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Journal articles on the topic 'Limit (Logic)'

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Published: 4 June 2021

Last updated: 30 July 2024

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1

Welles, James. "A Limit on Logic." Journal of Clinical Research and Reports 8, no. 3 (June 24, 2021): 01. http://dx.doi.org/10.31579/2690-1919/176.

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One of the problems with logic is that it cannot be self-refuting–if it is, it is not logical. This make logic its own sacred cow. It likewise makes the expression “By logical extension” irrelevant or at least suspect in a curved universe. One may extend logic, but even after one step, its use is dubious at best.

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2

Freedman, M. H. "Limit, logic, and computation." Proceedings of the National Academy of Sciences 95, no. 1 (January 6, 1998): 95–97. http://dx.doi.org/10.1073/pnas.95.1.95.

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3

Lipparini, Paolo. "Limit ultrapowers and abstract logics." Journal of Symbolic Logic 52, no. 2 (June 1987): 437–54. http://dx.doi.org/10.2307/2274393.

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AbstractWe associate with any abstract logic L a family F(L) consisting, intuitively, of the limit ultrapowers which are complete extensions in the sense of L.For every countably generated [ω, ω]-compact logic L, our main applications are:(i) Elementary classes of L can be characterized in terms of ≡L only.(ii) If and are countable models of a countable superstable theory without the finite cover property, then .(iii) There exists the “largest” logic M such that complete extensions in the sense of M and L are the same; moreover M is still [ω, ω]-compact and satisfies an interpolation property stronger than unrelativized ⊿-closure.(iv) If L = Lωω(Qx), then cf(ωx) > ω and λω < ωx, for all λ < ωx.We also prove that no proper extension of Lωω generated by monadic quantifiers is compact. This strengthens a theorem of Makowsky and Shelah. We solve a problem of Makowsky concerning Lκλ-compact cardinals. We partially solve a problem of Makowsky and Shelah concerning the union of compact logics.

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4

BERARDI, STEFANO. "Classical logic as limit completion." Mathematical Structures in Computer Science 15, no. 1 (February 2005): 167–200. http://dx.doi.org/10.1017/s0960129504004529.

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5

Losada, Marcelo, Sebastian Fortin, and Federico Holik. "Classical Limit and Quantum Logic." International Journal of Theoretical Physics 57, no. 2 (October 24, 2017): 465–75. http://dx.doi.org/10.1007/s10773-017-3579-0.

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6

Batens, Diderik. "Devising the set of abnormalities for a given defeasible rule." Logical Investigations 26, no. 1 (August 6, 2020): 9–35. http://dx.doi.org/10.21146/2074-1472-2020-26-1-9-35.

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Devising adaptive logics usually starts with a set of abnormalities and a deductive logic. Where the adaptive logic is ampliative, the deductive logic is the lower limit logic, the rules of which are unconditionally valid. Where the adaptive logic is corrective, the deductive logic is the upper limit logic, the rules of which are valid in case the premises do not require any abnormalities to be true. In some cases, the idea for devising an adaptive logic does not relate to a set of abnormalities, but to one or more defeasible rules, and perhaps also to one of the deductive logics. Defeasible rules are not universally valid, but are valid in ‘normal situations’ or for unproblematic parts of premise set. Where the idea is such, the set of abnormalities has to be delineated in view of the rules. The way in which this task may be tackled is by no means obvious and is the main topic studied in the present paper. The outcome is an extremely simple and transparent recipe. It is shown that, except for very special cases, the recipe leads to an adequate result.

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7

Almadi, Abdulla I. M., Rabia Emhamed Al Mamlook, Yahya Almarhabi, Irfan Ullah, Arshad Jamal, and Nishantha Bandara. "A Fuzzy-Logic Approach Based on Driver Decision-Making Behavior Modeling and Simulation." Sustainability 14, no. 14 (July 20, 2022): 8874. http://dx.doi.org/10.3390/su14148874.

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The present study proposes a decision-making model based on different models of driver behavior, aiming to ensure integration between road safety and crash reduction based on an examination of speed limitations under weather conditions. The present study investigated differences in road safety attitude, driver behavior, and weather conditions I-69 in Flint, Genesee County, Michigan, using the fuzzy logic approach. A questionnaire-based survey was conducted among a sample of Singaporean (n = 100) professional drivers. Safety level was assessed in relation to speed limits to determine whether the proposed speed limit contributed to a risky or safe situation. The experimental results show that the speed limits investigated on different roads/in different weather were based on the participants’ responses. The participants could increase or keep their current speed limit or reduce their speed limit a little or significantly. The study results were used to determine the speed limits needed on different roads/in different weather to reduce the number of crashes and to implement safe driving conditions based on the weather. Changing the speed limit from 80 mph to 70 mph reduced the number of crashes occurring under wet road conditions. According to the results of the fuzzy logic study algorithm, a driver’s emotions can predict outputs. For this study, the fuzzy logic algorithm evaluated drivers’ emotions according to the relation between the weather/road condition and the speed limit. The fuzzy logic would contribute to assessing a powerful feature of human control. The fuzzy logic algorithm can explain smooth relationships between the input and output. The input–output relationship estimated by fuzzy logic was used to understand differences in drivers’ feelings in varying road/weather conditions at different speed limits.

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8

Apter, Arthur W. "On measurable limits of compact cardinals." Journal of Symbolic Logic 64, no. 4 (December 1999): 1675–88. http://dx.doi.org/10.2307/2586805.

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AbstractWe extend earlier work (both individual and joint with Shelah) and prove three theorems about the class of measurable limits of compact cardinals, where a compact cardinal is one which is either strongly compact or supercompact. In particular, we construct two models in which every measurable limit of compact cardinals below the least supercompact limit of supercompact cardinals possesses non-trivial degrees of supercompactness. In one of these models, every measurable limit of compact cardinals is a limit of supercompact cardinals and also a limit of strongly compact cardinals having no non-trivial degree of supercompactness. We also show that it is consistent for the least supercompact cardinal κ to be a limit of strongly compact cardinals and be so that every measurable limit of compact cardinals below κ has a non-trivial degree of supercompactness. In this model, the only compact cardinals below κ with a non-trivial degree of supercompactness are the measurable limits of compact cardinals.

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9

Petrakis, Iosif. "Limit spaces with approximations." Annals of Pure and Applied Logic 167, no. 9 (September 2016): 737–52. http://dx.doi.org/10.1016/j.apal.2016.04.013.

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10

Kurfirst, Robert. "Term-Limit Logic: Paradigms and Paradoxes." Polity 29, no. 1 (September 1996): 119–40. http://dx.doi.org/10.2307/3235277.

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11

Shelah, Saharon. "Isomorphic limit ultrapowers for infinitary logic." Israel Journal of Mathematics 246, no. 1 (October 30, 2021): 21–46. http://dx.doi.org/10.1007/s11856-021-2226-x.

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12

Niemistö, Hannu. "Zero-one law and definability of linear order." Journal of Symbolic Logic 74, no. 1 (March 2009): 105–23. http://dx.doi.org/10.2178/jsl/1231082304.

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§1. Introduction. A logic ℒ has a limit law, if the asymptotic probability of every query definable in ℒ converges. It has a 0–1-law if the probability converges to 0 or 1. The 0–1-law for first-order logic on relational vocabularies was independently found by Glebski et al. [6] and Fagin [5]. Later it has been shown for many other logics, for instance for fragments of second order logic [12], for finite variable logic [13] and for FO extended with the rigidity quantifier [3]. Lynch [14] has shown a limit law for first-order logic on vocabularies with unary functions.We say that two formulas or two logics are almost everywhere equivalent, if they are equivalent on a class of structures whose asymptotic probability measure is one [7]. A 0–1-law is usually proved by showing that every quantifier of the logic has almost everywhere quantifier elimination, i.e., every formula with just one quantifier in front of it is almost everywhere equivalent to a quantifier-free formula. Besides proving 0–1-law, this implies that the logic is (weakly) almost everywhere equivalent to first-order logic.The aim of this paper is to study, whether a logic with a 0–1-law can have greater expressive power than FO in the almost everywhere sense and to what extent. In particular, we are interested on the definability of linear order. Because a 0–1-law determines the almost everywhere expressive power of the sentences of the logic completely, but does not say anything about formulas explicitly, we have to assume some regularity on logics. We will therefore mostly consider extensions of first-order logic with generalized quantifiers.

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13

Landes, Jürgen, Soroush Rafiee Rad, and Jon Williamson. "Towards the entropy-limit conjecture." Annals of Pure and Applied Logic 172, no. 2 (February 2021): 102870. http://dx.doi.org/10.1016/j.apal.2020.102870.

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14

BRIAN, WILL. "ABSTRACT ω-LIMIT SETS." Journal of Symbolic Logic 83, no. 2 (June 2018): 477–95. http://dx.doi.org/10.1017/jsl.2018.11.

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AbstractThe shift map σ on ω* is the continuous self-map of ω* induced by the function n ↦ n + 1 on ω. Given a compact Hausdorff space X and a continuous function f : X → X, we say that (X, f) is a quotient of (ω*, σ) whenever there is a continuous surjection Q : ω*→ X such that Q ○ σ = σ ○ f.Our main theorem states that if the weight of X is at most ℵ1, then (X, f) is a quotient of (ω*, σ), if and only if f is weakly incompressible (which means that no nontrivial open U ⊆ X has $f\left( {\bar{U}} \right) \subseteq U$). Under CH, this gives a complete characterization of the quotients of (ω*, σ) and implies, for example, that (ω*, σ−1) is a quotient of (ω*, σ).In the language of topological dynamics, our theorem states that a dynamical system of weight ℵ1 is an abstract ω-limit set if and only if it is weakly incompressible.We complement these results by proving (1) our main theorem remains true when ℵ1 is replaced by any κ < p, (2) consistently, the theorem becomes false if we replace ℵ1 by ℵ2, and (3) OCA + MA implies that (ω*, σ−1) is not a quotient of (ω*, σ).

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15

D’Aquino, Paola, Julia Knight, and Karen Lange. "Limit computable integer parts." Archive for Mathematical Logic 50, no. 7-8 (June 18, 2011): 681–95. http://dx.doi.org/10.1007/s00153-011-0241-z.

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16

Teslyk, M. V., O. M. Teslyk, and L. V. Zadorozhna. "Quantum Logic under Semiclassical Limit: Information Loss." Ukrainian Journal of Physics 67, no. 5 (August 29, 2022): 352. http://dx.doi.org/10.15407/ujpe67.5.352.

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We consider the quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semiclassical limit. We show that this reduction is caused by the fact that any elementary quantum logic operation (gate) suffers the information loss during the transition to its classical analog. Amount of the information lost is estimated for any gate from the complete set. We demonstrate that the largest loss is obtained for non-commuting gates. This allows us to consider the non-commutativity as the quantum computational speed-up resource. Our method allows us to quantify advantages of a quantum computation as compared to the classical one by the direct analysis of the involved basic logic. The obtained results are illustrated by the application to a quantum discrete Fourier transform and Grover search algorithms.

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17

Bergier, Hugolin. "How Combinatory Logic Can Limit Computing Complexity." EPJ Web of Conferences 244 (2020): 01009. http://dx.doi.org/10.1051/epjconf/202024401009.

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As computing capabilities are extending, the amount of source code to manage is inevitably becoming larger and more complex. No matter how hard we try, the bewildering complexity of the source code always ends up overwhelming its own creator, to the point of giving the appearance of chaos. As a solution to the cognitive complexity of source code, we are proposing to use the framework of Combinatory Logic to construct complex computational concepts that will provide a model of description of the code that is easy and intuitive to grasp. Combinatory Logic is already known as a model of computation but what we are proposing here is to use a logic of combinators and operators to reverse engineer more and more complex computational concept up from the source code. Through the two key notions of computational concept and abstract operator, we will show that this model offers a new, meaningful and simple way of expressing what the intricate code is about.

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18

Min, Kyung Chan. "Fuzzy limit spaces." Fuzzy Sets and Systems 32, no. 3 (September 1989): 343–57. http://dx.doi.org/10.1016/0165-0114(89)90267-4.

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19

Berardi, Stefano, and Yoriyuki Yamagata. "A sequent calculus for limit computable mathematics." Annals of Pure and Applied Logic 153, no. 1-3 (April 2008): 111–26. http://dx.doi.org/10.1016/j.apal.2008.01.006.

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20

Normann, Dag, and Geir Waagb. "Limit spaces and transfinite types." Archive for Mathematical Logic 41, no. 6 (August 1, 2002): 525–39. http://dx.doi.org/10.1007/s001530100131.

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21

Glymour, Clark. "Inductive inference in the limit." Erkenntnis 22, no. 1-3 (January 1985): 23–31. http://dx.doi.org/10.1007/bf00269958.

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22

Aytar, Salih, Musa A. Mammadov, and Serpil Pehlivan. "Statistical limit inferior and limit superior for sequences of fuzzy numbers." Fuzzy Sets and Systems 157, no. 7 (April 2006): 976–85. http://dx.doi.org/10.1016/j.fss.2005.10.014.

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23

Li, Duo, and Prakash Ranjitkar. "A fuzzy logic-based variable speed limit controller." Journal of Advanced Transportation 49, no. 8 (July 1, 2015): 913–27. http://dx.doi.org/10.1002/atr.1320.

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24

CHENG, YONG. "FINDING THE LIMIT OF INCOMPLETENESS I." Bulletin of Symbolic Logic 26, no. 3-4 (December 2020): 268–86. http://dx.doi.org/10.1017/bsl.2020.9.

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AbstractIn this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem ($\textsf {G1}$ for short). We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ (i.e., T is weaker than $\mathbf {R}$ w.r.t. interpretation) and $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds.

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25

LARSON, PAUL B. "THE FILTER DICHOTOMY AND MEDIAL LIMITS." Journal of Mathematical Logic 09, no. 02 (December 2009): 159–65. http://dx.doi.org/10.1142/s0219061309000872.

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The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from [Formula: see text] to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. We show that the Filter Dichotomy implies that there are no medial limits.

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26

Taschner, Rudolf. "The swap of integral and limit in constructive mathematics." Mathematical Logic Quarterly 56, no. 5 (September 20, 2010): 533–40. http://dx.doi.org/10.1002/malq.200910107.

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27

Belair-Gagnon, Valerie, Seth C. Lewis, and Colin Agur. "Failure to Launch: Competing Institutional Logics, Intrapreneurship, and the Case of Chatbots." Journal of Computer-Mediated Communication 25, no. 4 (July 1, 2020): 291–306. http://dx.doi.org/10.1093/jcmc/zmaa008.

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Abstract This article explores the institutional logics of intrapreneurial units, or groups within organizations that are designated to foster organizational innovation. Drawing on interviews with news intrapreneurs developing chatbots in news media organizations, this study shows that innovation can be stymied because of conflicting institutional logics. News intrapreneurs adopt a logic of experimentation, audience orientation, and efficiency-seeking, but that approach clashes with a journalistic logic prioritizing news workflows, formats, and associated autonomy for newsworkers. These clashing logics limit the adoption and influence of chatbots. This study illustrates the shaping influence of competing institutional logics and their negotiation in the development, deployment, and success or failure of intrapreneurial activities within organizations. The lesson is not that the existence of competing logics is, by default, a defeating proposition for innovation. Rather, this study advances scholarly understanding of the role of institutional logics in frustrating or facilitating technological adoption in organizations.

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28

Villaveces, Andrés, and Pedro Zambrano. "Limit models in metric abstract elementary classes: the categorical case." Mathematical Logic Quarterly 62, no. 4-5 (August 2016): 319–34. http://dx.doi.org/10.1002/malq.201300060.

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29

Mazari-Armida, Marcos. "Algebraic description of limit models in classes of abelian groups." Annals of Pure and Applied Logic 171, no. 1 (January 2020): 102723. http://dx.doi.org/10.1016/j.apal.2019.102723.

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30

Wu, You De, Jin Chun Feng, Bai Lin Li, and Qi Hong. "The Research on CNC Machine Tool’s Position Limit Protection Equipments Based on Negative Logic Control." Applied Mechanics and Materials 84-85 (August 2011): 134–38. http://dx.doi.org/10.4028/www.scientific.net/amm.84-85.134.

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Position-limit protection equipment is the major control equipment on CNC machine, whose logic control method is the assurance of normal work of position-limit protection equipments. It will reduce the effect of position-limit protection or cause it malfunction, if we apply the logical control method not suitably. Current CNC machines are provided with a positive control limitation protection device, and then it is likely to happen malfunction even cause accidents due to its electric circuit errors or its open circuit. In order to solve this shortcoming, somebody has worked out a new method, which is called negative logic control. This paper introduces the new logic control method’s basic principle and its practical usage.

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31

Stathis, J. H., and D. J. DiMaria. "Oxide scaling limit for future logic and memory technology." Microelectronic Engineering 48, no. 1-4 (September 1999): 395–401. http://dx.doi.org/10.1016/s0167-9317(99)00413-x.

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32

Gárdos, Éva. "On the monotone classes of maximal limit-logic $M$." Publicationes Mathematicae Debrecen 28, no. 3-4 (July 1, 2022): 199–207. http://dx.doi.org/10.5486/pmd.1981.28.3-4.02.

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Liang, Xin Rong, and Di Qian Wang. "Design and Simulation of Speed Limit Controller Based on Fuzzy Logic Inference." Applied Mechanics and Materials 220-223 (November 2012): 988–91. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.988.

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Speed limit control is of great importance in freeway traffic control. This study aims to determine the reasonable speed limit through the application of a fuzzy inference method. Firstly, the components of a fuzzy logic controller are formulated. Then the influential factors of speed limit control are analyzed and the speed limit controller based on fuzzy logic is designed according to such information as the number of vehicles on the freeway, the road grade, and the weather conditions. Gauss, g-bell and triangle curves are used for the membership functions of the fuzzy variables. The rule base including 45 fuzzy rules is also established. Finally, the speed limit controller is simulated. Simulation results show that the speed limit values are reasonable. Fuzzy inference method provides a novel and practical way to realize speed limit control.

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34

Pap, Endre, and Ivana Štajner-Papuga. "A limit theorem for triangle functions." Fuzzy Sets and Systems 157, no. 2 (January 2006): 292–307. http://dx.doi.org/10.1016/j.fss.2005.04.008.

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35

Fang, Jinming. "Stratified L-ordered quasiuniform limit spaces." Fuzzy Sets and Systems 227 (September 2013): 51–73. http://dx.doi.org/10.1016/j.fss.2013.04.007.

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36

NEŠETŘIL, JAROSLAV, and PATRICE OSSONA DE MENDEZ. "EXISTENCE OF MODELING LIMITS FOR SEQUENCES OF SPARSE STRUCTURES." Journal of Symbolic Logic 84, no. 02 (March 7, 2019): 452–72. http://dx.doi.org/10.1017/jsl.2018.32.

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AbstractA sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a standard probability space, with the property that every definable set is Borel. It was known that FO-convergent sequence of graphs do not always admit a modeling limit, but it was conjectured that FO-convergent sequences of sufficiently sparse graphs have a modeling limits. Precisely, two conjectures were proposed:1.If a FO-convergent sequence of graphs is residual, that is if for every integer d the maximum relative size of a ball of radius d in the graphs of the sequence tends to zero, then the sequence has a modeling limit.2.A monotone class of graphs ${\cal C}$ has the property that every FO-convergent sequence of graphs from ${\cal C}$ has a modeling limit if and only if ${\cal C}$ is nowhere dense, that is if and only if for each integer p there is $N\left( p \right)$ such that no graph in ${\cal C}$ contains the pth subdivision of a complete graph on $N\left( p \right)$ vertices as a subgraph.In this article we prove both conjectures. This solves some of the main problems in the area and among others provides an analytic characterization of the nowhere dense–somewhere dense dichotomy.

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37

van Benthem, Johan. "Logic in a Social Setting." Episteme 8, no. 3 (October 2011): 227–47. http://dx.doi.org/10.3366/epi.2011.0019.

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AbstractTaking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.

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Kish, Laszlo B. "Comments on “Sub-kBT Micro-Electromechanical Irreversible Logic Gate”." Fluctuation and Noise Letters 15, no. 04 (September 29, 2016): 1620001. http://dx.doi.org/10.1142/s0219477516200017.

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In a recent paper, [M. López-Suárez, I. Neri and L. Gammaitoni, Sub-[Formula: see text] micro-electromechanical irreversible logic gate, Nat. Commun. 7 (2016) 12068] the authors claimed that they demonstrated sub-[Formula: see text] energy dissipation at elementary logic operations. However, the argumentation is invalid because it neglects the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode, which totally dissipates during the full (0-1-0) cycle of logic values. The neglected dissipation phenomenon is identical with the mechanism that leads to the lower physical limit of dissipation (70–100 [Formula: see text] in today’s microprocessors (CMOS logic) and in any other system with thermally activated errors thus the same limit holds for the new scheme, too.

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39

Jäger, Gerhard, and Thomas Studer. "Extending the system T0 of explicit mathematics: the limit and Mahlo axioms." Annals of Pure and Applied Logic 114, no. 1-3 (April 2002): 79–101. http://dx.doi.org/10.1016/s0168-0072(01)00076-8.

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40

Csima, Barbara F., Valentina S. Harizanov, Russell Miller, and Antonio Montalbán. "Computability of Fraïssé limits." Journal of Symbolic Logic 76, no. 1 (March 2011): 66–93. http://dx.doi.org/10.2178/jsl/1294170990.

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AbstractFraïssé studied countable structures through analysis of the age of , i.e., the set of all finitely generated substructures of . We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fraïssé limit. We also show that degree spectra of relations on a sufficiently nice Fraïssé limit are always upward closed unless the relation is definable by a quantifier-free formula. We give some sufficient or necessary conditions for a Fraïssé limit to be spectrally universal. As an application, we prove that the computable atomless Boolean algebra is spectrally universal.

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41

Chisholm, John, Ekaterina B. Fokina, Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight, and Sara Quinn. "Intrinsic bounds on complexity and definability at limit levels." Journal of Symbolic Logic 74, no. 3 (September 2009): 1047–60. http://dx.doi.org/10.2178/jsl/1245158098.

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AbstractWe show that for every computable limit ordinal α, there is a computable structure that is categorical, but not relatively categorical (equivalently, it does not have a formally Scott family). We also show that for every computable limit ordinal α, there is a computable structure with an additional relation R that is intrinsically on , but not relatively intrinsically on (equivalently, it is not definable by a computable Σα formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α.

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42

Clote, Peter. "A Generalization of the Limit Lemma and Clopen Games." Journal of Symbolic Logic 51, no. 2 (June 1986): 273. http://dx.doi.org/10.2307/2274051.

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43

Griffiths, Evan J. "Limit lemmas and jump inversion in the enumeration degrees." Archive for Mathematical Logic 42, no. 6 (August 1, 2003): 553–62. http://dx.doi.org/10.1007/s00153-002-0161-z.

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Shu, Wenjun, Bing Yu, and Hongwei Ke. "A Novel Method on Min–Max Limit Protection for Aircraft Engine Control." MATEC Web of Conferences 166 (2018): 04002. http://dx.doi.org/10.1051/matecconf/201816604002.

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Min–Max selector structure is widely employed in current aircraft engine control logic. And the structure must provide desired thrust and prevent the engine from exceeding any safety or operational limits. In this paper, a new control scheme, that is Min–Max selector structure composed of Sliding Mode (SM) regulator and linear regulator, is presented. The main regulator is a linear regulator and all limit regulators are SM regulators. It could overcome the possibility of limit violation for the traditional Min-Max, and don’ t need the augmented state references that is one drawback of SMC Min-Max(all regulators are SM regulator). The simulation results show that the proposed approach could effectively prevent limit violation and can improve Min–Max limit protection for aircraft engine control.

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MAHER, MICHAEL J., ILIAS TACHMAZIDIS, GRIGORIS ANTONIOU, STEPHEN WADE, and LONG CHENG. "Rethinking Defeasible Reasoning: A Scalable Approach." Theory and Practice of Logic Programming 20, no. 4 (February 24, 2020): 552–86. http://dx.doi.org/10.1017/s1471068420000010.

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AbstractRecent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.

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Guang-Quan, Zhang. "Fuzzy limit theory of fuzzy complex numbers." Fuzzy Sets and Systems 46, no. 2 (March 1992): 227–35. http://dx.doi.org/10.1016/0165-0114(92)90135-q.

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Beklemishev, Lev D., and Albert Visser. "On the limit existence principles in elementary arithmetic and Σn0-consequences of theories." Annals of Pure and Applied Logic 136, no. 1-2 (October 2005): 56–74. http://dx.doi.org/10.1016/j.apal.2005.05.005.

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Klein, Moshe, and Oded Maimon. "Soft logic and numbers." Pragmatics and Cognition 23, no. 3 (December 31, 2016): 473–84. http://dx.doi.org/10.1075/pc.23.3.09kle.

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In this paper, we propose to see the Necker cube phenomenon as a basis for the development of a mathematical language in accordance with Leibniz’s vision of soft logic. By the development of a new coordinate system, we make a distinction between −0 and +0. This distinction enables us to present a new model for nonstandard analysis, and to develop a calculus theory without the need of the concept of limit. We also established a connection between “Recursive Distinctioning” and soft logic, and use it as a basis for a new computational model. This model has a potential to change the current computational paradigm.

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Ketchersid, Richard, Paul B. Larson, and Jindřich Zapletal. "Regular embeddings of the stationary tower and Woodin's maximality theorem." Journal of Symbolic Logic 75, no. 2 (June 2010): 711–27. http://dx.doi.org/10.2178/jsl/1268917500.

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AbstractWe present Woodin's proof that if there exists a measurable Woodin cardinal δ then there is a forcing extension satisfying all sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in Vδ. We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding j: V → M with critical point such that M is countably closed in the forcing extension.

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Lempp, Steffen, and Theodore A. Slaman. "A limit on relative genericity in the recursively enumerable sets." Journal of Symbolic Logic 54, no. 2 (June 1989): 376–95. http://dx.doi.org/10.2307/2274854.

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AbstractWork in the setting of the recursively enumerable sets and their Turing degrees. A set X is low if X′, its Turing jump, is recursive in ∅′ and high if X′ computes ∅″. Attempting to find a property between being low and being recursive, Bickford and Mills produced the following definition. W is deep, if for each recursively enumerable set A, the jump of A ⊕ W is recursive in the jump of A. We prove that there are no deep degrees other than the recursive one.Given a set W, we enumerate a set A and approximate its jump. The construction of A is governed by strategies, indexed by the Turing functionals Φ. Simplifying the situation, a typical strategy converts a failure to recursively compute W into a constraint on the enumeration of A, so that (W ⊕ A)′ is forced to disagree with Φ(−;A′). The conversion has some ambiguity; in particular, A cannot be found uniformly from W.We also show that there is a “moderately” deep degree: There is a low nonzero degree whose join with any other low degree is not high.

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