx.doi.org/10.1017/s0140525x05280019.

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In general, we agree with Pothos's claim that similarity and rule knowledge are best viewed as situated on the extreme points of a single representational continuum. However, we contend that a distinction can be made between “rule-like” and “rule-based” knowledge: Rule-based, symbolic knowledge is necessarily conscious when it is applied. Awareness thus provides a useful criterion for distinguishing between sensitivity to functional similarity and knowledge of symbolic rules.

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5

Dancs, Michael J., and Tian-Xiao He. "-Analogues of Symbolic Operators." Journal of Discrete Mathematics 2013 (July 14, 2013): 1–6. http://dx.doi.org/10.1155/2013/487546.

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Here presented are -extensions of several linear operators including a novel -analogue of the derivative operator . Some -analogues of the symbolic substitution rules given by He et al., 2007, are obtained. As sample applications, we show how these -substitution rules may be used to construct symbolic summation and series transformation formulas, including -analogues of the classical Euler transformations for accelerating the convergence of alternating series.

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6

Greenberg, Gabriel. "The Iconic-Symbolic Spectrum." Philosophical Review 132, no. 4 (2023): 579–627. http://dx.doi.org/10.1215/00318108-10697558.

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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.

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HATZILYGEROUDIS, I., and J. PRENTZAS. "NEURULES: IMPROVING THE PERFORMANCE OF SYMBOLIC RULES." International Journal on Artificial Intelligence Tools 09, no. 01 (2000): 113–30. http://dx.doi.org/10.1142/s0218213000000094.

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In this paper, we present a method for improving the performance of classical symbolic rules. This is achieved by introducing a type of hybrid rules, called neurules, which integrate neurocomputing into the symbolic framework of production rules. Neurules are produced by converting existing symbolic rules. Each neurule is considered as an adaline unit, where weights are considered as significance factors. Each significance factor represents the significance of the associated condition in drawing the conclusion. A rule is fired when the corresponding adaline output becomes active. This significantly reduces the size of the rule base and, due to a number of heuristics used in the inference process, increases efficiency of the inferences.

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Cheng, C. K., X. Deng, Y. Z. Liao, and S. Z. Yao. "Symbolic layout compaction under conditional design rules." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 11, no. 4 (1992): 475–86. http://dx.doi.org/10.1109/43.125095.

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S.V.S., Ganga Devi. "FUZZY RULE EXTRACTION FOR FRUIT DATA CLASSIFICATION." COMPUSOFT: An International Journal of Advanced Computer Technology 02, no. 12 (2013): 400–403. https://doi.org/10.5281/zenodo.14613549.

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Decision Tree algorithms provide one of the most popular methodologies for symbolic knowledge acquisition. The resulting knowledge, a symbolic Decision Tree along with a simple inference mechanism, has been praised for comprehensibility. The most comprehensible Decision Trees have been designed and then rules are extracted for perfect symbolic data. Over the years, additional methodologies have been investigated and proposed to deal with continuous or multi-valued data and with missing or noisy features. Recently, with the growing popularity of fuzzy representation in Decision Trees are introduced to deal with similar situations. Fuzzy representation bridges the gap between symbolic and non-symbolic data by linking qualitative linguistic terms with quantitative data. In this paper first Fuzzy Decision Tree for Fruit data classification is constructed and then the fuzzy classification rules are extracted. 

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Fujii, Makoto, and Takeshi Furuhashi. "A Rule Discovery by Fuzzy Classifier System Utilizing Symbolic Information." Journal of Advanced Computational Intelligence and Intelligent Informatics 4, no. 1 (2000): 24–30. http://dx.doi.org/10.20965/jaciii.2000.p0024.

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This paper presents a new fuzzy classifier system (FCS) that can discover effective fuzzy rules efficiently. The system incorporates human knowledge in the form of symbolic information, and effectively limits its search space for fuzzy rules by using knowledge. The system also extracts symbolic information from acquired fuzzy rules for efficient exploration of other new fuzzy rules. Simulations are done to demonstrate the feasibility of the proposed method.

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Chakraborty, Manomita. "Symbolic Interpretation of Trained Neural Network Ensembles." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 32, no. 05 (2024): 695–719. http://dx.doi.org/10.1142/s0218488524500168.

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Symbolically representing the knowledge acquired by a neural network is a profound endeavor aimed at illuminating the latent information embedded within the network. The literature offers a multitude of algorithms dedicated to extracting symbolic classification rules from neural networks. While some excel in producing highly accurate rules, others specialize in generating rules that are easily comprehensible. Nevertheless, only a scant few algorithms manage to strike a harmonious balance between comprehensibility and accuracy. One such exemplary technique is the Rule Extraction from Neural Network Using Classified and Misclassified Data (RxNCM) algorithm, which adeptly generates straightforward and precise rules outlining input data ranges with commendable accuracy. This article endeavors to enhance the classification performance of the RxNCM algorithm by leveraging ensemble technique. Ensembles, a burgeoning field, focus on augmenting classifier performance by harnessing the strengths of individual classifiers. Extraction of rules through neural network ensembles is relatively underexplored, this paper bridges the gap by introducing the Rule extraction using Neural Network Ensembles (RENNE) algorithm. RENNE is designed to refine the classification rules derived from the RxNCM algorithm through ensemble strategy. Specifically, RENNE leverages patterns correctly predicted by an ensemble of neural networks during the rule generation process. The efficacy of the algorithm is validated using seven datasets sourced from the UCI repository. The outcomes indicate that the proposed RENNE algorithm outperforms the RxNCM algorithm in terms of performance.

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Seridi, Hamid, Herman Akdag, Rachid Mansouri, and Mohamed Nemissi. "Approximate Reasoning in Supervised Classification Systems." Journal of Advanced Computational Intelligence and Intelligent Informatics 10, no. 4 (2006): 586–93. http://dx.doi.org/10.20965/jaciii.2006.p0586.

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In knowledge-based systems, uncertainty in propositions can be represented by various degrees of belief encoded by numerical or symbolic values. The use of symbolic values is necessary in areas where the exact numerical values associated with a fact are unknown by experts. In this paper we present an expert system of supervised automatic classification based on a symbolic approach. This last is composed of two sub-systems. The first sub-system automatically generates the production rules using training set; the generated rules are accompanied by a symbolic degree of belief which characterizes their classes of memberships. The second is the inference system, which receives in entry the base of rules and the object to classify. Using classical reasoning (Modus Ponens), the inference system provides the membership class of this object with a certain symbolic degree of belief. Methods to evaluate the degree of belief are numerous but they are often tarnished with uncertainty. To appreciate the performances of our symbolic approach, tests are made on the Iris data basis.

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Sathasivam, Saratha. "Applying Different Learning Rules in Neuro-Symbolic Integration." Advanced Materials Research 433-440 (January 2012): 716–20. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.716.

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Pseudo inverse learning rule and new activation unction performance will be evaluated and compared with the primitive learning rule, Hebb rule. Comparisons are made between these three rules to see which rule is better or outperformed other rules in the aspects of computation time, memory and complexity. From the computer simulation that has been carried out, the new activation function performs better than the other two learning methods.

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Cui, Heming, Gang Hu, Jingyue Wu, and Junfeng Yang. "Verifying systems rules using rule-directed symbolic execution." ACM SIGARCH Computer Architecture News 41, no. 1 (2013): 329–42. http://dx.doi.org/10.1145/2490301.2451152.

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Cui, Heming, Gang Hu, Jingyue Wu, and Junfeng Yang. "Verifying systems rules using rule-directed symbolic execution." ACM SIGPLAN Notices 48, no. 4 (2013): 329–42. http://dx.doi.org/10.1145/2499368.2451152.

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Derwing, Bruce L., and Royal Skousen. "Real-Time Morphology: Symbolic Rules or Analogical Networks?" Annual Meeting of the Berkeley Linguistics Society 15 (November 25, 1989): 48. http://dx.doi.org/10.3765/bls.v15i0.1758.

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17

Sen, Prithviraj, Breno W. S. R. de Carvalho, Ryan Riegel, and Alexander Gray. "Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (2022): 8212–19. http://dx.doi.org/10.1609/aaai.v36i8.20795.

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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 a strong connection to classical Boolean logic thus allowing for precise interpretation of learned rules while harboring parameters that can be trained with gradient-based optimization to effectively fit the data. We extend LNNs to induce rules in first-order logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable and can achieve comparable or higher accuracy due to their flexible parameterization.

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Thierry-Mieg, Yann. "Symbolic and Structural Model-Checking." Fundamenta Informaticae 183, no. 3-4 (2022): 319–42. http://dx.doi.org/10.3233/fi-2021-2090.

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Brute-force model-checking consists in exhaustive exploration of the state-space of a Petri net, and meets the dreaded state-space explosion problem. In contrast, this paper shows how to solve model-checking problems using a combination of techniques that stay in complexity proportional to the size of the net structure rather than to the state-space size. We combine an SMT based over-approximation to prove that some behaviors are unfeasible, an under-approximation using memory-less sampling of runs to find witness traces or counter-examples, and a set of structural reduction rules that can simplify both the system and the property. This approach was able to win by a clear margin the model-checking contest 2020 for reachability queries as well as deadlock detection, thus demonstrating the practical effectiveness and general applicability of the system of rules presented in this paper.

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Shreyash, Tambe*, Thakur Bhushan, and Vishwakarma Avnish. "EFFECTIVE DATA MINING USING NEURAL NETWORKS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 4 (2016): 8–13. https://doi.org/10.5281/zenodo.48819.

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Classification is one of the data mining problems receiving great attention recently in the database community. This paper presents an approach to discover symbolic classification rules using neural networks. Neural networks have not been thought suited for data mining because how the classifications were made is not explicitly stated as symbolic rules that are suitable for verification or interpretation by humans. With the proposed approach, concise symbolic rules with high accuracy can be extracted from a neural network. The network is first trained to achieve the required accuracy rate. Redundant connections of the network are then removed by a network pruning algorithm. The activation values of the hidden units in the network are analyzed, and classification rules are generated using the result of this analysis. The effectiveness of the proposed approach is clearly demonstrated by the experimental results on a set of standard data mining test problems. 

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Lafrance, Stéphane. "Symbolic Approach to the Analysis of Security Protocols." JUCS - Journal of Universal Computer Science 10, no. (9) (2004): 1156–98. https://doi.org/10.3217/jucs-010-09-1156.

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The specification and validation of security protocols often requires viewing function calls - like encryption/decryption and the generation of fake messages - explicitly as actions within the process semantics. Following this approach, this paper introduces a symbolic framework based on value-passing processes able to handle symbolic values like fresh nonces, fresh keys, fake addresses and fake messages. The main idea in our approach is to assign to each value-passing process a formula describing the symbolic values conveyed by its semantics. In such symbolic processes, called constrained processes, the formulas are drawn from a logic based on a message algebra equipped with encryption, signature and hashing primitives. The symbolic operational semantics of a constrained process is then established through semantic rules updating formulas by adding restrictions over the symbolic values, as required for the process to evolve. We then prove that the logic required from the semantic rules is decidable. We also define a bisimulation equivalence between constrained processes, this amounts to a generalisation of the standard bisimulation equivalence between (non-symbolic) value-passing processes. Finally, we provide a complete symbolic bisimulation method for constructing the bisimulation between constrained processes.

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Fradejas-García, Ignacio, and Noel B. Salazar. "Mobility rules." Focaal 2024, no. 99 (2024): 1–14. http://dx.doi.org/10.3167/fcl.2024.990101.

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Abstract In this introductory article, we critically analyze which rules govern human mobility and how mobility regulations and codes are resisted, transgressed, broken, and remade. To play by the rules of mobility means to follow habits and laws governed by social norms and institutional control. Our point of departure is that social and institutional mobility rules both abound and are intertwined and that they are routinely disputed by individuals, groups, and institutions. Drawing on ethnographic examples and the literature on legal anthropology, mobilities, and transnational migration, the article disentangles the specific mechanisms, principles, and symbolic power of mobility rules—written and non-written, legal and non-legal, formal and informal, codified and non-codified, explicit and implicit. In short, we address how people are navigating rules of mobility that operate in contradictory, ambiguous, and hidden ways.

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Wang, Zhe, Suxue Ma, Kewen Wang, and Zhiqiang Zhuang. "Rule-Guided Graph Neural Networks for Explainable Knowledge Graph Reasoning." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 12 (2025): 12784–91. https://doi.org/10.1609/aaai.v39i12.33394.

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The connections between symbolic rules and neural networks have been explored in various directions, including rule mining through neural networks and rule-based explanation for neural networks. These approaches allow symbolic rules to be extracted from neural network models, which offers explainability to the models. However, the plausibility of the extracted rules is rarely analysed. In this paper, we show that the confidence degrees of extracted rules are generally not high, and we propose a new family of Graph Neural Networks that can be trained with the guidance of rules. Hence, the inference of our model simulates the rule reasoning. Moreover, rules with high confidence degrees can be extracted from the trained model that aligns with the inference of the model, which verifies the effectiveness of the rule guidance. Experimental evaluation of knowledge graph reasoning tasks further demonstrates the effectiveness of our model.

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Kim, Segwang, Hyoungwook Nam, Joonyoung Kim, and Kyomin Jung. "Neural Sequence-to-grid Module for Learning Symbolic Rules." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (2021): 8163–71. http://dx.doi.org/10.1609/aaai.v35i9.16994.

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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.

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Morris, G. H., and Robert Hopper. "Symbolic action as alignment: A synthesis of rules approaches." Research on Language & Social Interaction 21, no. 1-4 (1987): 1–29. http://dx.doi.org/10.1080/08351818709389283.

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Bloomer, W. F., T. S. Dillon, and M. Witten. "Hybrid BRAINNE: Further developments in extracting symbolic disjunctive rules." Expert Systems with Applications 13, no. 3 (1997): 163–68. http://dx.doi.org/10.1016/s0957-4174(97)00030-4.

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Prentzas, Jim, and Ioannis Hatzilygeroudis. "Improving efficiency of merging symbolic rules into integrated rules: splitting methods and mergability criteria." Expert Systems 32, no. 2 (2014): 244–60. http://dx.doi.org/10.1111/exsy.12085.

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27

Brenner, C. H. "Symbolic Kinship Program." Genetics 145, no. 2 (1997): 535–42. http://dx.doi.org/10.1093/genetics/145.2.535.

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This paper discusses a computerized algorithm to derive the formula for the likelihood ratio for a kinship problem with any arbitrarily defined relationships based on genetic evidence. The ordinary paternity case with the familiar likelihood formula 1/2q is the commonest example. More generally, any miscellaneous collection of people can be genetically tested to help settle some argument about how they are related, what one might call a “kinship” case. Examples that geneticists and DNA identification laboratories run into include sibship, incest, twin, inheritance, motherless, and corpse identification cases. The strength of the genetic evidence is always described by a likelihood ratio. The general method is described by which the computer program finds the formulas appropriate to these various situations. The benefits and the interest of the program are discussed using many examples, including analyses that have previously been published, some practical problems, and simple and useful rules for dealing with scenarios in which ancestral or fraternal types substitute for those of the alleged father.

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Speck, David, Florian Geißer, Robert Mattmüller, and Álvaro Torralba. "Symbolic Planning with Axioms." Proceedings of the International Conference on Automated Planning and Scheduling 29 (May 25, 2021): 464–72. http://dx.doi.org/10.1609/icaps.v29i1.3511.

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Axioms are an extension for classical planning models that allow for modeling complex preconditions and goals exponentially more compactly. Although axioms were introduced in planning more than a decade ago, modern planning techniques rarely support axioms, especially in cost-optimal planning. Symbolic search is a popular and competitive optimal planning technique based on the manipulation of sets of states. In this work, we extend symbolic search algorithms to support axioms natively. We analyze different ways of encoding derived variables and axiom rules to evaluate them in a symbolic representation. We prove that all encodings are sound and complete, and empirically show that the presented approach outperforms the previous state of the art in costoptimal classical planning with axioms.

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Pasula, H. M., L. S. Zettlemoyer, and L. P. Kaelbling. "Learning Symbolic Models of Stochastic Domains." Journal of Artificial Intelligence Research 29 (July 21, 2007): 309–52. http://dx.doi.org/10.1613/jair.2113.

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In this article, we work towards the goal of developing agents that can learn to act in complex worlds. We develop a probabilistic, relational planning rule representation that compactly models noisy, nondeterministic action effects, and show how such rules can be effectively learned. Through experiments in simple planning domains and a 3D simulated blocks world with realistic physics, we demonstrate that this learning algorithm allows agents to effectively model world dynamics.

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Rahimi, Zeinab, and Mehrnoush Shamsfard. "A Neuro Symbolic Approach for Contradiction Detection in Persian Text." JUCS - Journal of Universal Computer Science 29, no. 3 (2023): 242–64. http://dx.doi.org/10.3897/jucs.90646.

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Detection of semantic contradictory sentences is a challenging and fundamental issue for some NLP applications, such as textual entailments recognition. In this study, contradiction means different types of semantic confrontation, such as negation, antonymy, and numerical. Due to the lack of sufficient data to apply precise machine learning and, specifically, deep learning methods to Persian and other low-resource languages, rule-based approaches are of great interest. Also, recently, the emergence of new methods such as transfer learning has opened up the possibility of deep learning for low-resource languages. This paper introduces a hybrid contradiction detection approach for detecting seven categories of contradictions in Persian texts: Antonymy, negation, numerical, factive, structural, lexical and world knowledge. The proposed method consists of 1) a novel data mining method and 2) a transformer-based deep neural method for contradiction detection . Also, a simple baseline is presented for comparison. The data mining method uses frequent rule mining to extract appropriate contradiction detection rules employing a development set. Extracted rules are tested for different categories of contradictory sentences. In the first step, a classifier checks whether the rules work for an input sentence pair. Then, according to the result, rules are used for three categories of negation, numerical, and antonym. In this part, the highest F-measure is obtained for detecting the negation category (90%), the average F-measure for these three categories is 86%, and for the other four categories, in which the rules have a lower F-measure of 62%, the transformer-based method achieved 76%. The proposed hybrid approach has an overall f-measure of higher than 80%.&nbsp;

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Rahimi, Zeinab, and Mehrnoush Shamsfard. "A Neuro Symbolic Approach for Contradiction Detection in Persian Text." JUCS - Journal of Universal Computer Science 29, no. (3) (2023): 242–64. https://doi.org/10.3897/jucs.90646.

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Detection of semantic contradictory sentences is a challenging and fundamental issue for some NLP applications, such as textual entailments recognition. In this study, contradiction means different types of semantic confrontation, such as negation, antonymy, and numerical. Due to the lack of sufficient data to apply precise machine learning and, specifically, deep learning methods to Persian and other low-resource languages, rule-based approaches are of great interest. Also, recently, the emergence of new methods such as transfer learning has opened up the possibility of deep learning for low-resource languages. This paper introduces a hybrid contradiction detection approach for detecting seven categories of contradictions in Persian texts: Antonymy, negation, numerical, factive, structural, lexical and world knowledge. The proposed method consists of 1) a novel data mining method and 2) a transformer-based deep neural method for contradiction detection . Also, a simple baseline is presented for comparison. The data mining method uses frequent rule mining to extract appropriate contradiction detection rules employing a development set. Extracted rules are tested for different categories of contradictory sentences. In the first step, a classifier checks whether the rules work for an input sentence pair. Then, according to the result, rules are used for three categories of negation, numerical, and antonym. In this part, the highest F-measure is obtained for detecting the negation category (90%), the average F-measure for these three categories is 86%, and for the other four categories, in which the rules have a lower F-measure of 62%, the transformer-based method achieved 76%. The proposed hybrid approach has an overall f-measure of higher than 80%.

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Canefe, Nergis. "Turkish nationalism and ethno‐symbolic analysis: the rules of exception." Nations and Nationalism 8, no. 2 (2002): 133–55. http://dx.doi.org/10.1111/1469-8219.00043.

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Rich, Albert, Patrick Scheibe, and Nasser Abbasi. "Rule-based integration: An extensive system of symbolic integration rules." Journal of Open Source Software 3, no. 32 (2018): 1073. http://dx.doi.org/10.21105/joss.01073.

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Avner, Stéphane. "Extraction of comprehensive symbolic rules from a multi-layer perceptron." Engineering Applications of Artificial Intelligence 9, no. 2 (1996): 137–43. http://dx.doi.org/10.1016/0952-1976(96)00004-8.

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Vannucchi, Claudia, Michelangelo Diamanti, Gianmarco Mazzante, et al. "Symbolic verification of event–condition–action rules in intelligent environments." Journal of Reliable Intelligent Environments 3, no. 2 (2017): 117–30. http://dx.doi.org/10.1007/s40860-017-0036-z.

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Werner, Luisa. "Neuro-Symbolic Integration for Reasoning and Learning on Knowledge Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 21 (2024): 23429–30. http://dx.doi.org/10.1609/aaai.v38i21.30415.

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The goal of this thesis is to address knowledge graph completion tasks using neuro-symbolic methods. Neuro-symbolic methods allow the joint utilization of symbolic information defined as meta-rules in ontologies and knowledge graph embedding methods that represent entities and relations of the graph in a low-dimensional vector space. This approach has the potential to improve the resolution of knowledge graph completion tasks in terms of reliability, interpretability, data-efficiency and robustness.

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Singh, Mukul, José Cambronero Sánchez, Sumit Gulwani, et al. "Cornet: Learning Table Formatting Rules By Example." Proceedings of the VLDB Endowment 16, no. 10 (2023): 2632–44. http://dx.doi.org/10.14778/3603581.3603600.

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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.

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Zavala Aránguiz, Ignacio. "Cultura de la cancelación y capital simbólico: aportes teóricos desde la teoría del campo artístico de Pierre Bourdieu." Tercio Creciente, no. 27 (January 1, 2025): 255–72. https://doi.org/10.17561/rtc.27.8911.

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This study provides a theoretical approach to the phenomenon of cancel culture within the context of art and artists, using Pierre Bourdieu's structural-constructivist conceptual framework regarding symbolic capital, the rules of the artistic field, and some relevant agents within it. It examines how cancellation affects artists' perception of symbolic capital, whose legitimacy and recognition depend heavily on interactions with other agents in the field, and how the relationship between the public and creators can be influenced and determined by this practice. Firstly, a brief characterization of cancel culture is sought, both as a criterion for personal parameter verification and as a tool for action for marginalized groups, followed by the identification of some concepts from Bourdieu's theoretical section, such as habitus, symbolic capital, artistic field, and rules of art, in addition to the characterization the author provides of artists and creators. Furthermore, it explores how cancellation can redefine the rules and agency boundaries of participants in the artistic field, especially regarding certain moral expectations imposed on artists by those who engage in cancellation, within a field that assumes operating with relative autonomy and differing expectations from the public. Thus, the tension between moral presuppositions - by the public identifying with cancellation - attributed to major holders of symbolic capital - artists and cultural producers - and the autonomous logic governing the art field based on ethical neutrality and internal operational criteria is highlighted.

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Anders, Torsten, and Benjamin Inden. "Machine learning of symbolic compositional rules with genetic programming: dissonance treatment in Palestrina." PeerJ Computer Science 5 (December 16, 2019): e244. http://dx.doi.org/10.7717/peerj-cs.244.

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We describe a method for automatically extracting symbolic compositional rules from music corpora. Resulting rules are expressed by a combination of logic and numeric relations, and they can therefore be studied by humans. These rules can also be used for algorithmic composition, where they can be combined with each other and with manually programmed rules. We chose genetic programming (GP) as our machine learning technique, because it is capable of learning formulas consisting of both logic and numeric relations. GP was never used for this purpose to our knowledge. We therefore investigate a well understood case in this study: dissonance treatment in Palestrina’s music. We label dissonances with a custom algorithm, automatically cluster melodic fragments with labelled dissonances into different dissonance categories (passing tone, suspension etc.) with the DBSCAN algorithm, and then learn rules describing the dissonance treatment of each category with GP. Learning is based on the requirement that rules must be broad enough to cover positive examples, but narrow enough to exclude negative examples. Dissonances from a given category are used as positive examples, while dissonances from other categories, melodic fragments without dissonances, purely random melodic fragments, and slight random transformations of positive examples, are used as negative examples.

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Gordon, Michael J. C. "Programming Combinations of Deduction and BDD-based Symbolic Calculation." LMS Journal of Computation and Mathematics 5 (2002): 56–76. http://dx.doi.org/10.1112/s1461157000000693.

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AbstractA generalisation of Milner's ‘LCF approach’ is described. This allows algorithms based on binary decision diagrams (BDDs) to be programmed as derived proof rules in a calculus of representation judgements. The derivation of representation judgements becomes an LCF-style proof by defining an abstract type for judgements analogous to the LCF type of theorems. The primitive inference rules for representation judgements correspond to the operations provided by an efficient BDD package coded in C (BuDDy). Proof can combine traditional inference with steps inferring representation judgements. The resulting system provides a platform to support a tight and principled integration of theorem proving and model checking. The methods are illustrated by using them to solve all instances of a generalised Missionaries and Cannibals problem.

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Hasim, Irfan Sabarilah, Indah Widiastuti, and Iwan Sudradjat. "Symbolic interactionism in vernacular cultural landscape research." ARTEKS : Jurnal Teknik Arsitektur 8, no. 1 (2023): 135–44. http://dx.doi.org/10.30822/arteks.v8i1.2080.

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Customary and traditional villages, also called vernacular cultural landscapes, are local settlement units whose inhabitants adhere to ancestral beliefs. It is important to conduct research on vernacular cultural landscapes in Indonesia, given the usual and concerning degradation of cultural landscapes. Different places have different cultures and different customary rules and habits. Each has its uniqueness and distinctiveness, so there is no one standardized approach or method that can be adapted to study the vernacular cultural landscape. Different places may require different research approaches or methods; even the same place if studied under a different topic or time frame, may also require a different approach or method. There are research approaches commonly used by the researcher of the vernacular cultural landscape, including phenomenology, narrative study, case study, grounded theory, and ethnography. This article will review one approach that can be an alternative for the researcher of the vernacular cultural landscape, namely Symbolic Interactionism. Symbolic Interactionism is an approach that can be effectively applied to study human groups, community life, and social interactions. Symbolic interactionism is able to reveal the relationships that occur naturally among members of the society, particularly the relationship between intangible symbols, rules, norms, and daily activities, with tangible things such as the formation of space, buildings, circulation, and other physical configurations.

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Evans, Richard, and Edward Grefenstette. "Learning Explanatory Rules from Noisy Data." Journal of Artificial Intelligence Research 61 (January 26, 2018): 1–64. http://dx.doi.org/10.1613/jair.5714.

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Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model, yielding a nearly ubiquitous overfitting problem. Although mitigated by a variety of model regularisation methods, the common cure is to seek large amounts of training data--which is not necessarily easily obtained--that sufficiently approximates the data distribution of the domain we wish to test on. In contrast, logic programming methods such as Inductive Logic Programming offer an extremely data-efficient process by which models can be trained to reason on symbolic domains. However, these methods are unable to deal with the variety of domains neural networks can be applied to: they are not robust to noise in or mislabelling of inputs, and perhaps more importantly, cannot be applied to non-symbolic domains where the data is ambiguous, such as operating on raw pixels. In this paper, we propose a Differentiable Inductive Logic framework, which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with. Furthermore, as it is trained by backpropagation against a likelihood objective, it can be hybridised by connecting it with neural networks over ambiguous data in order to be applied to domains which ILP cannot address, while providing data efficiency and generalisation beyond what neural networks on their own can achieve.

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GUAN, JUNBIAO, SHAOWEI SHEN, CHANGBING TANG, and FANGYUE CHEN. "EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE." International Journal of Bifurcation and Chaos 17, no. 12 (2007): 4245–59. http://dx.doi.org/10.1142/s0218127407019925.

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We establish the relation between the extended (i.e. I = ∞) one-dimensional binary Cellular Automata (1D CA) and the bi-infinite symbolic sequences in symbolic dynamics. That is, the 256 local rules of 1D CA correspond to 256 local rule mappings in the symbolic space. By employing the two homeomorphisms T† and [Formula: see text] from [Chua et al., 2004] for finite I, we classify these 256 local rule mappings into the same 88 equivalence classes identified in [Chua et al., 2004] and [Chua, 2006]. Different mappings in the same equivalence class are mutually topologically conjugate.

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NOBRE, C., E. MARTINELI, A. BRAGA, et al. "Knowledge Extraction: A Comparison Between Symbolic and Connectionist Methods." International Journal of Neural Systems 09, no. 03 (1999): 257–64. http://dx.doi.org/10.1142/s0129065799000265.

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The use of a linguistic representation for expressing knowledge acquired by learning systems is an important issue as regards to user understanding. Under this assumption, and to make sure that these systems will be welcome and used, several techniques have been developed by the artificial intelligence community, under both the symbolic and the connectionist approaches. This work discusses and investigates three knowledge extraction techniques based on these approaches. The first two techniques, the C4.5 [12] and CN2 [6] symbolic learning algorithms, extract knowledge directly from the data set. The last technique, the TREPAN algorithm [10] extracts knowledge from a previously trained neural network. The CN2 algorithm induces if … then rules from a given data set. The C4.5 algorithm extracts decision trees, although it can also extract ordered rules, from the data set. Decision trees are also the knowledge representation used by the TREPAN algorithm.

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Ho, C. Y., and Jen Sriwattanathamma. "Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators." Robotica 7, no. 3 (1989): 243–54. http://dx.doi.org/10.1017/s026357470000610x.

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SUMMARYSolving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule–based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the System. A verification of the System has been demonstrated in case of several industrial robots.

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Babusci, D., G. Dattoli, K. Górska, and K. A. Penson. "Symbolic methods for the evaluation of sum rules of Bessel functions." Journal of Mathematical Physics 54, no. 7 (2013): 073501. http://dx.doi.org/10.1063/1.4812325.

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Kulunchakov. "Creation of parametric rules to rewrite algebraic expressions in Symbolic Regression." Machine Learning and Data Analysis 3, no. 1 (2017): 6–19. http://dx.doi.org/10.21469/22233792.3.1.01.

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Prentzas, Jim, and Ioannis Hatzilygeroudis. "Neurules and connectionist expert systems: Unexplored neuro-symbolic reasoning aspects." Intelligent Decision Technologies 15, no. 4 (2022): 761–77. http://dx.doi.org/10.3233/idt-210211.

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Neuro-symbolic approaches combine neural and symbolic methods. This paper explores aspects regarding the reasoning mechanisms of two neuro-symbolic approaches, that is, neurules and connectionist expert systems. Both provide reasoning and explanation facilities. Neurules are a type of neuro-symbolic rules tightly integrating the neural and symbolic components, giving pre-eminence to the symbolic component. Connectionist expert systems give pre-eminence to the connectionist component. This paper explores reasoning aspects about neurules and connectionist expert systems that have not been previously addressed. As far as neurules are concerned, an aspect playing a role in conflict resolution (i.e., order of neurules) is explored. Experimental results show an improvement in reasoning efficiency. As far as connectionist expert systems are concerned, variations of the reasoning mechanism are explored. Experimental results are presented for them as well showing that one of the variations generally performs better than the others.

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Liu, Anji, Hongming Xu, Guy Van den Broeck, and Yitao Liang. "Out-of-Distribution Generalization by Neural-Symbolic Joint Training." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 10 (2023): 12252–59. http://dx.doi.org/10.1609/aaai.v37i10.26444.

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This paper develops a novel methodology to simultaneously learn a neural network and extract generalized logic rules. Different from prior neural-symbolic methods that require background knowledge and candidate logical rules to be provided, we aim to induce task semantics with minimal priors. This is achieved by a two-step learning framework that iterates between optimizing neural predictions of task labels and searching for a more accurate representation of the hidden task semantics. Notably, supervision works in both directions: (partially) induced task semantics guide the learning of the neural network and induced neural predictions admit an improved semantic representation. We demonstrate that our proposed framework is capable of achieving superior out-of-distribution generalization performance on two tasks: (i) learning multi-digit addition, where it is trained on short sequences of digits and tested on long sequences of digits; (ii) predicting the optimal action in the Tower of Hanoi, where the model is challenged to discover a policy independent of the number of disks in the puzzle.

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Zittoun, Tania. "Difficult secularity: Talmud as symbolic resource." Outlines. Critical Practice Studies 8, no. 2 (2006): 59–75. http://dx.doi.org/10.7146/ocps.v8i2.2092.

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Religious systems are organised semiotic structures providing people with values and rules, identities, regularity, and meaning. Consequently, a person moving out of a religious system might be exposed to meaning-ruptures. The paper presents the situation of young people who have been in Yeshiva, a rabbinic high-school, and who have to join secular university life. It analyses the changes to which they are exposed. On the bases of this case study, the paper examines the following questions: can the religious symbolic system internalised by a person in a religious sphere of experience be mobilised as a symbolic resource once the person moves to a secular environment? If yes, how do religious symbolic resources facilitate the transition to a secular life? And if not, what other symbolic and social resources might facilitate such transitions?

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