This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture (...) and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are (...) discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

The third volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents an in-depth exploration of the cutting-edge developments in uncertain combinatorics and set theory. This comprehensive collection highlights innovative methodologies such as graphization, hyperization, and uncertainization, which enhance combinatorics by incorporating foundational concepts from fuzzy, neutrosophic, soft, and rough set theories. These advancements open new mathematical horizons, offering novel approaches to managing uncertainty within complex systems. Combinatorics, a discipline focused (...) on counting, arrangement, and structure, often faces challenges when uncertainty is present. Set theory, which underpins combinatorial problems, has evolved to tackle these challenges. The introduction of fuzzy and neutrosophic sets has expanded the toolkit for modeling uncertainty by incorporating elements of truth, indeterminacy, and falsehood into decision-making processes. These innovations seamlessly intersect with graph theory, providing new ways to represent uncertain structures through "graphized" forms such as hypergraphs and superhypergraphs. This volume also introduces advanced concepts like Neutrosophic Oversets, Undersets, and Offsets, which push the boundaries of classical graph theory and offer deeper insights into the mathematical and practical challenges posed by real-world systems. By blending combinatorics, set theory, and graph theory, the authors have created a robust framework for addressing uncertainty in both mathematical systems and their real-world applications. This foundation sets the stage for future breakthroughs in combinatorics, set theory, and related fields. Each chapter in this volume contributes both theoretical foundations and practical applications, demonstrating the power of integrating graph theory, set theory, and uncertainty models. The new ideas, algorithms, and mathematical tools presented here will drive the future of combinatorial research and its applications in uncertain environments. In the first chapter, “Introduction to Upside-Down Logic: Its Deep Relation to Neutrosophic Logic and Applications”, the authors present Upside-Down Logic, a novel logical framework that systematically transforms truths into falsehoods and vice versa, based on contextual shifts. Introduced by F. Smarandache, this paper provides a mathematical definition of Upside-Down Logic, including applications related to the Japanese language. The chapter also introduces Contextual Upside-Down Logic, an extension that adjusts logical connectives alongside flipped truth values, as well as Indeterm-Upside-Down Logic and Certain Upside-Down Logic to address indeterminacy. A simple algorithm is also proposed to demonstrate the computational aspects of this logic. In the second chapter, “Local-Neutrosophic Logic and Local-Neutrosophic Sets: Incorporating Locality with Applications”, the authors introduce Local-Neutrosophic Logic and Local-Neutrosophic Sets, which integrate the concept of locality into Neutrosophic Logic. By defining locality as the influence of immediate surroundings on an object or system, this chapter explores how it affects indeterminacy in real-world problems. The paper also examines potential applications and provides mathematical definitions for these new concepts. The third chapter, “A Review of Fuzzy and Neutrosophic Offsets: Connections to Some Set Concepts and Normalization Function”, extends the concept of offsets in uncertain set-theoretic frameworks, such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets. This chapter introduces several advanced types of offsets, including Nonstationary Fuzzy Offset, Multi-valued Plithogenic Offset, and Subset-valued Neutrosophic Offset, offering deeper insights into handling uncertainty in mathematical models. In the fourth chapter, “Review of Plithogenic Directed, Mixed, Bidirected, and Pangene OffGraph”, the authors build upon Plithogenic Graphs to propose extensions such as Plithogenic Directed OffGraph, Plithogenic BiDirected OffGraph, and Plithogenic Mixed OffGraph. These new concepts, including the Plithogenic Pangene OffGraph, are explored in detail, with a focus on their mathematical properties and potential applications in uncertain graph theory. The fifth chapter, “Short Note on Neutrosophic Closure Matroids”, explores the extension of matroid concepts into Neutrosophic and Turiyam Neutrosophic set theories, introducing Neutrosophic closure matroids. This concept integrates uncertainty, indeterminacy, and liberal states into matroid theory, enhancing its applicability in optimization and combinatorial problems. In the sixth chapter, “Some Graph Parameters for Superhypertree-width and Neutrosophic Tree-width”, the authors discuss graph parameters such as Superhypertree-width and Neutrosophic tree-width. These parameters play a crucial role in the study of graph characteristics, particularly in algorithms and real-world applications. The chapter explores the generalization of hypergraphs to SuperHyperGraphs and examines how these concepts extend tree-width parameters within the context of Neutrosophic logic. (shrink)

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina (...) Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar. (shrink)

Analytical philosophy is ruled by the alliance of logic, linguistics and mathematics since its beginnings in the syllogistic calculus of terms and premises in Aristotle's Analytica protera, in the theories of medieval logic that dealt with what are Proprietatis Terminorum (significatio, suppositio, appellatio), in the theological apologetics of argumentation with the combinatorics of symbols by Raymundus Llullus in the work Ars Magna, Generalis et Ultima (1305-08), in what is presented as Theologia Combinata (cf. Tomus II.p.251) in Ars Magna (...) Sciendi sive Combinatoria by Athanasius Kircher (1669), in analytical combinatorics based in Leibniz's dissertation Ars Combinatoria (1666), where language is understood as a lingua characteristica and as a calculus ratiocinator, in the combinatorics of classes that have the meanings 1 or 0 given in the idea of Boolean functions (1854), in Frege's work Begriffschrift, eine der arithmeticeschen nachgebildete Fomelsprache des reinen Denkens (Concept letter, the language of formulas of pure thought made according to the model in arithmetical language), in Cantor's study of set theory / Grundlagen einer allgemeinen Mannigfaltigkeitstheorie (1883) and up to algorithms of fuzzy logic as a "means of approximate thinking that is in the human prior" (Zadeh, 1990) and fuzzy linguistics in computer semantics (Burghard B. Rieger, 1993). These are all the philosophical ideas of mathematicians and logicians that founded what we call logical pragmatism here as a demand that logic be absolutely used in every way in which it will dominate the grammar of language until logic itself becomes the philosophical grammar of the mind!!! (shrink)

This article focuses on the criticisms of current approaches in educational research methodology. Itsummarizes rationales for mixed methods and argues that the mixing quantitative paradigm andqualitative paradigm is problematic due to practical and philosophical arguments. It is alsoindicated that the current rise of mixed methods work has increased problems with quantitativeand qualitative methods. In this article we offer a different symbolic system, with differentlogical form for describing educational phenomena based on the philosophical assumptions andnew mathematical reasoning: para-quantitativism. Para-quantitative theory (...) is an approachwhich has been developed in respect to close relationship between paradigm and method, using apostpositivist transcendental realism as a philosophical beginning of the research methodology,taking Operational Logic System or Fuzzy Logic System (OLS/FLS) as logic of scientificresearch in education. (shrink)

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the (...) values it takes, which represent the possible results and the possible indeterminacy. Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples. -/- . (shrink)

Accurate and precise trajectory tracking is crucial for a quadrotor to operate in disturbed environments. This paper presents a novel tracking hybrid controller for a quadrotor UAV that combines the Adaptive and Fuzzy logic controller. The Adaptive fuzzy controller is implemented to govern the behavior of two degrees of freedom quadrotor UAV. The proposed controller allows controlling the movement of UAVs to track a given trajectory in a 2D vertical plane. The Fuzzy Logic system provides (...) an automatic adjustment of the Adaptive parameters to reduce tracking errors and improve the quality of the controller. The results showed perfect behavior for the control law to control a quadrotor trajectory tracking task. To show the effectiveness of the intelligent controller, simulation results are given to confirm the advantages of the proposed control method, compared with Fuzzy and Proportional integral derivative (PID) control methods. (shrink)

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and (...) to not exist at the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the (...) system is sound and complete, and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

Proportional integral observer (PIO) for tracking a nonlinear method has a lower sentiency to cipher the state and output variables. So a more nonlinear controller has to be else to control to activity. In this paper, a fuzzy logic (FLC) controller has been added to the PIO to meliorate the calculation transmute. A fuzzy proportional integral observer (FPIO) for following a nonlinear system has been premeditated to decimate the susceptibleness to cipher the tell and turnout variables with (...) the existent posit and product variables. The FPIO controller has been tested for improving the estimation control using a nonlinear quarter vehicle active suspension system with a nonlinear hydraulic actuator. A comparison simulation of the proposed nonlinear system for estimating the state variables and tracking the output (suspension deflection) with a set point bump road disturbance using FPIO and PIO. The comparison simulation result shows that the estimated state variables and system output match the actual ones perfectly using a fuzzy PIO controller. (shrink)

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and (...) Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018). (shrink)

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy (...) them. It turns out that the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics. (shrink)

An AC servomotor which is mostly a two-phase induction motor with two stator field coils placed 90 electrical degrees apart used for controlling position, speed and acceleration in manufacturing industries. In this paper, a two-phase induction motor has been designed with a fuzzy logic and observer based controllers to improve the performance of the system. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done using (...) Matlab/Simulink toolbox and a promising result obtained. (shrink)

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing (...) measures in refined neutrosophic fuzzy sets. (shrink)

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in (...) the graphing of mutually referential triples. (shrink)

Book information: Deviant Logic, Fuzzy Logic: Beyond The Formalism. By SUSAN HAACK. Chicago, Ill.: University of Chicago Press, 1996. Pp. xxvi, 291.

Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Gödel (Kurt Gödel collected works (Volume I) Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski (Actes du Congrés International de Philosophie Scientifique, VI. Philosophie des Mathématiques, Actualités Scientifiques et Industrielles 393:58–61, 1936) to be a countably many valued logic. In this paper, we provide alternative proofs for these theorems by using models of Kripke (J Symbol Logic 24(1):1–14, (...) 1959). Gödel’s proof gave rise to an intermediate propositional logic (between intuitionistic and classical), that is known nowadays as Gödel or the Gödel-Dummett Logic, and is studied by fuzzy logicians as well. We also provide some results on the inter-definability of propositional connectives in this logic. (shrink)

The main target of this paper is to control the speed of DC motor by comparing the actual and the desired speed set point. The DC motor is designed using Fuzzy logic and MPC controllers. The comparison is made between the proposed controllers for the control target speed of the DC motor using square and white noise desired input signals with the help of Matlab/Simulink software. It has been realized that the design based on the fuzzy (...) class='Hi'>logic controller track the set pointwith the best steady state and transient system behavior than the design with MPC controller. Finally, the comparative simulation result prove the effectiveness of the DC motor with fuzzy logic controller. (shrink)

Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned from foremost philosophers, mathematicians and philosophers of science, to address (...) the wide range of problematics and influences in this most important strand of Deleuze’s thinking. Contributors are Charles Alunni, Alain Badiou, Gilles Châtelet, Manuel DeLanda, Simon Duffy, Robin Durie, Aden Evens, Arkady Plotnitsky, Jean-Michel Salanskis, Daniel Smith and David Webb. (shrink)

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic (...) integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description (...) logic as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions R t and R T of R and their fuzzy extensions FRt and FRT , respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics.

This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and R T of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and R T, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social (...) scientists who wish to work with multi expert models. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...) the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

In this paper, a Magnetic Levitation (MAGLEV) train is designed with a single degree of freedom electromagnet-based system that allows the train to levitate vertically up and down. Fuzzy logic, PID and Mras controllers are used to improve the Magnetic Levitation train passenger comfort and road handling. A matlab Simulink model is used to compare the performance of the three controllers using step input signals. The stability of the Magnetic Levitation train is analyzed using root locus technique. Controller (...) output response for different time period and change of air gap with different time period is analyzed for the three controllers. Finally the comparative simulation and experimental results demonstrate the effectiveness of the presented fuzzy logic controller. (shrink)

While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions are (...) required, and mathematical criteria were derived to design molecular models capable of pattern generation. The classical embryological feature of proportion regulation can be incorporated into the models. The conditions are mathematically necessary for the simplest two-factor case, and are likely to be a fair approximation in multi-component systems in which activation and inhibition are systems parameters subsuming the action of several agents. Gradients, symmetric and periodic patterns, in one or two dimensions, stable or pulsing in time, can be generated on this basis. Our basic concept of autocatalysis in conjunction with lateral inhibition accounts for self-regulatory biological features, including the reproducible formation of structures from near-uniform initial conditions as required by the logic of the generation cycle. Real tissue form, for instance that of budding Hydra, may often be traced back to local curvature arising within an initially relatively flat cell sheet, the position of evagination being determined by morphogenetic fields. Shell theory developed for architecture may also be applied to such biological processes. (shrink)

A generalized information theory is proposed as a natural extension of Shannon's information theory. It proposes that information comes from forecasts. The more precise and the more unexpected a forecast is, the more information it conveys. If subjective forecast always conforms with objective facts then the generalized information measure will be equivalent to Shannon's information measure. The generalized communication model is consistent with K. R. Popper's model of knowledge evolution. The mathematical foundations of the new information theory, the generalized (...) communication model , information measures for semantic information and sensory information, and the coding meanings of generalized entropy and generalized mutual information are introduced. Assessments and optimizations of pattern recognition, predictions, and detection with the generalized information criterion are discussed. For economization of communication, a revised version of rate-distortion theory: rate-of-keeping-precision theory, which is a theory for datum compression and also a theory for matching an objective channels with the subjective understanding of information receivers, is proposed. Applications include stock market forecasting and video image presentation. (shrink)

In 1685, in The Art of Discovery, Leibniz set down an extraordinary idea: "The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [calculemus], without further ado, to see who is right." Calculemus.

Intermediary metabolism molecules are orchestrated into logical pathways stemming from history (L-amino acids, D-sugars) and dynamic constraints (hydrolysis of pyrophosphate or amide groups is the driving force of anabolism). Beside essential metabolites, numerous variants derive from programmed or accidental changes. Broken down, variants enter standard pathways, producing further variants. Macromolecule modification alters enzyme reactions specificity. Metabolism conform thermodynamic laws, precluding strict accuracy. Hence, for each regular pathway, a wealth of variants inputs and produces metabolites that are similar to but not (...) the exact replicas of core metabolites. As corollary, a shadow, paralogous metabolism, is associated to standard metabolism. We focus on a logic of paralogous metabolism based on diversion of the core metabolic mimics into pathways where they are modified to minimize their input in the core pathways where they create havoc. We propose that a significant proportion of paralogues of well-characterized enzymes have evolved as the natural way to cope with paralogous metabolites. A second type of denouement uses a process where protecting/deprotecting unwanted metabolites - conceptually similar to the procedure used in the laboratory of an organic chemist - is used to enter a completely new catabolic pathway. (shrink)

I aim to develop a tool for comparing theories of vagueness, using Structured Query Language. Relevant SQL snippets will be used throughout.

The major point in [1] chapter 2 is the following claim: “Any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction.” So, in the case we wish to save Classical Logic we should change our Computational Model. As we see in chapter two, the mentioned contradiction is about and around the concept of time, as it is in the contradiction of modified version of paradox. It is (...) natural to try fabricating the paradox not by time but in some other linear ordering or the concept of space. Interestingly, the attempts to have similar contradiction by the other concepts like space and linear ordering, is failed. It is remarkable that, the paradox is considered either Epistemological or Logical traditionally, but by new considerations the new version of paradox should be considered as either Logical or Physical paradox. Hence, in order to change our Computational Model, it is natural to change the concept of time, but how? We start from some models that are different from the classical one but they are intuitively plausible. The idea of model is somewhat introduced by Brouwer and Husserl [3]. This model doesn’t refute the paradox, since the paradox and the associated contradiction would be repeated in this new model. The model is introduced in [2]. Here we give some more explanations. (shrink)

This essay presents Husserl’s Formal and Transcendental Logic (1929) in three main sections following the layout of the work itself. The first section focuses on Husserl’s introduction where he explains the method and the aim of the essay. The method used in FTL is radical Besinnung and with it an intentional explication of proper sense of formal logic is sought for. The second section is on formal logic. The third section focuses on Husserl’s “transcendental logic,” which (...) is needed to make Husserl’s conception complete, i.e., to understand what makes Besinnung radical, how the proper sense of formal logic has been reached and how all this relates to transcendental constitution of an object in the world. Husserl’s work is connected to his context (in exact sciences) and the relevance of his views for the contemporary approaches is discussed. (shrink)

The reason ability of considering time as a fuzzy concept is demonstrated in [7],[8]. One of the major questions which arise here is the new definitions of Complexity Classes. In [1],[2],…,[11] we show why we should consider time a fuzzy concept. It is noticeable to mention that that there were many attempts to consider time as a Fuzzy concept, in Philosophy, Mathematics and later in Physics but mostly based on the personal intuition of the authors or as (...) a style of Fuzzifying different various of the concepts. Consequently, fuzzifying time doesn’t go to be popular. In the new attempts we are trying to show why we are somewhat forced to consider time as a Fuzzy concept. It is mostly based on the “Unexpected Hanging Paradox” introduced by a Swedish Mathematician Lennart Ekbom. Our question is:” what will be the impact of it in Theory of Computation and Physics?”. Here, we discuss about the impact of fuzzifying time on Theory of Computation. (shrink)

We expect the laws of nature that describe the universe to be exact, but what if that isn't true? In this popular science article, I discuss the possibility that some candidate fundamental laws of nature, such as the Past Hypothesis, may be vague. This possibility is in conflict with the idea that the fundamental laws of nature can always and faithfully be described by classical mathematics. -/- [Bibliographic note: this article is featured on the magazine website under a different title (...) as "The fuzzy law that could break the idea of a mathematical universe" and on the magazine cover as "The Flaw at the Heart of Reality: Why precise mathematical laws can never fully explain the universe." It is a popular version of the article "Nomic Vagueness" that can be found on arXiv: 2006.05298.]. (shrink)

In this paper, a Magnetic Levitation (MAGLEV) train is designed with a first degree of freedom electromagnetbased totally system that permits to levitate vertically up and down. Fuzzy logic, PID and MRAS controllers are used to improve the Magnetic Levitation train passenger comfort and road handling. A Matlab Simulink model is used to compare the performance of the three controllers using step input signals. The stability of the Magnetic Levitation train is analyzed using root locus technique. Controller output (...) response for different time period and change of air gap with different time period is analyzed for the three controllers. Finally the comparative simulation and experimental results demonstrate the effectiveness of the presented fuzzy logic controller. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...) the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

View more Abstract If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. ‘Televisions are televisions’ and ‘TVs are televisions’ neither sound alike nor are used interchangeably. Interception synonymy gets assumed because (...) logical sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The ‘=’ of mathematics is an objectual relation between numbers; the ‘=’ of logic marks a syntactic relation of coreferring terms. -/- . (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar (...) efforts continue, but have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can (...) be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the (...) basic theory faces. The final view appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)

Shell tube surface condenser (STSC) is a heat exchanger system that exchange a high pressure steam into low pressure water and it is widely used in applications like textile industries and nuclear power plants. The modelling of the system has been established based on lumped parameters. In this paper, a fuzzy expert system is developed in order to improve the performance of the condenser. A pressure feedback system has been developed to analyze the effect of the condenser output temperature, (...) circulating water flow and heat developed. An experiment has been made for the closed loop system using fuzzy tuned PI, fuzzy logic and PID controllers and a promising results have been obtained successfully. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency (...) about the width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are (...) vulnerable to such arguments while mathematical, logical, and normative beliefs are not—the very construction of Harman-style skeptical arguments requires the truth of significant fragments of our mathematical, logical, and normative beliefs, but requires no such thing of our moral beliefs. Given this property, Harman-style skeptical arguments against logical, mathematical, and normative beliefs are self-effacing; doubting these beliefs on the basis of such arguments results in the loss of our reasons for doubt. But we can cleanly doubt the truth of morality. (shrink)