Logical Inference Rules Research Articles

Challenges for Non-Classical Reasoning in Contemporary AI Applications

In knowledge representation and reasoning, a key area in artificial intelligence research, non-classical logics play a prominent double role: firstly, non-classical logic languages allow for a precise and transparent encoding of domain specific knowledge. Secondly, as the logical languages are equipped with custom-tailored rules of logical inference, they make available a principled approach to derive new knowledge from previous information. In practice, the first aspect addresses data storage and retrieval, the second aspect the utilization of available information. This article briefly surveys contemporary challenges of NCL research in AI.

Integrating adaptive fuzzy embedding with topology and property hypergraphs: Enhancing membership degree-aware knowledge graph reasoning

Knowledge Graphs (KG) leverage the Resource Description Framework (RDF) to model clear and static resources, enabling the revelation of latent meanings through embedding and reasoning. However, their effectiveness diminishes when facing the inherent vagueness and dynamism of real-world information. To overcome this limitation, we introduce a novel adaptive fuzzy RDF KG embedding approach. This method represents fuzzy knowledge by integrating topological structures and descriptive properties while generating membership degrees to enhance the reasoning capabilities of KG. Specifically, our approach introduces a way to create embeddings based on local and global topological pattern mining. Then, path quality-based adaptive learning is implemented. Next, we incorporate entity descriptive information and construct a property hypergraph from another perspective to learn embeddings. By creatively combining these three components, our method can generate a fuzzy membership degree to aid knowledge reasoning. To thoroughly assess the method's effectiveness, experiments were conducted around four key questions, evaluating algorithm performance compared with other work and assessing knowledge reasoning effectiveness based on logical inference rules on Unmanned Aerial Vehicle (UAV) datasets.

Синтез обнаруживающих тестов для нечетких автоматов с конечной памятью

The problem of test synthesis for fuzzy automata with finite memory is considered. The paper is based on the results obtained by the author earlier. They study linear automata (LA), a subclass of which are automata with finite memory (AFM). Both types of automata are used as models in diagnostics of discrete devices and in other applications. The advantages of LA are simplicity of realization and availability of developed mathematical apparatus for their study. AFMs allow describing the dependencies between inputs and outputs in the past and present moments of time without using states of the automata. This property is used in the development of finite-automation cryptosystems, in the generation of exhaustive tests for discrete devices, in the formulation of fuzzy rules of logical inference and others. The paper proposes a method for synthesis of detecting tests for fuzzy AFMs, based on reducing it to the case of its analog for crisp AFMs. Fuzzy AFM (as a subclass of LA) can be described using transition and output functions represented as equations with characteristic matrices. Fuzzy AFM is realized using matrices containing some fuzzy elements. These elements obtain values randomly from alternative sets given for them. The other (crisp) elements of the matrices are fixed values from the field GF(p), over which the AFM is defined. After all possible substitutions in the matrices of fuzzy AFM of all fuzzy elements (from alternative sets) we obtain a set of crisp automata describing the "behavior" of the considered fuzzy automaton under all possible "scenarios" of substitutions. Each faulty AFM is obtained by changing the values of the elements of its characteristic matrices. As a set of admissible faults, all possible changes in these matrices obtained by substitutions and insertion of fault introduction are considered. Now we can use the method of test synthesis proposed earlier by the author of the submitted paper, organizing the procedure of sequential analysis and comparison of "behavior" of crisp pairs (faultless AFM, faulty AFM). The AFMs obtained after substitutions should be used sequentially as faultless AFMs and as faulty AFMs after faults have been introduced. Conclusions about the faultless AFM or the presence of a fault in it are made on the basis of analyzing the totality of the results obtained. A generalization of the synthesis method proposed earlier by the author of the submitted paper the is described for µ-defined (and synchronizable) AFMs. The method is based on obtaining tests as solutions of systems of linear equations, for which there is a well-developed mathematical apparatus in algebra.

Analysis of models and development of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure

The direction associated with the construction and research of models that can be used to predict the impact of vibration effects of vehicles on surrounding infrastructure facilities is relevant given the increasing pace of civil engineering in large cities and taking into account the expansion of transport networks. The development of models for evaluating vibration effects and for subsequent use in monitoring and diagnostic systems requires the use of modern methods of nonlinear analysis, discrete mathematics, as well as tools for the development of expert systems and artificial intelligence technologies. The purpose of the article is to obtain the results of the analysis of a complex mathematical model of spatial interactions, the development of algorithmic support and a description of the structure of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure. A model of spatial interactions is proposed to assess the levels of vibration exposure with the construction of a graph of the placement of objects connected by vibration propagation channels and using the mathematical apparatus of modeling hybrid dynamic systems, expert knowledge and fuzzy rules of logical inference. Examples of constructing a model of spatial interactions taking into account three objects of vibrational observation are considered. The VibCalcAlg algorithm has been developed to calculate the states of a three-component model. The structure of the VibCalc software package is described, which includes a block of fuzzy logic, a block of model construction and a block of visualization. The results can be used in solving mathematical modeling problems related to the assessment and prediction of vibration impacts in the field of transport and civil engineering, as well as in solving environmental protection problems. The results are aimed at improving intelligent monitoring systems and decision support systems in the design, construction and operation of transport facilities.

THE COMPLEX PROBLEM OF EXPANDING THE CAPABILITIES OF CADASTRAL SYSTEMS AND WAYS TO SOLVE IT

The development of cadastral systems in various countries, including Ukraine, has gone through creating information systems that serve users (stakeholders) in one of the subject areas, such as land administration, real estate construction, water resources, and others. Modern cadastral systems have no capacity to solve complex problems, and, at the same time, their structure does not contain specialised mathematical support in the form of models capable of simulating complex processes. Intelligent cadastres will be able to solve complex problems. Along with the existing types of cadastre support, intelligent cadastres should have well-structured mathematical and heuristic support. It should allow for solving private computing and service tasks, as well as loosely structured ones with a high degree of uncertainty, and provide good visualisation and detailing of objects, processes, and phenomena based on cloud and other modern information technologies. We propose introducing an intelligent cadastral system, presented as a geoinformation system with components of both a decision support system and a system for manipulating thematic layers. The decision support system should contain typical models used during the formalisation of one or another subject area or as a variant of the formal model of the subject areas’ description. The thematic layers manipulation system should allow the integration of attributive data belonging to different subject areas. In this case, ensuring prompt and fruitful work of cognitologists with experts is essential. The shortage of time and the variety of problems to be solved require the development of technology for formalising the knowledge of experts or specific subject areas. Implementing this technology and ensuring its implementation will require the creation of banks of typical knowledge models, which should store standardised procedures for formal representations. The bank of formal representations of heuristic knowledge includes procedures for forming production rules, building semantic and other networks, building frame representations and genetic algorithms, and so on. The bank of formal logical procedures contains procedures for creating logical rules based on the logic of statements, rules of logical inference based on the predicate logic, procedures of other modal logics, in particular, the presence logic, and procedures for building logical constructions based on the theory of categories and functors. Keywords: cadastral system, geoinformation system, decision support system, thematic layer manipulation system, formalisation.

Analysis of the Consistency of Prerequisites and Learning Outcomes of Educational Programme Courses by Using the Ontological Approach

The article presents the results of the application of an ontological approach to the description of the structure and content of the educational programme, and its subsequent analysis for the consistency of prerequisites and learning outcomes of courses. The practical result of the work is an ontology approach implemented in the Protégé 5.5.0 editor, which reflects the studied disciplines in terms of the skills they form and the entrance requirements (prerequisites) for the qualification of the student. The curriculum model includes sequences of semesters and courses of study (academic year) related by time relationships. The developed ontology approach is filled with data from the educational programme “Software Engineering”. The authors have earned queries in DL Query and SPARQL languages, which, using logical inference procedures, make it possible to analyse an educational programme for consistency of disciplines in terms of input requirements and the skills of the learner formed during the training period. The developed ontology and rules of logical inference can be used as a part of the educational process management information systems and educational programme designers, for the intellectual analysis of programme integrity and the consistency of learning prerequisites and outcomes in disciplines.

Representation and Construction of Discipline Knowledge Systems Based on Cognitive Sequence Relationship

For students, it’s an important but difficult thing to form a discipline knowledge system based on the sequence of cognition, and they would need teachers’ assistance for that. Therefore, how to arrange the scattered knowledge points in a sequence that conforms to the law of cognition, construct a complete discipline knowledge system, and help students attain, familiarize, absorb, and internalize the new knowledge in a scientific way are urgent issues to be solved for educationalists. To attempt to solve these questions, in a research background that the smart education has been applied and promoted widely, this paper took the finance discipline as an example to study the representation and construction of discipline knowledge system based on cognitive sequence. At first, this paper took a Back Propagation Neural Network (BPNN) based on complex rules as the Cognitive Sequence Relationship (CSR) construction algorithm for correcting contradictions in the CSR of knowledge points in the finance discipline knowledge system, gave the structure of the model for inferring the CSR of knowledge points in the finance discipline knowledge system, and adjusted the existing logical inference rules. Then, when building the CSR for the target discipline, this paper introduced a momentum factor σ into the network model to solve problems such as network oscillation and slow convergence. After that, the established finance discipline knowledge system was corrected to ensure that the old and new knowledge in the system could keep balance, and a fragment in the finance discipline knowledge dataset was introduced as an example. At last, the effectiveness of the proposed algorithm was verified by the experimental results.

Improved DC-Link Voltage Controller for Photo Voltaic ON-Grid Systems

The DC-link voltage is an essential intermediate stage between the DC/DC and DC/AC converters in solar energy system. Due to the voltage fluctuations and current disturbances, a controller should be suitably designed to maintain the DC-link voltage well stabilized. In this paper, a variant of an adaptive DC-link voltage controller is proposed, namely PI-Fuzzy controller. The proposed controller has a fixed integral gain, while the proportional gain is determined based on a set of Fuzzy logic inference rules. Moreover, an anti-windup mechanism is added to the proposed controller to overcome integrator windup when the actuator saturates. Simulation results show that the proposed controller provides better rejection of current disturbances and fastest rise-time comparing to recently proposed PI-controllers for the DC-link voltage control.

Does Frege Have a Metalinguistic Truth-Predicate in Begriffsschrift?

AbstractIn the explanations of logical laws and inference rules of the mature version of Begriffsschrift in Grundgesetze, Frege uses the predicate “… is the True.” Scholars like Greimann maintain that this predicate is a metalinguistic truth-predicate for Frege. This paper examines an argument for this claim that is based on the “nominal reading” of Frege’s conception of sentences—the claim that for Frege a sentence “$ p $” is equivalent to a nonsentential phrase like “the truth-value of the thought that $ p $.” In particular, this paper attempts to establish two points concerning this argument based on the nominal reading. First, the argument implies a claim about the nature of assertion which Frege repeatedly denies in his mature works. Secondly, the nominal reading on which the argument depends is false. A sentence “$ p $” is not equivalent to a nonsentential phrase like “the truth-value of the thought that $ p $” for Frege. Our discussion will lead to an important lesson about Frege’s conception of sentences and of assertion.

A novel vector-space-based lightweight privacy-preserving RFID authentication protocol for IoT environment

Internet of Things (IoT) is a novel paradigm that connects several physical devices and the cyber world over the Internet. IoT technology is growing rapidly and soon will have an enormous innovation in our daily lives. With the increasing number of connected IoT devices making our daily lives more convenient, it puts personal data at serious risk too. Radio frequency identification (RFID) contributes to IoT applications in the automatic identification of the connected devices. However, the primary concerns with the RFID tag connected devices are their security and privacy. The communication channel is deemed to be wireless or insecure between the tags and the readers, which makes RFID system vulnerable to the various known attacks. To deal with these security flaws, we have put forward a novel vector-space-based lightweight RFID authentication protocol for IoT environment named VLPRAP. The proposed protocol integrates vector space, linear mapping and basis mechanism that achieves secure authentication and improves security and privacy without increasing the computational cost. The correctness of the proposed VLPRAP protocol has been validated using BAN logic inference rules. The formal and informal security analysis demonstrates that our proposed protocol resists various malicious security threats, providing better security and higher efficiency. Furthermore, the performance analysis of our proposed protocol has been measured in terms of computation operations, storage requirement and communication overhead, which shows that better performance as compared to related existing protocols.

Semantic techniques for discovering architectural patterns in building information models

Architectural patterns, a concept devised by the Viennese architect Christopher Alexander, have inspired the world of patterns, especially in software engineering. Two objectives have been addressed in this work: to realise a semantic representation of Alexander's patterns by developing an OWL ontology, and to devise a rule-based system for discovering the patterns into a concrete building model, represented in IFC format, one of the pillars of the BIM - an approach now widely spread in the architectural and civil engineering design world. This paper shows how semantic and logical inference rules have been applied to discover Alexander's pattern on a generic IFC model of a building.

Semantic techniques for discovering architectural patterns in building information models

Architectural patterns, a concept devised by the Viennese architect Christopher Alexander, have inspired the world of patterns, especially in software engineering. Two objectives have been addressed in this work: to realise a semantic representation of Alexander's patterns by developing an OWL ontology, and to devise a rule-based system for discovering the patterns into a concrete building model, represented in IFC format, one of the pillars of the BIM - an approach now widely spread in the architectural and civil engineering design world. This paper shows how semantic and logical inference rules have been applied to discover Alexander's pattern on a generic IFC model of a building.

A Novel Understanding of Legal Syllogism as a Starting Point for better Legal Symbolic AI Systems

In the two most relevant categories of legal systems, the codified law systems and the case law systems, legal argumentation and legal reasoning are at the heart of legal theory and practice. Here we show that the concept of legal syllogism can be used as a starting point in both legal systems for new computational models of legal reasoning. We argue that legal syllogisms are not merely analytic logical inference rules but involve ampliative analogical inference. We aim to operationalize our account in terms of Context Graphs, i.e. internally consistent logical theories linked through rigorously defined analogical relations called views and argumentative relations such as attack and support.

Legal argumentation in Mesopotamia since Ur III

Abstract In this paper, I show that we can find some foundations of logic and legal argumentation in the tablets of Mesopotamia at least since the dynasty of Ur III. In these texts, we see the oldest correct application of logical inference rules (e.g. modus ponens). As concerns the legal argumentation established in Mesopotamia, we can reconstruct on the basis of the tablets the following rules of dispute resolutions during trials: (1) There are two parties of disputants: (i) a protagonist who formulates a standpoint and (ii) an antagonist who disagrees with the protagonist’s standpoint and formulates an alternative statement. (2) There is a rational judge represented by high-ranking citizens who should follow only logical conclusions from facts and law articles as premises.

Begriffsschrift’s Logic

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should be amended. In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument.

Forming a method for determining the coordinates of sound anomalies based on data from a computerized microphone system

Special features in the process of determining the coordinates of sound anomalies according to the sound series were considered. Sound anomalies have been shown to be a source of information about events, phenomena that are already occurring, or are their harbingers. It has been stated that audio interception systems complement thermal imagers and provide savings in financial and human resources when used in combination with the benefits of unmanned aerial vehicles. The methods facilitating solution of the problem of surveillance and prediction by finding coordinates of sound anomalies were presented. Indirect methods for solving problems of searching for sound anomaly coordinates with three microphones in accordance with a linear scheme of approximants and linear and quadratic approximation were proposed. Solutions were reduced to analytical complete expressions that make it possible to calculate coordinates according to the input conditions for three or four microphones. Also, a problem of finding coordinates of a sound anomaly for three and four microphones was set and solved by direct methods. Solutions were presented as expressions that make it possible to calculate coordinates of sound anomalies. Numerical experiments were performed during which coordinates of sound anomalies, the absolute error of their determination at each iteration, and total time spent for calculation were found. Systems with coordinates of microphones and sound sources almost identical or coinciding have been shown to have the greatest error. Under these conditions, for direct methods, values of the equation coefficients decreased to almost zero or turned to zero and the difference of values of the sought coordinates between iterations increased sharply which slowed down the process of solution convergence. It was shown that the application of approximate methods to the search for coordinates by solving the minimization problems with the involvement of the recurrent approximation method makes it possible to construct simple algorithms. Their implementation to solve the problems of numerical experiments has given quick and practically accurate coordinate values. It was found, that the application of algorithms to the methods of logical analysis and rules of logical inference reduces the number of iterations and the total calculation time

Learning Inference Rules from Data

This paper considers the possibility of designing AI that can learn logical or non-logical inference rules from data. We first provide an abstract framework for learning logics. In this framework, an agent $${{{\mathcal {A}}}}$$ provides training examples that consist of formulas S and their logical consequences T. Then a machine $${{{\mathcal {M}}}}$$ builds an axiomatic system that makes T a consequence of S. Alternatively, in the absence of an agent $$\mathcal{A}$$ , a machine $${{{\mathcal {M}}}}$$ seeks an unknown logic underlying given data. We next consider the problem of learning logical inference rules by induction. Given a set S of propositional formulas and their logical consequences T, the goal is to find deductive inference rules that produce T from S. We show that an induction algorithm LF1T, which learns logic programs from interpretation transitions, successfully produces deductive inference rules from input data. Finally, we consider the problem of learning non-logical inference rules. We address three case studies for learning abductive inference, frame axioms, and conversational implicature. Each case study uses machine learning techniques together with metalogic programming.

An Algorithm for Severity Estimation of Plant Leaf Diseases by the Use of Colour Threshold Image Segmentation and Fuzzy Logic Inference: A Proposed Algorithm to Update a “Leaf Doctor” Application

This paper explains a proposed algorithm for severity estimation of plant leaf diseases by using maize leaf diseased samples. In the literature, a number of researchers have addressed the problem of plant leaf disease severity estimation, but a few, such as Sannakki et al., have used fuzzy logic to determine the severity estimations of the plant leaf diseases. The present paper aims to update the current algorithm used in the “Leaf Doctor” application that is used to estimate the severities of the plant leaf diseases by introducing the benefits of fuzzy logic decision making rules. This method will contribute to precision agriculture technology as it introduces an algorithm that may be embedded in smartphone devices and used in applications, such as a “Leaf Doctor” application. The applications designed based on the algorithm proposed in this study will help users who are inexperienced and not plant pathologists understand the level of the estimated disease severity. The use of fuzzy logic inference rules along with image segmentation determines the novelty of this approach in comparison with the available methods in the literature.

Formal Method for Security Analysis of Electronic Payment Protocols

Electronic payment protocols play a vital role in electronic commerce security, which is essential for secure operation of electronic commerce activities. Formal method is an effective way to verify the security of protocols. But current formal method lacks the description and analysis of timeliness in electronic payment protocols. In order to improve analysis ability, a novel approach to analyze security properties such as accountability, fairness and timeliness in electronic payment protocols is proposed in this paper. This approach extends an existing logical method by adding a concise time expression and analysis method. It enables to describe the event time, and extends the time characteristics of logical inference rules. We analyzed the Netbill protocol with the new approach and found that the fairness of the protocol is not satisfied, due to timeliness problem. The result illustrates the new approach is able to analyze the key properties of electronic payment protocols. Furthermore, the new approach can be introduced to analyze other time properties of cryptographic protocols.

A logic-based framework for collection/item metadata relationships

PurposeThe purpose of this paper is to present a framework for the articulation of relationships between collection-level and item-level metadata as logical inference rules. The framework is intended to allow the systematic generation of relevant propagation rules and to enable the assessment of those rules for particular contexts and the translation of rules into algorithmic processes.Design/methodology/approachThe framework was developed using first order predicate logic. Relationships between collection-level and item-level description are expressed as propagation rules – inference rules where the properties of one entity entail conclusions about another entity in virtue of a particular relationship those individuals bear to each other. Propagation rules for reasoning between the collection and item level are grouped together in the framework according to their logical form as determined by the nature of the propagation action and the attributes involved in the rule.FindingsThe primary findings are the analysis of relationships between collection-level and item-level metadata, and the framework of categories of propagation rules. In order to fully develop the framework, the paper includes an analysis of colloquial metadata records and the collection membership relation that provides a general method for the translation of metadata records into formal knowledge representation languages.Originality/valueThe method for formalizing metadata records described in the paper represents significant progress in the application of knowledge representation techniques to problems of metadata creation and management, providing a flexible technique for encoding colloquial metadata as a set of statements in first-order logic. The framework of rules for collection/item metadata relationships has a range of potential applications for the enhancement or metadata systems and vocabularies.