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Статті в журналах з теми "Algebraic category of LM-logic algebras"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

Ciungu, Lavinia Corina. "Convergence with a fixed regulator in perfect MV-algebras." Demonstratio Mathematica 41, no. 1 (2008): 1–10. http://dx.doi.org/10.1515/dema-2013-0044.

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AbstractMV-algebras were introduced by Chang as an algebraic counterpart of the Łukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian

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2

Ion, C. Baianu, Georgescu George, F. Glazebrook James, and Brown Ronald. "BRAIN Journal - Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 1–11. https://doi.org/10.5281/zenodo.1037321.

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ABSTRACT The fundamentals of ÃLukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the Schr¨odinger representation, with both initial and boundary

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3

Adámek, Jiří, Liang-Ting Chen, Stefan Milius, and Henning Urbat. "Reiterman’s Theorem on Finite Algebras for a Monad." ACM Transactions on Computational Logic 22, no. 4 (2021): 1–48. http://dx.doi.org/10.1145/3464691.

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Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes of finite algebras closed under finite products, subalgebras and quotients. In this article, Reiterman’s theorem is generalized to finite Eilenberg-Moore algebras for a monad T on a category D: we prove that a class of finite T -algebras is a pseudovariety iff it is presentable by profinite equations. As a key technical tool, we introduce the concept of a profinite monad T ^ associated to the monad T , which gi

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4

Coniglio, Marcelo E., Aldo Figallo-Orellano, and Ana Claudia Golzio. "Non-deterministic algebraization of logics by swap structures1." Logic Journal of the IGPL 28, no. 5 (2018): 1021–59. http://dx.doi.org/10.1093/jigpal/jzy072.

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Abstract Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are

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5

PAVLOVIĆ, DUšKO. "Categorical logic of names and abstraction in action calculi." Mathematical Structures in Computer Science 7, no. 6 (1997): 619–37. http://dx.doi.org/10.1017/s0960129597002296.

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Milner's action calculus implements abstraction in monoidal categories, so that familiar λ-calculi can be subsumed together with the π-calculus and the Petri nets. Variables are generalised to names, which allow only a restricted form of substitution.In the present paper, the well-known categorical semantics of the λ-calculus is generalised to the action calculus. A suitable functional completeness theorem for symmetric monoidal categories is proved: we determine the conditions under which the abstraction is definable. Algebraically, the distinction between the variables and the names boils do

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6

Basti, Gianfranco. "The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic." Philosophies 7, no. 6 (2022): 121. http://dx.doi.org/10.3390/philosophies7060121.

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This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pur

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7

Grosu, Radu, Dorel Lucanu, and Gheorghe Stefanescu. "Mixed Relations as Enriched Semiringal Categories." JUCS - Journal of Universal Computer Science 6, no. (1) (2000): 112–29. https://doi.org/10.3217/jucs-006-01-0112.

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A study of the classes of finite relations as enriched strict monoidal categories is presented in [CaS91]. The relations there are interpreted as connections in flowchart schemes, hence an angelic theory of relations is used. Finite relations may be used to model the connections between the components of dataflow networks [BeS98, BrS96], as well. The corresponding algebras are slightly different enriched strict monoidal categories modeling a forward-demonic theory of relations. In order to obtain a full model for parallel programs one needs to mix control and reactive parts, hence a richer the

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8

Corradini, Andrea, Hartmut Ehrig, Grzegorz Rozenberg, and Gabriele Taentzer. "Introduction." Mathematical Structures in Computer Science 12, no. 2 (2002): 111. http://dx.doi.org/10.1017/s0960129501003504.

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This special issue of Mathematical Structures in Computer Science is devoted to the theory and applications of graph transformations. This research area dates back to the early seventies and is based on mathematical techniques from graph theory, algebra, logic and category theory. The theory of graph transformations has become attractive as a modelling and programming paradigm for complex graphical structures in a large variety of areas in computer science and for applications to other fields. During the Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems (GRATRA 2000) – a satel

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9

Sharma, Amit. "On the Left Properness of the Model Category of Permutative Categories." Axioms 12, no. 1 (2023): 87. http://dx.doi.org/10.3390/axioms12010087.

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In this paper, we introduce a notion of free cofibrations of permutative categories. We show that each cofibration of permutative categories is a retract of a free cofibration. The main goal of this paper is to show that the natural model category of permutative categories is a left proper model category.

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10

Gu, Aihua, Zhongzhen Yan, Xixi Zhang, and Yongsheng Xiang. "Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates." Axioms 13, no. 1 (2024): 62. http://dx.doi.org/10.3390/axioms13010062.

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This paper focuses on the modeling of automatic pricing and replenishment strategies for perishable products with time-varying deterioration rates based on an improved SVR-LSTM-ARIMA hybrid model. This research aims to support supermarkets in planning future strategies, optimizing category structure, reducing loss rates, and improving profit margins and service quality. Specifically, the paper selects perishable vegetables as the research category and calculates the cost-plus ratio for each vegetable category. Correlation analysis is conducted with total sales, and a non-parametric relationshi

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11

Cabbolet, Marcoen J. T. F. "A Finitely Axiomatized Non-Classical First-Order Theory Incorporating Category Theory and Axiomatic Set Theory." Axioms 10, no. 2 (2021): 119. http://dx.doi.org/10.3390/axioms10020119.

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It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the Löwenheim–Skolem theorem. This paper presents the axioms one has to accept to get rid of these two features. For that matter, some twenty axioms are formulated in a non-classical first-order language with countably many constants: to this collection of axioms is associated a universe of discourse consisting of a class of objects, each of

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12

Patel, Uma Devi, Vesna Todorcevic, Slobodan Radojevic та Stojan Radenović. "Best Proximity Point for ΓτF-Fuzzy Proximal Contraction". Axioms 12, № 2 (2023): 165. http://dx.doi.org/10.3390/axioms12020165.

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In this writing, first, we disclose the first and second category of a ΓτF-fuzzy proximal contraction for a mapping O:U→V which is nonself and also declare a fuzzy q-property to confirm the existence of the best proximity point for nonself function O. Then, we discover a few results using the ΓτF-fuzzy proximal contraction of the first category for a continuous and discontinuous nonself function O in a non-Archimedean fuzzy metric space. Later, we discuss another result for the ΓτF-fuzzy proximal contraction of the second category as well. In between the fuzzy proximal theorems, many examples

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13

Jäger, Gunther, and T. M. G. Ahsanullah. "Characterization of Transitivity in L-Tolerance Spaces by Convergence and Closure." Axioms 10, no. 4 (2021): 268. http://dx.doi.org/10.3390/axioms10040268.

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We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations compatible with group structures are also characterized by convergence and it is shown that they are transitive.

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14

McGuirk, Zachary, and Byungdo Park. "A Model of Directed Graph Cofiber." Axioms 11, no. 1 (2022): 32. http://dx.doi.org/10.3390/axioms11010032.

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In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a construction of a cofiber of a directed graph map whose image is contractible in the cofiber. Our work reveals that a category-theoretically correct construction in continuous setup is no longer correct when it is discretized and hence leads to look at canonical constructions in category theory in a different perspective.

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15

Tao, Wenyue, Chaoran Wu, Ting Wu, and Fuyuan Chen. "Research on the Optimization of Pricing and the Replenishment Decision-Making Problem Based on LightGBM and Dynamic Programming." Axioms 13, no. 4 (2024): 257. http://dx.doi.org/10.3390/axioms13040257.

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Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the “small production and big market” setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical model of replenishment plans and pricing strategies for each category of vegetables and individual products. In this paper, we analyze the following three questions: Question One: What is the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two:

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16

Abramsky, Samson. "Structure and Power: an Emerging Landscape." Fundamenta Informaticae 186, no. 1-4 (2022): 1–26. http://dx.doi.org/10.3233/fi-222116.

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In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer Science, but there may also be something of interest for model theorists and other logicians. The basic setting involves studying the category of relational structures via a resource-indexed family of adjunctions with some process category - which unfolds relational structures into tree-like forms, allowing natural resource parameters to be assigned to these unfo

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17

Kwon, Namhee. "Vanishing Property of BRST Cohomology for Modified Highest Weight Modules." Axioms 12, no. 6 (2023): 550. http://dx.doi.org/10.3390/axioms12060550.

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We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective covers. We also prove that both these projective covers and the quasi highest weight modules satisfy the vanishing property of BRST cohomology.

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18

Aponte, Elvis, Vadakasi Subramanian, Jhixon Macías, and Muthumari Krishnan. "On Semi-Continuous and Clisquish Functions in Generalized Topological Spaces." Axioms 12, no. 2 (2023): 130. http://dx.doi.org/10.3390/axioms12020130.

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In this paper, we will focus on three types of functions in a generalized topological space, namely; lower and upper semi-continuous functions, and cliquish functions. We give some results for nowhere dense sets and for second category sets. Further, we discuss the nature of cliquish functions in generalized metric spaces and provide the characterization theorem for cliquish functions in terms of nowhere dense sets.

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19

Ameen, Zanyar A., and Mesfer H. Alqahtani. "Congruence Representations via Soft Ideals in Soft Topological Spaces." Axioms 12, no. 11 (2023): 1015. http://dx.doi.org/10.3390/axioms12111015.

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This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft

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20

Hofmann, Karl H., and Sidney A. Morris. "Advances in the Theory of Compact Groups and Pro-Lie Groups in the Last Quarter Century." Axioms 10, no. 3 (2021): 190. http://dx.doi.org/10.3390/axioms10030190.

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This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century. It begins with developments in the 18th and 19th centuries. Next is from Hilbert’s Fifth Problem in 1900 to its solution in 1952 by Montgomery, Zippin, and Gleason and Yamabe’s important structure theorem on almost connected locally compact groups. This half century included profound contributions by Weyl and Peter, Haar, Pontryagin, van Kampen, Weil, and Iwasawa. The focus in the last quarter c

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21

Jovanović, Stanislav, Edmundas Kazimieras Zavadskas, Željko Stević, Milan Marinković, Adel F. Alrasheedi, and Ibrahim Badi. "An Intelligent Fuzzy MCDM Model Based on D and Z Numbers for Paver Selection: IMF D-SWARA—Fuzzy ARAS-Z Model." Axioms 12, no. 6 (2023): 573. http://dx.doi.org/10.3390/axioms12060573.

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One of the most important challenges when building road infrastructure is the selection of appropriate mechanization, on which the efficiency of construction and the life of exploitation depends largely. As construction machinery, pavers occupy a significant place in civil engineering projects, so their selection, depending on a road category, is a very important activity. The objective of this paper is to develop an intelligent Fuzzy MCDM (Multi-Criteria Decision-Making) model, which consists of the integration of D and Z numbers for the selection of construction machinery. The IMF D-SWARA (I

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22

Younas, Sajida, Sajida Kousar, Majed Albaity, and Tahir Mahmood. "Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group ▵*(3,q,r) for q < r Primes." Axioms 12, no. 12 (2023): 1128. http://dx.doi.org/10.3390/axioms12121128.

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Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of finitely generated groups. The best known example of a simple group is the alternating group An, where n≥5. This article establishes a relation between the hyperbolic triangle group denoted as ▵*(3,7,r) and the alternating group. The approach involves employing coset diagrams to establish this connection.

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23

Rezk, Haytham M., Ahmed I. Saied, Maha Ali, Belal A. Glalah, and Mohammed Zakarya. "Novel Hardy-Type Inequalities with Submultiplicative Functions on Time Scales Using Delta Calculus." Axioms 12, no. 8 (2023): 791. http://dx.doi.org/10.3390/axioms12080791.

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In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales delta calculus. A time scale, denoted by T, is any closed nonempty subset of R. In time scale calculus, results are unified and extended. As particular cases of our findings (when T=R), we have the continuous analogues of inequalities established in some the literature. Furthermore, we can find other inequalities in different time scales, such as T=N, which, to the

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24

Eddahbi, Mhamed, Omar Kebiri, and Abou Sene. "Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients." Axioms 12, no. 12 (2023): 1068. http://dx.doi.org/10.3390/axioms12121068.

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In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the Itô–Krylov’s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable an

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25

Ramirez, Martha, and Patricia Melin. "A New Perspective for Multivariate Time Series Decision Making through a Nested Computational Approach Using Type-2 Fuzzy Integration." Axioms 12, no. 4 (2023): 385. http://dx.doi.org/10.3390/axioms12040385.

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The integration of key indicators from the results of the analysis of time series represents a constant challenge within organizations; this could be mainly due to the need to establish the belonging of each indicator within a process, geographic region or category. This paper thus illustrates how both primary and secondary indicators are relevant for decision making, and why they need to be integrated by making new final fuzzy indicators. Thus, our proposal consists of a type-2 fuzzy integration of multivariate time series, such as OECD country risk classification, inflation, population and g

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26

Kotoulas, Thomas. "Families of Orbits Produced by Three-Dimensional Central and Polynomial Potentials: An Application to the 3D Harmonic Oscillator." Axioms 12, no. 5 (2023): 461. http://dx.doi.org/10.3390/axioms12050461.

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We study three-dimensional potentials of the form V=U(xp+yp+zp), where U is an arbitrary function of C2-class, and p∈Z, which produces a preassigned two-parametric family of spatial regular orbits given in the solved form f(x,y,z) = c1, g(x,y,z) = c2 (c1, c2 = const). These potentials have to satisfy two linear PDEs, which are the basic equations of the 3D inverse problem of Newtonian dynamics. The functions f and g can be represented uniquely by the ”slope functions” α(x,y,z) and β(x,y,z). The orbital functions α(x,y,z) and β(x,y,z) have to satisfy three differential conditions according to t

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27

Mikki, Said. "Set Theory, Dynamism, and the Event: Reinjecting Time into the Foundations of Mathematics." Axioms 11, no. 12 (2022): 670. http://dx.doi.org/10.3390/axioms11120670.

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This article concentrates on exploring the relevance of the postmodernist concept of the event to mathematical philosophy and the foundations of mathematics. In both the scientific and philosophical study of nature, and particularly event ontology, we find that space and dynamism are fundamental. However, whether based on set theory or category theory, modern mathematics faces conceptual and philosophical difficulties when the temporal is intentionally invoked as a key aspect of that intrinsic dynamism so characteristic of mathematical being, physical becoming, process, and thought. We present

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28

Borzooei, Rajab Ali, Narges Akhlaghinia, Mona Aaly Kologani, and Xiao Long Xin. "The category of EQ-algebras." Bulletin of the Section of Logic, January 20, 2021. http://dx.doi.org/10.18778/0138-0680.2021.01.

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   EQ-algebras were introduced by Nova ́k in [15] as an algebraic structure of truth values for fuzzy type theory (FFT). In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculate coprodut and pushout in a special case. Also, we construct a free EQ-algebra on a singleton.  

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29

San Martín, Hernán J., and Valeria A. Sígal. "Dualities for Bounded Prelinear Hilbert Algebras." Logic Journal of the IGPL, February 1, 2021. http://dx.doi.org/10.1093/jigpal/jzab001.

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Abstract This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.

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30

Çetin, Selim, and Utku Gürdal. "A characterization of crossed self-similarity on crossed modules in L-algebras." Logic Journal of the IGPL, February 28, 2024. http://dx.doi.org/10.1093/jigpal/jzae003.

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Abstract We introduce crossed modules in cycloids, as a generalization of cycloids, which are algebraic logical structures arising in the context of the quantum Yang–Baxter equation. As a spacial case, we in particular focus on the crossed modules of $L-$algebras. These types of crossed modules are exceptional, since the category of $L-$algebras is not protomodular, nor Barr-exact, but it nevertheless has natural semidirect products that have not been described in category theoretic terms. We identify crossed ideals of crossed module in $L-$algebras, and obtain some characteristics of these ob

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31

Lachman, Dominik. "The Category of $$\omega $$-Effect Algebras: Tensor Product and $$\omega $$-Completion." Order, August 30, 2024. http://dx.doi.org/10.1007/s11083-024-09680-y.

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AbstractEffect algebras are certain ordered structures that serve as a general framework for studying the algebraic semantics of quantum logic. We study effect algebras which obtain suprema of countable monotone sequences – so-called $$\omega $$ ω -effect algebras. This assumption is necessary to capture basic (non-discrete) probabilistic concepts. We establish a free $$\omega $$ ω -completion of effect algebras (i.e., a left adjoint to the functor that forgets the existence of $$\omega $$ ω -suprema) and the existence of a tensor product in the category of $$\omega $$ ω -effect algebras. Thes

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32

Di Nola, Antonio, Giacomo Lenzi, and Luca Spada. "Sheaf representations and locality of Riesz spaces with order unit." Journal of Logic and Analysis 13 (May 11, 2021). http://dx.doi.org/10.4115/jla.2021.13.2.

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We present an algebraic study of Riesz spaces (=real vector lattices) with a (strong) order unit. We exploit a categorical equivalence between those structures and a variety of algebras called RMV-algebras. We prove two different sheaf representations for Riesz spaces with order unit: the first represents them as sheaves of linearly ordered Riesz spaces over a spectral space, the second represent them as sheaves of "local" Riesz spaces over a compact Hausdorff space. Motivated by the latter representation we study the class of local RMV-algebras. We study the algebraic properties of local RMV-

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33

Celani, Sergio, and Hernán J. San Martín. "On the implicative‐infimum subreducts of weak Heyting algebras." Mathematical Logic Quarterly, July 6, 2024. http://dx.doi.org/10.1002/malq.202300021.

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AbstractThe variety of weak Heyting algebras was introduced in 2005 by Celani and Jansana. This corresponds to the strict implication fragment of the normal modal logic which is also known as the subintuitionistic local consequence of the class of all Kripke models. Subresiduated lattices are a generalization of Heyting algebras and particular cases of weak Heyting algebras. They were introduced during the 1970s by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. In this paper we study the class of implicative‐infimum s

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Coniglio, Marcelo Esteban, and Guilherme Vicentin de Toledo. "Weakly Free Multialgebras." Bulletin of the Section of Logic, August 23, 2021. http://dx.doi.org/10.18778/0138-0680.2021.19.

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In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in exploring the foundations of multialgebras ap

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Ugolini, Sara. "The polyhedral geometry of Wajsberg hoops." Journal of Logic and Computation, March 23, 2023. http://dx.doi.org/10.1093/logcom/exad007.

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Abstract We show that the algebraic category of finitely presented Wajsberg hoops is equivalent to a non-full subcategory of finitely presented MV-algebras. We use this connection to show how methods and techniques developed to study MV-algebras can be adapted to study Wajsberg hoops, as well. In particular, we show that finitely presented Wajsberg hoops are dually equivalent to a subcategory of rational polyhedra with $\mathbb {Z}$-maps. We use the duality to provide a geometrical characterization of finitely generated projective and exact Wajsberg hoops. As applications, we study logical pro

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Rogozin, Daniel. "Categorical and algebraic aspects of the intuitionistic modal logic IEL― and its predicate extensions." Journal of Logic and Computation, December 28, 2020. http://dx.doi.org/10.1093/logcom/exaa082.

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Abstract The system of intuitionistic modal logic $\textbf{IEL}^{-}$ was proposed by S. Artemov and T. Protopopescu as the intuitionistic version of belief logic (S. Artemov and T. Protopopescu. Intuitionistic epistemic logic. The Review of Symbolic Logic, 9, 266–298, 2016). We construct the modal lambda calculus, which is Curry–Howard isomorphic to $\textbf{IEL}^{-}$ as the type-theoretical representation of applicative computation widely known in functional programming.We also provide a categorical interpretation of this modal lambda calculus considering coalgebras associated with a monoidal

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Rot, Jurriaan, Bart Jacobs, and Paul Blain Levy. "Steps and traces." Journal of Logic and Computation, August 23, 2021. http://dx.doi.org/10.1093/logcom/exab050.

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Abstract In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg–Moore category. This paper elaborates two new unifying ideas: (i) coalgebraic,draftrules trace semantics is naturally presented in terms of corecursive algebras, and (ii) all three approaches arise as instances of the same abstract setting. Our perspective puts the different approaches under a common roof and allows to derive conditions under which some of them coincide.

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Butz, Carsten. "Finitely Presented Heyting Algebras." BRICS Report Series 5, no. 30 (1998). http://dx.doi.org/10.7146/brics.v5i30.19436.

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In this paper we study the structure of finitely presented Heyting<br />algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact co- Heyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model property. Our main technical tool is a representation of finitely presented Heyting algebras in terms of a colimit of finite distributive lattices. As applications we construct explicitly the m

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Noura, Boudiaf, and Chaoui Allaoua. "Double Reduction of Ada-ECATNet Representation using Rewriting Logic." October 22, 2008. https://doi.org/10.5281/zenodo.1080971.

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One major difficulty that faces developers of concurrent and distributed software is analysis for concurrency based faults like deadlocks. Petri nets are used extensively in the verification of correctness of concurrent programs. ECATNets [2] are a category of algebraic Petri nets based on a sound combination of algebraic abstract types and high-level Petri nets. ECATNets have 'sound' and 'complete' semantics because of their integration in rewriting logic [12] and its programming language Maude [13]. Rewriting logic is considered as one of very powerful logics in terms of description, verific

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Garner, Richard, and Jean-Simon Pacaud Lemay. "Cartesian Differential Categories as Skew Enriched Categories." Applied Categorical Structures, June 18, 2021. http://dx.doi.org/10.1007/s10485-021-09649-7.

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AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential

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Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o

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Emmerson, Parker. "Vector Calculus: Infinity Logic Ray Calculus with Quasi-Quanta Algebra Limits (Rough Draft)." July 25, 2023. https://doi.org/10.5281/zenodo.8176414.

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Golden Ratio Angle in Infinity Logic Ray Calculus with Quasi-Quanta Algebra LimitsThis document explores the relationship between the golden ratio and ray tracing in the context of Infinity Logic Ray Calculus with Quasi-Quanta Algebra Limits (ILR-QAL). The paper focuses on two key aspects:<strong>Densified Sweeping Subnet:</strong> This concept involves enriching the sweeping process by incorporating an additional factor into the definition of the sweeping subnet. This results in a denser and more detailed representation of the system dynamics.<strong>Golden Ratio Angle:</strong> The analysis

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Emmerson, Parker. "Conditional Integral of Phenomenological Velocity." October 21, 2024. https://doi.org/10.5281/zenodo.13959848.

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Published with great Thanksgiving to Jesus. Described herein is a method whereby which one can integrate conditionally the variance of phenomenological velocity, a product of technical differences between the expression of factoring square root functions present within height functions of difference between varying geometric forms. Indeed, this is a true proof, because it requires the exterior trigonometric identity to be brought into the equation, thus making the cancellation non-tautological.   Higher - dimensional calculus and integral transformation play crucial roles in advancing our

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