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Journal articles on the topic 'Bounded-degree logics'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Juba, Brendan. "Polynomial-Time Probabilistic Reasoning with Partial Observations via Implicit Learning in Probability Logics." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7866–75. http://dx.doi.org/10.1609/aaai.v33i01.33017866.

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Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which efficient algorithms are generally not known. In this work we consider the use of bounded-degree fragments of the “sum-of-squares” logic as a probability logic. Prior work has shown that we can decide refutability for such fragments in polynomial-time. We propose to use such fragments to decide queries about whether a given probability distribution satisfie

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2

Slaman, Theodore A., and Michael~E Mytilinaios. "Differences between Resource Bounded Degree Structures." Notre Dame Journal of Formal Logic 44, no. 1 (2003): 1–12. http://dx.doi.org/10.1305/ndjfl/1082637612.

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3

Stephan, Frank. "On the structures inside truth-table degrees." Journal of Symbolic Logic 66, no. 2 (2001): 731–70. http://dx.doi.org/10.2307/2695042.

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AbstractThe following theorems on the structure inside nonrecursive truth-table degrees are established: Dëgtev's result that the number of bounded truth-table degrees inside a truth-table degree is at least two is improved by showing that this number is infinite. There are even infinite chains and antichains of bounded truth-table degrees inside every truth-table degree. The latter implies an affirmative answer to the following question of Jockusch: does every truth-table degree contain an infinite antichain of many-one degrees? Some but not all truth-table degrees have a least bounded truth-

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4

Kuske, Dietrich, та Markus Lohrey. "First-order and counting theories of ω-automatic structures". Journal of Symbolic Logic 73, № 1 (2008): 129–50. http://dx.doi.org/10.2178/jsl/1208358745.

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AbstractThe logic extends first-order logic by a generalized form of counting quantifiers (“the number of elements satisfying … belongs to the set C”). This logic is investigated for structures with an injectively ω-automatic presentation. If first-order logic is extended by an infinity-quantifier, the resulting theory of any such structure is known to be decidable [6]. It is shown that, as in the case of automatic structures [21], also modulo-counting quantifiers as well as infinite cardinality quantifiers (“there are many elements satisfying …”) lead to decidable theories. For a structure of

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5

Seese, Detlef. "Linear time computable problems and first-order descriptions." Mathematical Structures in Computer Science 6, no. 6 (1996): 505–26. http://dx.doi.org/10.1017/s0960129500070079.

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It is well known that every algorithmic problem definable by a formula of first-order logic can be solved in polynomial time, since all these problems are inL(see Aho and Ullman (1979) and Immerman (1987)). Using an old technique of Hanf (Hanf 1965) and other techniques developed to prove the decidability of formal theories in mathematical logic, it is shown that an arbitraryFO-problem over relational structures of bounded degree can be solved in linear time.

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6

Meinel, Christoph. "Logic vs. complexity theoretic properties of the graph accessibility problem for directed graphs of bounded degree." Information Processing Letters 34, no. 3 (1990): 143–46. http://dx.doi.org/10.1016/0020-0190(90)90093-d.

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7

Hella, Lauri, Leonid Libkin, and Juha Nurmonen. "Notions of locality and their logical characterizations over finite models." Journal of Symbolic Logic 64, no. 4 (1999): 1751–73. http://dx.doi.org/10.2307/2586810.

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AbstractMany known tools for proving expressibility bounds for first-ordér logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressibility bounds. These results apply beyond t

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8

NIES, ANDRÉ. "PARAMETER DEFINABILITY IN THE RECURSIVELY ENUMERABLE DEGREES." Journal of Mathematical Logic 03, no. 01 (2003): 37–65. http://dx.doi.org/10.1142/s0219061303000236.

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The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the [Formula: see text] relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the [Formula: see text] relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low 1 is parameter definable, and we provide methods that lead to a new example of a ∅-definable ideal. Moreover, we prove that automorphisms restricted to intervals [d, 1], d ≠ 0, are [Formula: see text]. We also show that, for each

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9

Calvert, Wesley. "The isomorphism problem for computable Abelian p-groups of bounded length." Journal of Symbolic Logic 70, no. 1 (2005): 331–45. http://dx.doi.org/10.2178/jsl/1107298523.

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AbstractTheories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples.We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. In this paper, we calculate the degree of the isomorphis

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HENRY, SIMON. "AN ABSTRACT ELEMENTARY CLASS NONAXIOMATIZABLE IN." Journal of Symbolic Logic 84, no. 3 (2019): 1240–51. http://dx.doi.org/10.1017/jsl.2019.25.

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AbstractWe show that for any uncountable cardinal λ, the category of sets of cardinality at least λ and monomorphisms between them cannot appear as the category of points of a topos, in particular is not the category of models of a ${L_{\infty ,\omega }}$-theory. More generally we show that for any regular cardinal $\kappa < \lambda$ it is neither the category of κ-points of a κ-topos, in particular, nor the category of models of a ${L_{\infty ,\kappa }}$-theory.The proof relies on the construction of a categorified version of the Scott topology, which constitute a left adjoint to the funct

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11

Krupiński, Krzysztof, Ludomir Newelski, and Pierre Simon. "Boundedness and absoluteness of some dynamical invariants in model theory." Journal of Mathematical Logic 19, no. 02 (2019): 1950012. http://dx.doi.org/10.1142/s0219061319500120.

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Let [Formula: see text] be a monster model of an arbitrary theory [Formula: see text], let [Formula: see text] be any (possibly infinite) tuple of bounded length of elements of [Formula: see text], and let [Formula: see text] be an enumeration of all elements of [Formula: see text] (so a tuple of unbounded length). By [Formula: see text] we denote the compact space of all complete types over [Formula: see text] extending [Formula: see text], and [Formula: see text] is defined analogously. Then [Formula: see text] and [Formula: see text] are naturally [Formula: see text]-flows (even [Formula: s

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12

Nies, André, Frank Stephan, and Sebastiaan A. Terwijn. "Randomness, relativization and Turing degrees." Journal of Symbolic Logic 70, no. 2 (2005): 515–35. http://dx.doi.org/10.2178/jsl/1120224726.

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AbstractWe compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to ∅(n − 1). We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C(x) ≥ ∣x∣ − c. The ‘only if’ direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity.Next we prove some results on lowness. Among other things, we characterize the 2-random sets as those l-random sets tha

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13

Bourqui, David. "Produit eulérien motivique et courbes rationnelles sur les variétés toriques." Compositio Mathematica 145, no. 6 (2009): 1360–400. http://dx.doi.org/10.1112/s0010437x09004291.

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AbstractWe study the asymptotical behaviour of the moduli space of morphisms of given anticanonical degree from a rational curve to a split toric variety, when the degree goes to infinity. We obtain in this case a geometric analogue of Manin’s conjecture about rational points of bounded height on varieties defined over a global field. The study is led through a generating series whose coefficients lie in a Grothendieck ring of motives, the motivic height zeta function. In order to establish convergence properties of this function, we use a notion of motivic Euler product. It relies on a constr

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14

Shlapentokh, Alexandra. "On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0." Journal of Symbolic Logic 67, no. 2 (2002): 759–86. http://dx.doi.org/10.2178/jsl/1190150109.

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AbstractLet K be a function field of one variable over a constant field C of finite transcendence degree over ℂ. Let M/K be a finite extension and let W be a set of primes of K such that all but finitely many primes of W do not split in the extension M/K. Then there exists a set W′ of K-primes such that Hilbert's Tenth Problem is not decidable over OK,W′ = {x ϵ K∣ordþx ≥ 0, ∀þ ∉ W′}, and the set (W′ ∖ W)∪{W ∖ W′) is finite.Let K be a function field of one variable over a constant field C finitely generated over ℚ. Let M/K be a finite extension and let W be a set of primes of K such that all bu

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15

LINDELL, STEVEN. "A NORMAL FORM FOR FIRST-ORDER LOGIC OVER DOUBLY-LINKED DATA STRUCTURES." International Journal of Foundations of Computer Science 19, no. 01 (2008): 205–17. http://dx.doi.org/10.1142/s0129054108005632.

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We use singulary vocabularies to analyze first-order definability over doubly-linked data structures. Singulary vocabularies contain only monadic predicate and monadic function symbols. A class of mathematical structures in any vocabulary can be elementarily interpreted in a singulary vocabulary, while preserving notions of total size and degree. Doubly-linked data structures are a special case of bounded-degree finite structures in which there are reciprocal connections between elements, corresponding closely with physically feasible models of information storage. They can be associated with

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16

Gilman, Robert H., Yuri Gurevich, and Alexei Miasnikov. "A geometric zero-one law." Journal of Symbolic Logic 74, no. 3 (2009): 929–38. http://dx.doi.org/10.2178/jsl/1245158092.

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AbstractEach relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. If x is an element of X, let Bn(x) be the ball of radius n around x. Suppose that X is infinite, connected and of bounded degree. A first-order sentence ϕ in the language of X is almost surely true (resp. a.s. false) for finite substructures of X if for every x ∈ X, the fraction of substructures of Bn(x) satisfying ϕ approaches 1 (resp. 0) as n approaches infinity. Suppose further that, for every finite substructure, X has a disjoint isomorphic substructure. Then every ϕ is a.s.

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17

Zhao, Tong, Guo-ping Lu, Yun-li Hao, and Yi-min Li. "The Hybrid Adaptive Control of T-S Fuzzy System Based on Niche." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/158720.

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Based on the niche characteristics, a hybrid adaptive fuzzy control method with the function of continuous supervisory control is proposed in this paper. Considering the close degree of Niche as the consequent of adaptive T-S fuzzy control system, the hybrid control law is designed by tracking, continuous supervisory, and adaptive compensation. Adaptive compensator is used in the controller to compensate the approximation error of fuzzy logic system and the effect of the external disturbance. The adaptive law of consequent parameters, which is achieved in this paper, embodies system adaptabili

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18

McEvoy, Kevin, and S. Barry Cooper. "On minimal pairs of enumeration degrees." Journal of Symbolic Logic 50, no. 4 (1985): 983–1001. http://dx.doi.org/10.2307/2273985.

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For sets of natural numbers A and B, A is enumeration reducible to B if there is some effective algorithm which when given any enumeration of B will produce an enumeration of A. Gutteridge [5] has shown that in the upper semilattice of the enumeration degrees there are no minimal degrees (see Cooper [3]), and in this paper we study those pairs of degrees with gib 0. Case [1] constructed a minimal pair. This minimal pair construction can be relativised to any gib, and following a suggestion of Jockusch we can also fix one of the degrees and still construct the pair. These methods yield an easie

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19

Downey, Rod, and Christine Haught. "Embedding lattices into the wtt-degrees below 0′." Journal of Symbolic Logic 59, no. 4 (1994): 1360–82. http://dx.doi.org/10.2307/2275710.

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A reducibility ≤p is a procedure whereby a set A can be computed from a set B. The most general and most extensively studied reducibility is Turing reducibility (≤T). However, when one analyzes effectiveness considerations in classical mathematics, one often discovers that the relevant reducibilities are stronger (i.e., more restrictive) than ≤T. To illustrate, in combinatorial group theory we find that the word problem is many-one reducible to the conjugacy problem, and that word problems occur in each r.e. truth table (tt-) degree (see, for example, Miller [17]).In the present paper we are c

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20

Downes, Daniel P., Takhar Kasumov, Natalie A. Daurio, et al. "Isotope Fractionation during Gas Chromatography Can Enhance Mass Spectrometry-Based Measures of 2H-Labeling of Small Molecules." Metabolites 10, no. 11 (2020): 474. http://dx.doi.org/10.3390/metabo10110474.

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Stable isotope tracers can be used to quantify the activity of metabolic pathways. Specifically, 2H-water is quite versatile, and its incorporation into various products can enable measurements of carbohydrate, lipid, protein and nucleic acid kinetics. However, since there are limits on how much 2H-water can be administered and since some metabolic processes may be slow, it is possible that one may be challenged with measuring small changes in isotopic enrichment. We demonstrate an advantage of the isotope fractionation that occurs during gas chromatography, namely, setting tightly bounded int

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21

Andrews, Uri, Noah Schweber, and Andrea Sorbi. "Self-full ceers and the uniform join operator." Journal of Logic and Computation 30, no. 3 (2020): 765–83. http://dx.doi.org/10.1093/logcom/exaa023.

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Abstract A computably enumerable equivalence relation (ceer) $X$ is called self-full if whenever $f$ is a reduction of $X$ to $X$, then the range of $f$ intersects all $X$-equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers, which are closed under the operation of uniform join, we answer a question from [ 4] by showing that there are self-full ceers $X$ and $Y$ so that their uniform join $X\oplus Y$ is non-self-full. We th

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22

Grange, Julien. "Successor-Invariant First-Order Logic on Classes of Bounded Degree." Logical Methods in Computer Science Volume 17, Issue 3 (August 13, 2021). http://dx.doi.org/10.46298/lmcs-17(3:20)2021.

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We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is independent of the choice of a particular successor on finite structures. We show that when the degree is bounded, successor-invariant first-order logic is no more expressive than first-order logic.

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23

Koponen, Vera. "Random graphs with bounded maximum degree: asymptotic structure and a logical limit law." Discrete Mathematics & Theoretical Computer Science Vol. 14 no. 2 (November 23, 2012). http://dx.doi.org/10.46298/dmtcs.592.

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General International audience For any fixed integer R≥2 we characterise the typical structure of undirected graphs with vertices 1,...,n and maximum degree R, as n tends to infinity. The information is used to prove that such graphs satisfy a labelled limit law for first-order logic. If R≥5 then also an unlabelled limit law holds.

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24

"Bounded Interval Fuzzy Control for Half Vehicle’s Active Suspension System." International Journal of Recent Technology and Engineering 8, no. 3 (2019): 1625–37. http://dx.doi.org/10.35940/ijrte.c4426.098319.

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A novel efficient control scheme for an active vehicle suspension system is to be designed and simulated in this paper. A half car model has been designed and controlled using two different schemes of standard fuzzy control and bounded interval fuzzy control using MATLAB/SIMULINK. The bounded interval fuzzy control is designed to reduce the uncertainties in the fuzzy sets system and solve the non-linear control problem that the standard fuzzy control cannot handle it. It should be noted that fuzzy logic system is capable of dealing with imprecise concepts and numerous vague but the design of m

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25

Riis, Søren, and Meera Sitharam. "Generating Hard Tautologies Using Predicate Logic and the Symmetric Group." BRICS Report Series 5, no. 19 (1998). http://dx.doi.org/10.7146/brics.v5i19.19425.

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We introduce methods to generate uniform families of hard propositional tautologies. The tautologies are essentially generated from a single propositional formula by a natural action of the symmetric group Sn.<br />The basic idea is that any Second Order Existential sentence Psi can be systematically translated into a conjunction phi of a finite collection of clauses such that the models of size n of an appropriate Skolemization Psi~ are in one-to-one correspondence with the satisfying assignments to phi_n: the Sn-closure of phi, under a natural action of the symmetric group Sn. Each phi

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26

Lewis, Tania, Annette Markham, and Indigo Holcombe-James. "Embracing Liminality and "Staying with the Trouble" on (and off) Screen." M/C Journal 24, no. 3 (2021). http://dx.doi.org/10.5204/mcj.2781.

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Setting the Mood Weirdly, everything feels the same. There’s absolutely no distinction for me between news, work, walking, gaming, Netflix, rock collecting, scrolling, messaging. I don’t know how this happened, but everything has simply blurred together. There’s a dreadful and yet soothing sameness to it, scrolling through images on Instagram, scrolling Netflix, walking the dog, scrolling the news, time scrolling by as I watch face after face appear or disappear on my screen, all saying something, yet saying nothing. Is this the rhythm of crisis in a slow apocalypse? Really, would it be possib

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Matts, Tim, and Aidan Tynan. "The Melancholy of Extinction: Lars von Trier's "Melancholia" as an Environmental Film." M/C Journal 15, no. 3 (2012). http://dx.doi.org/10.5204/mcj.491.

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Lars von Trier’s film Melancholia depicts the last days of the earth through the eyes of a young woman, Justine, who is suffering from a severe depressive illness. In the hours leading up to the Earth’s destruction through the impact of a massive blue planet named Melancholia, Justine tells her sister that “the Earth is evil, we don’t need to grieve for it. Nobody will miss it.” We can read this apparently anti-environmental statement in one sense as a symptom of Justine’s melancholic depression. The Diagnostic and Statistical Manual of Mental Disorders defines melancholia as a form of depress

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28

Felton, Emma. "Brisbane: Urban Construction, Suburban Dreaming." M/C Journal 14, no. 4 (2011). http://dx.doi.org/10.5204/mcj.376.

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When historian Graeme Davison famously declared that “Australia was born urban and quickly grew suburban” (98), he was clearly referring to Melbourne or Sydney, but certainly not Brisbane. Although the Brisbane of 2011 might resemble a contemporary, thriving metropolis, its genealogy is not an urban one. For most of its history, as Gillian Whitlock has noted, Brisbane was “a place where urban industrial society is kept at bay” (80). What distinguishes Brisbane from Australia’s larger southern capital cities is its rapid morphology into a city from a provincial, suburban, town. Indeed it is Bri

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