Inference Rules Research Articles

A Classification Model Based on Interval Rule Inference Network with Interpretability

Interpretability requirements, complex uncertain data processing, and limited training data are characteristics of classification in some real industry applications. The interval belief rule base (IBRB) can deal with various types of uncertainty and provides high interpretability. However, there is a large number of parameters in IBRB, which makes it difficult for experts to accurately set them manually, limiting its application scope. To address this issue, this paper proposes an interval rule inference network (IRIN) with interpretability for classification models to automatically generate IBRB through integrating the ideas of the IBRB and the neural network. Firstly, hybrid data with different types are transformed into an interval belief distribution for automatic generation processing. Secondly, the interval evidence reasoning method is utilized as the inference engine to transfer information ensuring the process’s interpretability. Finally, a reasonable IBRB is generated automatically by updating the parameters by employing the learning engine in the neural network. Moreover, the differentiability of the interval evidence reasoning method in the IRIN is proved as a theoretical foundation of the IRIN, and an interpretability analysis of the IRIN’s structures is discussed. Experimental results demonstrate that the proposed method possesses high interpretability, enhancing the reliability of classification and maintaining the accuracy. Its application in an actual engineering case illustrates that it is particularly suitable for engineering problems where the explanation of results is a critical requirement.

A Novel Conflict Deduction Algorithm Based on Contradiction Separation Inference Rule

Automated reasoning, a significant field within artificial intelligence, has attracted increased attention in recent years due to the rising demand for trustworthy AI. Binary resolution, among other inference rules, is crucial in automated reasoning of first-order logic, including the new conflict resolution method. Conflict resolution processes only two clauses in each deduction step and eliminates a complementary pairs of literals from input clauses. This paper proposes a contradiction separation conflict deduction (CSCD) method based on the contradiction separation rule to address these limitations. This novel resolution methodology, together with its automated reasoning theory and method, handles several clauses in each deduction step to seek for conflicts and generates learnt clauses through synergized deduction. Thus, the approach improves deduction by detecting conflicts more effectively, especially with lengthier input clauses. CSCD and conflict resolution are analyzed in detail, then how to create a practical CSCD algorithm and its implementation is summarized. We tested the CSCD algorithm to solve the CASC-26 problems and also applied it to the current leading ATP system (Eprover). Experimental results show that the CSCD deduction approach improves reasoning capability of conflict deduction method. Additionally, the Eprover with the proposed CSCD algorithm improves its performance and has solved various problems with a rating of 1 from the benchmark database TPTP.

Hybrid Models of Atmospheric Block Columns of Primary Oil Refining Unit Under Conditions of Initial Information Deficiency

Hybrid Models of Atmospheric Block Columns of Primary Oil Refining Unit Under Conditions of Initial Information Deficiency

Finite-Choice Logic Programming

Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while maintaining structural and logical constraints—there is no single canonical model. The notion of stable models for logic programs with negation has successfully captured programmer intuition about the set of valid solutions for such problems, giving rise to a family of programming languages and associated solvers known as answer set programming. Unfortunately, the definition of a stable model is frustratingly indirect, especially in the presence of rules containing free variables. We propose a new formalism, finite-choice logic programming, that uses choice, not negation, to admit multiple solutions. Finite-choice logic programming contains all the expressive power of the stable model semantics, gives meaning to a new and useful class of programs, and enjoys a least-fixed-point interpretation over a novel domain. We present an algorithm for exploring the solution space and prove it correct with respect to our semantics. Our implementation, the Dusa logic programming language, has performance that compares favorably with state-of-the-art answer set solvers and exhibits more predictable scaling with problem size.

Automatic Question Generation Based on Historical Panoramic Knowledge Graphs and Inference Rules

Automatic Question Generation Based on Historical Panoramic Knowledge Graphs and Inference Rules

Assessment of water quality of the Narmada River (India) using the fuzzy water quality index method

ABSTRACT This study aims to assess the water quality of the Narmada River utilizing the fuzzy water quality index (FWQI) method. In this context, samples of water were gathered from six stations for various parameters such as turbidity, pH, DO, BOD5, TDS, TSS, COD, EC, TH, TA, and chloride from 2017 to 2022. Due to contamination from urbanization, water quality assessment has become essential. To address this requirement, the water quality index (WQI) was developed which incorporates various water quality parameters and expresses total water quality into a single value. Nowadays, a new method, the FWQI has been developed. To develop FWQI, 11 inputs, single output, Mamdani method, And operators, fuzzy inference rules, and centroid methods for defuzzification have been used. The average values of FWQI at the first, second, third, fourth, fifth, and sixth stations were 61.28, 57.66, 62.18, 61.90, 50.00, and 49.96, respectively. Meanwhile, the average values of WQI for the same stations were 57.98, 57.40, 58.97, 58.85, 48.39, and 49.03. The findings from both methods revealed that water quality was poor at the first four stations and good at the last two stations. This new index could serve as an alternative approach to assessing water quality.

A Semantic Proof of Generalised Cut Elimination for Deep Inference

Multiplicative-Additive System Virtual (MAV) is a logic that extends Multiplicative-Additive Linear Logic with a self-dual non-commutative operator expressing the concept of "before" or "sequencing". MAV is also an extenson of the the logic Basic System Virtual (BV) with additives. Formulas in BV have an appealing reading as processes with parallel and sequential composition. MAV adds internal and external choice operators. BV and MAV are also closely related to Concurrent Kleene Algebras. Proof systems for MAV and BV are Deep Inference systems, which allow inference rules to be applied anywhere inside a structure. As with any proof system, a key question is whether proofs in MAV can be reduced to a normal form, removing detours and the introduction of structures not present in the original goal. In Sequent Calcluli systems, this property is referred to as Cut Elimination. Deep Inference systems have an analogous Cut rule and other rules that are not present in normalised proofs. Cut Elimination for Deep Inference systems has the same metatheoretic benefits as for Sequent Calculi systems, including consistency and decidability. Proofs of Cut Elimination for BV, MAV, and other Deep Inference systems present in the literature have relied on intrincate syntactic reasoning and complex termination measures. We present a concise semantic proof that all MAV proofs can be reduced to a normal form avoiding the Cut rule and other "non analytic" rules. We also develop soundness and completeness proofs of MAV (and BV) with respect to a class of models. We have mechanised all our proofs in the Agda proof assistant, which provides both assurance of their correctness as well as yielding an executable normalisation procedure.- Our technique extends to include exponentials and the additive units.

Basic sanitation evaluation model using Fuzzy Inference System

The debate on water supply and waste management is an economic and environmental issue that has been discussed since the earliest cities. Initially, sewage was dumped into rivers without treatment, but with scientific advances, new solutions have emerged. In Brazil, Law No. 11,445/2007 regulates basic sanitation, which includes water supply, sewage, solid waste management, and urban drainage. Investments in this area are essential for public health and sustainable development, but there are still many people without access to these services, which aggravates health problems and environmental degradation, according to UNICEF (2020). Technologies such as artificial intelligence and fuzzy inference systems have been applied to optimize the management of these services. This study developed a fuzzy inference model to assess the quality of basic sanitation services. The model analyzed indicators such as water supply, sewage, and waste management, using the fuzzy methodology to address uncertainties and generate more accurate diagnoses. The process included fuzzification of inputs, application of inference rules, and defuzzification to transform the results into interpretable data. The results demonstrated that fuzzy logic is effective in identifying critical points in sanitation, offering solutions to reduce costs and increase efficiency. The model is adaptable to different regional contexts, facilitating its application in other locations. With this tool, it was possible to direct corrective actions, contributing to the improvement of services and the universalization of sanitation. This supports the fulfillment of Sustainable Development Goal (SDG) 6, which aims to ensure universal and sustainable access to water and sanitation.

Enhancing Mood and Energy Detection in NLP through Fuzzy Logic Integration

This research presents a dual approach to textual analysis by utilizing fuzzy logic to detect both emotional and energy intensities in text. Through the use of trapezoidal membership functions to model diverse emotional and energy states and the application of an extensive set of fuzzy inference rules, the proposed methodology provides a nuanced, context-aware interpretation of moods and energy levels within text.

Tonk, Syntax, Semantics, Pragmatics

Abstract In 1960, A. N. Prior proposed a binary sentential functor defined by inferential rule (introduction) A ⊢ A tonk B, and (elimination) A tonk B ⊢ A. Later, this idea was discussed by several authors, including in the context of the question of whether the ab ove rule defines this functor in a sufficient manner. This paper shows that if we assume the standard matrix (truth-tables) characterization of classical sentential functors, no valuation agrees with rules generating the sense of tonk. Moreover, these inferential prescriptions are at odds with the principle that if premises are true, the conclusion has to be such as well. A new solution is proposed. It consists in considering tonk-rules via so-called rejection consequence operation, that is, a dual with respect to the standard Cn. The general moral stemming from the proposed analysis says that inferentialism, the view that inference rules are purely syntactical, is dubious, because logic has its basis also in semantic presuppositions as well as in pragmatic ones.

A Categorical Formalism for Conceptual Graphs

Abstract In this paper, we propose a formalism for knowledge manipulation, based on conceptual graphs, which is supported by category theory, and which can be the basis for the development of knowledge-based systems. The model we propose is an extension of the model based on conceptual graphs. In this model, the application of an inference rule between logical formulas represented by two conceptual graphs is reduced to the identification of an arrow in a category. To this end, we introduce several new notions such as: the category of conceptual graphs, the category of classes of conceptual graphs, the conceptual category of a model and the conceptual category of inference of a model.

Incremental learning and granular computing from evolving data streams: An application to speech-based bipolar disorder diagnosis

We apply an evolving granular-computing modeling approach, called evolving Optimal Granular System (eOGS), to bipolar mood disorder (BD) diagnosis based on speech data streams. The eOGS online learning algorithm reveals information granules in the flow and design the structure and parameters of a granular rule-based model with a certain degree of interpretability based on acoustic attributes obtained from phone calls made over 7 months to the Psychiatry department of a hospital. A multi-objective programming problem that trades-off information specificity, model compactness, and numerical and granular error indices is presented. Spectral and prosodic attributes are ranked and selected based on a hybrid Pearson-Spearman correlation coefficient. Low attribute-class correlation, ranging from 0.03 to 0.07, is observed, as well as high class overlap, which is typical in the psychiatric field. eOGS models for BD recognition overcome alternative computational-intelligence models, namely, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Fuzzy-set-Based evolving Modeling (FBeM-Gauss), by a small margin in both best and average cases; followed by eXtended Takagi-Sugeno (xTS) and evolving Takagi Sugeno (eTS) types of models. The proposed eOGS model using only 8 of the original acoustic attributes, and about 15 ‘If-Then’ inference rules, has exhibited the best root mean square error, 0.1361, and 91.8% accuracy in sharp BD class estimates. Granules associated to linguistic labels and a granular input-output map offer human understandability with relation to the inherent process of generating class estimates. Linguistically readable eOGS rules may assist physicians in explaining symptoms and making a diagnosis.

Generalized Entropy and Solution Information for Measuring Puzzle Difficulty

Metrics for problem difficulty are used by many puzzle generation algorithms, as well as by adaptive algorithms that want to provide players with the puzzles at the correct level of difficulty. A recently proposed general metric, puzzle entropy, combines an analysis of game mechanics with a model of player knowledge in the form of inference rules to predict problem difficulty. The entropy of a puzzle is the amount of information required, given a player’s knowledge about the puzzle, to describe a solution to a puzzle. This paper generalizes the concepts of puzzle entropy and solution information, providing a better foundation for the previous work and creating new algorithms, Minimum Solution Information and Total Solution Information. While functionally very similar to past work, the new algorithm allows knowledge about a puzzle to be represented as a policy, something that can be learned more easily. We then evaluate the impact of policies, inference rules, and player knowledge in the 2016 game, The Witness.

Ontology-based Data Integration Framework for Smart Pig Farms

Semantic web technology is known to enhance data for the connection of information using a network that can be easily read by machines. This work applies an ontology to integrate data involved in swine farm management towards the development of smart farm for swine. To realize environmental data, IoT devices including sensors, camera, and RFID readers were deployed in a pig farm. Despite differences in data format from different sources, an ontology was crafted to provide semantic annotations that could unify the data and enhance them with tangible relationships based on the domain knowledge. The core concepts of this ontology were sensing data with temporal information and identifiable data to represent relationship between real-time environmental features and the pigs within the pen to improve pig management. The semantically enhanced data can thus be applied with semantic-based queries and inference reasoner. Smart services including monitoring, decision support, alerting, and automatic executing based on the deployed IoT devices are thus enabled to support farm managements towards smart farm for swine. From the results, we found that the integrated sensing information from sensors and knowledge given in the developed ontology with inference rules assists the task of interpretation of monitored information and decision-making to improve swine farm management. The data gathered could be extended by combining two or more factors such as temperature and humidity into heat index using knowledge inference to precisely understand environmental information and activate the relevant machine automatically.

Intelligent Control of an Experimental Small-Scale Wind Turbine

Nowadays, wind turbines are one of the most popular devices for producing clean and renewable electric energy. The rotor blades catch the wind’s kinetic energy to produce rotational energy from the turbine and electric energy from the generator. In small-scale wind turbines, there are several methods to operate the blades to obtain the desired speed of rotation and power outputs. These methods include passive stall, active stall, and pitch control. Pitch control sets the angular position of the blades to face the wind to achieve a predefined relationship between turbine speed or power and wind velocity. Typically, conventional Proportional Integral (PI) controllers are used to set the angular position of the rotor blades or pitch angle. Nevertheless, the quality of speed or power regulation may vary substantially. This study introduces a rotor speed controller for a pitch-controlled small-scale wind turbine prototype based on fuzzy logic concepts. The basics of fuzzy systems required to implement this kind of controller are presented in detail to counteract the lack of such material in the technical literature. The knowledge base of the fuzzy speed controller is composed of Takagi–Sugeno–Kang (TSK) fuzzy inference rules that implement a dedicated PI controller for any desired interval of wind velocities. Each wind velocity interval is defined with a fuzzy set. Simulation experiments show that the TSK fuzzy PI speed controller can outperform the conventional PI controller in the speed and accuracy of response, stability, and robustness over the whole range of operation of the wind turbine prototype.

Sistema Especialista para Correção de Panes em Aeronaves

The article discusses the implementation of an Expert System (ES) for aircraft fault diagnosis, highlighting the complexity of modern systems and the need for qualified mechanics. The ES uses heuristics and a knowledge base to diagnose issues, allowing mechanics to follow a structured methodology during maintenance. Through inference rules, the ES not only improves efficiency in identifying faults but also elevates the professional level of mechanics by providing continuous and well-founded support. The adoption of this system can lead to more effective and safer maintenance of the Brazilian Air Force aircraft.

Intuitionistic Implication and Logics of Formal Inconsistency

Logics of Formal Inconsistency (LFI for short) are a class of paraconsistent logics that validate the principle of gentle explosion, meaning that any formula can be derived from the set of formulas: ∘α, α and ∼α. A unique feature of LFI is the use of the symbol ‘∘’ to represent notions of consistency at the object-language level. These logics are simple in essence, built upon all the axiom schemas of positive classical logic, axioms for negation and the so-called ‘consistency operator’ ∘, with the only inference rule being detachment. In this paper, we propose an alternative foundation for LFI, which is the positive fragment of intuitionistic propositional logic. We present bi-valuational ‘Loparić-like’ semantics for the resulting logics and discuss their potential extensions.

Dialetheism and the countermodel problem

AbstractAccording to some dialetheists, we ought to reject the distinction between object and meta‐languages. Given that dialetheists advocate truth‐value gluts within their object‐language, whether in order to solve the liar paradox or for some other reason, this rejection of the object‐/meta‐language distinction comes with the commitment to use a glutty metatheory. While it has been pointed out that a glutty metatheory brings with it expressive deficiencies, we highlight here another complication arising from the use of a glutty metatheory, this time evidential in nature. According to this countermodel problem, while the thoroughgoing dialetheist who embraces a glutty metatheory can justify their acceptance of a rule of inference's invalidity using countermodels, to justify their renunciation of an unwanted rule they actually require the means to warrant their rejection of the rule's validity—which cannot be supplied by countermodels based on a standard dialetheic semantics. We end by sketching out a possible solution for the thoroughgoing dialetheist using a bilaterialist semantics.

Multi-label classification with imbalanced classes by fuzzy deep neural networks

Multi-label classification is an advantageous technique for managing uncertainty in classification problems where each data instance is associated with several labels simultaneously. Such situations are frequent in real-world scenarios, where decisions rely on imprecise or noisy data and adaptable classification methods are preferred. However, the problem of class imbalance represents a common characteristic of several multi-label datasets, in which the distribution of samples and their corresponding labels is non-uniform across the data space. In this paper, we propose a multi-label classification approach utilizing fuzzy logic in order to deal with the class imbalance problem. To eliminate the need for an expert to determine the logical rules of inference, deep neural networks are adopted, which have proven to be exceptionally effective for such problems. By combining both fuzzy inference systems and deep neural networks, the strengths and weaknesses of each approach can be mitigated. As a further development, a symbolic representation of time series is put in place to reduce data dimensionality and speed up the training procedure. This allows for more flexibility in model application, in particular with respect to time constraints arising from the causality of observed time series. Tests carried out on a multi-label classification dataset related to the current and voltage profiles of several household appliances show that the proposed model outperforms four baseline models for time series classification.

Logics for at most countable first-order structures

Abstract In this paper we present two extensions of $\omega $-logic with infinitary inference rules, denoted $Arch$-$\omega $-logic and $non$-$Arch$-$\omega $-logic. We provide the corresponding Hilbert-style axiomatizations and prove their strong completeness with respect to countable Archimedean and non-Archimedean fields, respectively. Through several examples we illustrate a natural representation of various weight functions within the proposed framework and applications to non-monotonic reasoning and neuro-symbolic computing.