Inference Rules Research Articles

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.

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.

Exploring the Definition of Non-Monotonicity – Logical and Psychological Considerations

When humans reason, they are able to revise their beliefs in light of new information and abandon obsolete conclusions. Logicians argued, that in some cases, such reasonings appear to be non-monotonic. Thus, many different, seemingly non-monotonic systems were created to formally model such cases. The purpose of this article is to re-examine the definition of non-monotonicity and its implementation in non-monotonic logics and in examples of everyday human reasoning. We will argue that many non-monotonic logics employ some weakened versions of the definitions of non-monotonicity, since in-between different steps of reasoning they either: a) allow previously accepted premises to be removed, or b) change the rules of inference. Of the two strategies, the second one seems downright absurd, since changing the rules of a given logic is a mere replacement of that logic with the rules of another. As a consequence we obtain two logics, whereas the definition of a non-monotonic logic is supposed to define one. The definition of non-monotonicity does not permit either of these cases, which means that such logics are monotonic.

Type-3 fuzzy neural networks for dynamic system control

This paper presents a Type-3 Fuzzy Neural Network (T3FNN) for dynamic system control. The structure of the T3FNN controller, which is based on the compositional rule of inference of interval type-3 fuzzy systems, is proposed. TSK-type fuzzy rules, employing three-dimensional membership functions (MFs) in the antecedent part and linear functions with coefficients represented as interval sets in the consequent part, are utilized to design T3FNN. Gaussian functions with uncertain centers are employed to describe the type-3 membership functions. By employing three-dimensional MFs, type-3 fuzzy logic rules can accurately model a high degree of uncertainty and effectively handle uncertain information. The design of the T3FNN was accomplished by integrating the type-3 fuzzy logic system (T3FLS) with neural networks. The learning of the T3FNN was conducted using the genetic algorithms and gradient descent algorithm. As a result, the type-3 rule base of the system was effectively developed. The learning algorithms are presented and the proposed T3FNN structure is employed for the development of dynamic system control. The simulations of the T3FNN system for the control of the nonlinear and time-varying dynamic systems were carried out. The results obtained from the simulations indicate the suitability of using the T3FNN in controlling dynamic systems.

Explanatory Games in International Relations

Abstract Explanation plays a central role in international relations (IR). However, as different conceptions of explanation inform our conduct of practices in IR inquiry, such centrality is far from being a settled matter in the discipline. These conceptions tend to be subsumed under broad dichotomies—such as explanation vs. understanding, constitutive vs. causal explanation, and positivism vs. interpretivism—which, in turn, generate a sense of a perennially divided discipline, obfuscating in this process the explanatory pluralism that characterises IR research. In this paper, I argue that different approaches to explanation coexist in IR, with different explanatory games being played by scholars in various fields of international inquiry. Explanatory games are characterised by constitutive rules, rules of representation, rules of inference, and rules of scope, all of which provide the basis for tailoring explanations. Scholars play the game that works best for their explanatory puzzles, following a specific set of rules that validate their form of explanation and thus achieve their research goals. Ultimately, explanation in the discipline is inherently plural. Examining this explanatory pluralism, therefore, requires investigating the rules of our explanatory games.

Formal analysis of signal protocol based on logic of events theory

The Signal is an end-to-end encrypted communication protocol composed of a double ratchet (DR) protocol and an extended triple Diffie-Hellman (X3DH) protocol. Its complex ratchet structure and the characteristics of protocol composition make it challenging to realize formal analysis. A formal analysis method based on logic of events theory (LoET) is proposed to conduct a security analysis of the Signal protocol. The method includes inference rules with key relation and key chain as the core to realize the formal analysis of ratchet structure, and the inference relation between sub-protocols is established by putting forward the composition theorem. The proposed method achieves a formal analysis of Signal, revealing that it does not satisfy a strong authentication property during the X3DH phase. The results show that the LoET-based method can be effectively applied in the formal analysis of Signal protocols, thus promoting the application and development of these protocols with ratchet structure and composition properties.

Space‐efficient data structures for the inference of subsumption and disjointness relations

AbstractConventional database systems function as static data repositories, storing vast amounts of facts and offering efficient query processing capabilities. The sheer volume of data these systems store has a direct impact on their scalability, both in terms of storage space and query processing time. Deductive database systems, on the other hand, require far less storage space since they derive new knowledge by applying inference rules. The challenge is how to efficiently obtain the required derivations, compared to having them in explicit form. In this study, we concentrate on a set of predefined inference rules for subsumption and disjointness relations, including their negations. We use compact data structures to store the facts and provide algorithms to support each type of relation, minimizing even further the storage space requirements. Our experimental findings demonstrate the feasibility of this approach, which not only saves space but is often faster than a baseline that uses well‐known graph traversal algorithms implemented on top of a traditional adjacency list representation to derive the relations.

On trivalent logics, probabilistic weak deduction theorems, and a general import-export principle

In this paper we first recall some results for conditional events, compound conditionals, conditional random quantities, p-consistency, and p-entailment. We discuss the equivalence between conditional bets and bets on conditionals, and review de Finetti's trivalent analysis of conditionals. But we go beyond de Finetti's early trivalent logical analysis and his later ideas, aiming to take his proposals to a higher level. We examine two recent articles that explore trivalent logics for conditionals and their definitions of logical validity and compare them with the approach to compound conditionals introduced by Gilio and Sanfilippo within the framework of conditional random quantities. As we use the notion of p-entailment, the full deduction theorem does not hold. We prove a Probabilistic Weak Deduction Theorem for conditional events. After that we study some variants of it, with further results, and we present several examples. Moreover, we illustrate how to derive new inference rules related to selected Aristotelian syllogisms. We focus on iterated conditionals and the invalidity of the Import-Export principle in the light of our Probabilistic Weak Deduction Theorem. We use the inference from a disjunction, A or B, to the conditional, if not-A then B, as an example to show the invalidity of this principle. We introduce a General Import-Export principle by examining examples and counterexamples. In particular, when considering the inference rules of System P, we find that a General Import-Export principle is satisfied, even if the assumptions of the Probabilistic Weak Deduction Theorem do not hold. We also deepen further aspects related to p-entailment and p-consistency. Finally, we briefly discuss some related work relevant to AI.

Exploring Quadrilaterals: An Interactive Task for 7th Grade Students Using GeoGebra Classroom

Using a Dynamic Geometry System (DGS) students can engage in a dynamic learning process that allows them to experiment, create strategies, make conjectures, argue, and deduce mathematical properties. A DGS enables the introduction of proofs, by providing visual aids. The proof of the conjectures made emerges as the next step towards formalising and understanding the contents covered and the introduction of automated deduction systems at schools can be an added value. The implementation of automated deduction systems in schools faces several challenges, such as curriculum-issues, teacher knowledge and the discrepancy between automated theorem provers and traditional practices of proving in schools. Synthetic provers based on a set of inference rules and forward chaining reasoning may provide a possible help to these challenges. With the aim of introducing formal proofs and inspiring students towards this goal, a geometric conjecture was chosen for 7th grade students to engage with, based on a rule set discussed in a previous work, “A rule based theorem prover: an introduction to proofs in secondary schools”. The study also aimed to showcase the application of a Geometry Automated Theorem Prover within the classroom setting. A sequence of tasks was created for students to complete using GeoGebra Classroom. In the first phase, they were asked to identify quadrilaterals, construct a parallelogram, and measure sides and angles until they formulated a conjecture, which was strengthened by the dynamic possibility of changing the constructed parallelogram. In the second phase, the students were provided with four rules and were asked to justify their results using these rules. By the end of these justifications, the students had a complete proof of the initial conjecture. A short video of the proof made using JGEx (Java Geometry Expert) was also shown to the students.

A fuzzy control algorithm based on artificial intelligence for the fusion of traditional Chinese painting and AI painting

Recently, artificial intelligence (AI)-generated resources have gained popularity because of their high effectiveness and reliability in terms of output and capacity to be customized and broadened, especially in image generation. Traditional Chinese paintings (TCPs) are incomplete because their color contrast is insufficient, and object reality is minimal. However, combining AI painting (AIP) with TCP remains inadequate and uncertain because of image features such as patterns, styles, and color. Hence, an algorithm named variational fusion-based fuzzy accelerated painting (VF2AP) has been proposed to resolve this challenge. Initially, the collected TCP data source is applied for preprocessing to convert it into a grayscale image. Then, the feature extraction process is performed via fuzzy-based local binary pattern (FLBP) and brushstroke patterns to enhance the fusion of intelligent fuzzy logic to optimize the local patterns of textures in a noisy image. Second, the extracted features are used as inputs to the variational autoencoder (VAE), which is used to avoid latent space irregularities in the image and the reconstructed image by maintaining minimum reconstruction loss. Third, fuzzy inference rules are applied to avoid variation in the fusion process of the reconstructed and original images. Fourth, the feedback mechanism is designed with evaluation metrics such as area under the curve-receiver operating characteristic (AUC-ROC) analysis, mean square error (MSE), structural similarity index (SSIM), and Kullback‒Leibler (KL) divergence to enhance the viewer's understanding of fused painting images.

Evaluation of Total Risk-Weighted Assets in Islamic Banking through Fintech Innovations

The assessment of total risk-weighted assets (LTRWAs) in the banking sector is of the utmost importance. It serves as a critical component for regulatory compliance, risk management, and capital adequacy. By accurately assessing LTRWAs, banks can effectively meet regulatory requirements, efficiently allocate capital resources, and proactively manage risks. Moreover, the accurate assessment of LTRWAs supports performance evaluation and fosters investor confidence in the financial stability of banks. This study presents statistical analyses and machine learning methods to identify factors influencing LTRWAs. Data from Bahrain, Jordan, Qatar, the United Arab Emirates, and Yemen, spanning from 2010 to 2021, was utilized. Various statistical tests and models, including ordinary least squares, fixed effect, random effect, correlation, variance inflation factor, tolerance tests, and fintech models, were conducted. The results indicated significant impacts of the unemployment rate, inflation rate, natural logarithm of the loan-to-asset ratio, and natural logarithm of total assets on LTRWAs in regression models. The dataset was divided into a training group (90% of the data) and a testing group (10% of the data) to evaluate the predictive capabilities of various fintech models, including an adaptive network-based fuzzy inference system (ANFIS), a hybrid neural fuzzy inference system (HyFIS), a fuzzy system with the heuristic gradient descent (FS.HGD), and fuzzy inference rules with the descent method (FIR.DM) models. The selection of the optimal model is contingent upon assessing its performance according to specific error criteria. The HyFIS model outperformed others with lower errors in predicting LTRWAs. Independent t-tests confirmed statistically significant differences between original and predicted LTRWA for all models, with HyFIS showing closer predictions. This study provides valuable insights into LTRWA prediction using advanced statistical and machine learning techniques, based on a dataset from multiple countries and years.

Grounding operators: transitivity and trees, logicality and balance

We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and logical operators. Without fixing a particular notion of grounding or grounding relation, we present inferential rules that define, once a base grounding calculus has been fixed, three grounding operators: an operator for immediate grounding, one for mediate grounding – corresponding to the transitive closure of the immediate grounding one – and a grounding tree operator, which enables us to internalise chains of immediate grounding claims without losing any information about them. We then present an in-depth proof-theoretical study of the introduced rules by focussing, in particular, on the question whether grounding operators can be considered as logical operators and whether balanced rules for grounding operators can be defined.

ALLSTAR: Inference of ReliAble CausaL RuLes between Somatic MuTAtions and CanceR Phenotypes.

Recent advances in DNA sequencing technologies have allowed the detailed characterization of genomes in large cohorts of tumors, highlighting their extreme heterogeneity, with no two tumors sharing the same complement of somatic mutations. Such heterogeneity hinders our ability to identify somatic mutations important for the disease, including mutations that determine clinically relevant phenotypes (e.g., cancer subtypes). Several tools have been developed to identify somatic mutations related to cancer phenotypes. However, such tools identify correlations between somatic mutations and cancer phenotypes, with no guarantee of highlighting causal relations. We describe ALLSTAR, a novel tool to infer reliable causal relations between somatic mutations and cancer phenotypes. ALLSTAR identifies reliable causal rules highlighting combinations of somatic mutations with the highest impact in terms of average effect on the phenotype. While we prove that the underlying computational problem is NP-hard, we develop a branch-and-bound approach that employs protein-protein interaction networks and novel bounds for pruning the search space, while properly correcting for multiple hypothesis testing. Our extensive experimental evaluation on synthetic data shows that our tool is able to identify reliable causal relations in large cancer cohorts. Moreover, the reliable causal rules identified by our tool in cancer data show that our approach identifies several somatic mutations known to be relevant for cancer phenotypes as well as novel biologically meaningful relations. Code, data, and scripts to reproduce the experiments available at https://github.com/VandinLab/ALLSTAR. Supplementary data are available at Bioinformatics online.

Rethinking the Criteria for Liberal Education Courses

Sheldon Rothblatt argues that the subject does not define liberal education but rather that anything taught liberally constitutes liberal education. We partially agree with Rothblatt's assertion. In short, while we concur with his claim that not all traditional liberal arts automatically constitute liberal education, we believe that for liberal education to be taught and learned liberally, the curriculum should be centered around the traditional liberal arts. This argument unfolds in three distinct phases, each contributing to a deeper understanding of liberal education. The first phase delves into the elements that define liberal education, drawing on Rothblatt's assertion and the case of Harvard's general education. This analysis presents civic engagement and adaptability as crucial yet often overlooked components of liberal education. In the second phase, we introduce the concepts of ‘fundamentality’ and ‘openness’ as pivotal to liberal teaching within liberal education. ‘Fundamentality’ refers to the ability to question fundamental principles, laws, and assumptions openly. To satisfy these elements, we argue that disciplines from the traditional liberal arts are indispensable in liberal education. The final phase will demonstrate the need for ‘fundamentality’ and ‘openness’ through the example of logical education. We will illustrate issues that arise from using inference rules of classical logic without precisely understanding their meaning and show that overcoming these problems requires openness to questioning. This will show why the liberal education curriculum should be structured around traditional liberal arts disciplines.

Construction of a fuzzy model for managing the process of forming IT-competences

The relevance of this study is predetermined by the lack of models and algorithms for managing the formation of IT competencies in children of senior preschool age in the information and educational environment of a preschool organization. The object of the study is the process of managing the formation of IT competencies in children of senior preschool age. The problem under study is the need to build an effective system for assessing and managing the level of IT competencies, taking into account the uncertainty and subjectivity of assessments, as well as ensuring flexibility and adaptability of the process of developing competencies. The constructed model based on fuzzy logic takes into account the uncertainty of assessments and decomposes competencies into indicators of achievement (low, medium, high levels). The production model of knowledge representation based on fuzzy inference rules enables control adaptability. As a result, recommendations were compiled for assessing and developing competencies taking into account the individual characteristics of children and the educational environment. The approaches and tools proposed in this study help improve the quality of preschool education by providing teachers with effective tools for managing the educational process in the context of digitalization. The essence of the results is to build a model that makes it possible to integrate uncertain and subjective data into the process of assessing IT competencies, providing more accurate and objective assessments. The results could be used in the information and educational environments of preschool organizations, as well as in education systems that introduce modern technologies for assessing and managing competencies

Naturalizing relevance realization: why agency and cognition are fundamentally not computational.

The way organismic agents come to know the world, and the way algorithms solve problems, are fundamentally different. The most sensible course of action for an organism does not simply follow from logical rules of inference. Before it can even use such rules, the organism must tackle the problem of relevance. It must turn ill-defined problems into well-defined ones, turn semantics into syntax. This ability to realize relevance is present in all organisms, from bacteria to humans. It lies at the root of organismic agency, cognition, and consciousness, arising from the particular autopoietic, anticipatory, and adaptive organization of living beings. In this article, we show that the process of relevance realization is beyond formalization. It cannot be captured completely by algorithmic approaches. This implies that organismic agency (and hence cognition as well as consciousness) are at heart not computational in nature. Instead, we show how the process of relevance is realized by an adaptive and emergent triadic dialectic (a trialectic), which manifests as a metabolic and ecological-evolutionary co-constructive dynamic. This results in a meliorative process that enables an agent to continuously keep a grip on its arena, its reality. To be alive means to make sense of one's world. This kind of embodied ecological rationality is a fundamental aspect of life, and a key characteristic that sets it apart from non-living matter.

A neuro-fuzzy security risk assessment system for software development life cycle

This study aims to protect software development by creating a Software Risk Assessment (SRA) model for each phase of the Software Development Life Cycle (SDLC) using an Adaptive Neuro-Fuzzy Inference System (ANFIS) model. Software developers discovered and validated the risk variables affecting each SDLC phase, following which relevant data about risk factors and associated SRA for each SDLC phase were collected. To create the SRA model for SDLC phases, risk factors were used as inputs, and SRA was used as an output. The formulated model was simulated using 70 % and 80 % of the data for training, while 30 % and 20 % were used for testing the model. The performance of the SRA models using the test datasets was evaluated based on accuracy. According to the study findings, many risk variables were discovered and confirmed for the requirement, design, implementation, integration, and operation phases of SDLC 11, 8, 9, 4, and 6, respectively. The SRA model was formulated using the risk factors using 2048, 256, 512, 16, and 64 inference rules for the requirement, design, implementation, integration, and operation phases, respectively. The study concluded that using the SRA model to assess security risk at each SDLC phase provided a secured software development process.

Wittgenstein and the liar

Ludwig Wittgenstein’s remarks on contradictions and paradoxes have been met with incomprehension and have fueled the widespread and long-standing prejudice that his later thoughts on the foundations of logic and mathematics are the “surprisingly insignificant product of a sparkling mind” (Kreisel, British Journal for the Philosophy of Science 9:135–158, 1959, p. 158). This paper disagrees; it argues that Wittgenstein’s remarks on semantic paradoxes suggest an account of the Liar and its kin that is not only of historical interest but also represents a hitherto unnoticed paraconsistent alternative to established approaches to the Liar. In what follows, a reading of Wittgenstein’s remarks will be offered according to which Wittgenstein subscribes to a form of dialetheism (that is, the view that there are sentences that are both true and false). In contrast to modern dialetheist approaches to the Liar, however, some of Wittgenstein’s remarks suggest combining a dialetheist position with what is called ‘logical nihilism’ (that is, the view that there are no universally valid inference rules).

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.