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Academic literature on the topic 'Fundamental theorems of LM-logic algebra'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Fundamental theorems of LM-logic algebra"

1

Solomon, Reed. "Ordered Groups: A Case Study in Reverse Mathematics." Bulletin of Symbolic Logic 5, no. 1 (1999): 45–58. http://dx.doi.org/10.2307/421140.

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The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is best explained by an exam
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2

LAMBROPOULOU, SOFIA. "L-MOVES AND MARKOV THEOREMS." Journal of Knot Theory and Its Ramifications 16, no. 10 (2007): 1459–68. http://dx.doi.org/10.1142/s0218216507005919.

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Given a knot theory (virtual, singular, knots in a 3-manifold etc.), there are deep relations between the diagrammatic knot equivalence in this theory, the braid structures and a corresponding braid equivalence. The L-moves between braids, due to their fundamental nature, may be adapted to any diagrammatic situation in order to formulate a corresponding braid equivalence. In this short paper, we discuss and compare various diagrammatic set-ups and results therein, in order to draw the underlying logic relating diagrammatic isotopy, braid structures, Markov theorems and L-move analogues. Finall
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3

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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4

Iovino, José. "On the maximality of logics with approximations." Journal of Symbolic Logic 66, no. 4 (2001): 1909–18. http://dx.doi.org/10.2307/2694984.

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In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., including Banach algebras or other structures of functional analysis), and
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5

Khan, Wilayat, Muhammad Kamran, Syed Rameez Naqvi, Farrukh Aslam Khan, Ahmed S. Alghamdi, and Eesa Alsolami. "Formal Verification of Hardware Components in Critical Systems." Wireless Communications and Mobile Computing 2020 (February 20, 2020): 1–15. http://dx.doi.org/10.1155/2020/7346763.

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Hardware components, such as memory and arithmetic units, are integral part of every computer-controlled system, for example, Unmanned Aerial Vehicles (UAVs). The fundamental requirement of these hardware components is that they must behave as desired; otherwise, the whole system built upon them may fail. To determine whether or not a component is behaving adequately, the desired behaviour of the component is often specified in the Boolean algebra. Boolean algebra is one of the most widely used mathematical tools to analyse hardware components represented at gate level using Boolean functions.
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6

Oaknin, David H. "Bypassing the Kochen–Specker Theorem: An Explicit Non-Contextual Statistical Model for the Qutrit." Axioms 12, no. 1 (2023): 90. http://dx.doi.org/10.3390/axioms12010090.

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We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics, and thus, bypasses the constraints imposed by the Kochen–Specker theorem and its subsequent reformulations. We notice that these renowned theorems crucially rely on the implicitly assumed existence of an absolute frame of reference with respect to which physically indistinguishable tests related by spurious gauge transformations can supposedly be assigned well-defined distinct identities. We observe that the existence of such an absolute fr
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7

Srivastava, Hari Mohan, Bidu Bhusan Jena, and Susanta Kumar Paikray. "Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems." Axioms 10, no. 3 (2021): 229. http://dx.doi.org/10.3390/axioms10030229.

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In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein
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8

Rao, N. Seshagiri, and K. Kalyani. "Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces." Cubo (Temuco) 24, no. 2 (2022): 343–68. http://dx.doi.org/10.56754/0719-0646.2402.0343.

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The purpose of this paper is to prove some results on fixed point, coincidence point, coupled coincidence point and coupled common fixed point for the mappings satisfying generalized \((\phi, \psi)\)-contraction conditions in complete partially ordered \(b\)-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our findings.
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9

Taketomi, Nanami, and Takeshi Emura. "Consistency of the Estimator for the Common Mean in Fixed-Effect Meta-Analyses." Axioms 12, no. 5 (2023): 503. http://dx.doi.org/10.3390/axioms12050503.

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Fixed-effect meta-analyses aim to estimate the common mean parameter by the best linear unbiased estimator. Besides unbiasedness, consistency is one of the most fundamental requirements for the common mean estimator to be valid. However, conditions for the consistency of the common mean estimator have not been discussed in the literature. This article fills this gap by clarifying conditions for making the common mean estimator consistent in fixed-effect meta-analyses. In this article, five theorems are devised, which state regularity conditions for the common mean estimator to be consistent. T
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10

Benkerrouche, Amar, Mohammed Said Souid, Gani Stamov, and Ivanka Stamova. "Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order." Axioms 11, no. 11 (2022): 634. http://dx.doi.org/10.3390/axioms11110634.

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In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted.
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Books on the topic "Fundamental theorems of LM-logic algebra"

1

Parshin, A. N. Number Theory I: Fundamental Problems, Ideas and Theories. Springer Berlin Heidelberg, 1995.

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2

Rédei, Miklós. Quantum Logic in Algebraic Approach (Fundamental Theories of Physics). Springer, 1998.

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3

Current Research in Operational Quantum Logic: Algebras, Categories, Languages (Fundamental Theories of Physics). Springer, 2000.

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4

Pták, Pavel, and Sylvia Pulmannová. Orthomodular Structures as Quantum Logics: Intrinsic Properties, State Space and Probabilistic Topics (Fundamental Theories of Physics). Springer, 1991.

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5

Cotnoir, A. J., and Achille C. Varzi. Mereology. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198749004.001.0001.

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Mereology is the formal theory of parthood relations. Mereological theories—have become a chapter of central interest in metaphysics, but also with applications in logic, the philosophy of mathematics, the philosophy of language, and the philosophy of science. This book provides a critical survey and an up-to-date assessment of the main results in this area, with an eye to both their philosophical underpinnings and their formal properties. In doing so, it also aims to investigate the varieties of formal systems currently available. After a brief history of the development of mereology, introdu
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Book chapters on the topic "Fundamental theorems of LM-logic algebra"

1

Manzano, María. "Basic notions: model theory." In Model Theory. Oxford University PressOxford, 1999. http://dx.doi.org/10.1093/oso/9780198538516.003.0005.

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Abstract In the first chapter we studied structures and some relations between them, such as isomorphism and embedding, without using a formal language. In the second chapter we introduced the formal first order language in which we can speak of structures. We also defined the fundamental semantic notions. By using such notions we were able to assert, in some cases, that a certain formula is logically valid: i.e. that it is true in all possible interpretations of the symbols contained in it. In the third chapter we proved that the notion of consequence corresponds exactly to that of deducibili
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