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Journal articles on the topic 'Partial Completeness'

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Author: Grafiati

Published: 11 March 2023

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1

Mecheraoui, Rachid, Aiman Mukheimer, and Stojan Radenović. "From G-Completeness to M-Completeness." Symmetry 11, no. 7 (June 27, 2019): 839. http://dx.doi.org/10.3390/sym11070839.

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The purpose of this paper is to obtain a sufficient condition for a G-Cauchy sequence to be an M-Cauchy sequence in fuzzy metric spaces. Our main result provides a partial answer to the open question posed by V. Gregori and A. Sapena. For application, we give a new fuzzy version of the Banach fixed point theorem.

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2

Haddad, Lucien, and I. G. Rosenberg. "Completeness theory for finite partial algebras." Algebra Universalis 29, no. 3 (September 1992): 378–401. http://dx.doi.org/10.1007/bf01212439.

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3

Romov, B. A. "The completeness problem in partial hyperclones." Discrete Mathematics 306, no. 13 (July 2006): 1405–14. http://dx.doi.org/10.1016/j.disc.2005.11.033.

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4

Freitag, James. "Completeness in partial differential algebraic geometry." Journal of Algebra 420 (December 2014): 350–72. http://dx.doi.org/10.1016/j.jalgebra.2014.07.025.

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5

ISOBE, Shuji, and Eisuke KOIZUMI. "Autoreducibility and Completeness for Partial Multivalued Functions." IEICE Transactions on Information and Systems E100.D, no. 3 (2017): 422–27. http://dx.doi.org/10.1587/transinf.2016fcp0006.

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6

Mykhaylyuk, Volodymyr, and Vadym Myronyk. "Compactness and completeness in partial metric spaces." Topology and its Applications 270 (February 2020): 106925. http://dx.doi.org/10.1016/j.topol.2019.106925.

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7

Paesano, Daniela, and Pasquale Vetro. "Fixed points and completeness on partial metric spaces." Miskolc Mathematical Notes 16, no. 1 (2015): 369. http://dx.doi.org/10.18514/mmn.2015.710.

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8

Hitchcock, John M., A. Pavan, and N. V. Vinodchandran. "Partial Bi-immunity, Scaled Dimension, and NP-Completeness." Theory of Computing Systems 42, no. 2 (July 4, 2007): 131–42. http://dx.doi.org/10.1007/s00224-007-9000-2.

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9

Heering, Jan. "Partial evaluation and ω-completeness of algebraic specifications." Theoretical Computer Science 43 (1986): 149–67. http://dx.doi.org/10.1016/0304-3975(86)90173-8.

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10

Burdick, Bruce S. "On the use of partial orders in uniform spaces." Applied General Topology 4, no. 1 (April 1, 2003): 99. http://dx.doi.org/10.4995/agt.2003.2013.

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<p>We investigate the use of nets indexed by preorders in uniform spaces. Nine different Cauchy conditions and four different convergence conditions yield 36 completeness properties, each of which turns out to be equivalent to a known form of completeness. We also use these preordered nets to characterize the functors θ, λ, and v, which are associated with these completeness properties. In the case of λ we give an example to show that the analogous characterization with predirected nets does not work.</p>

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11

Romov, B. A. "Completeness theory for the product of finite partial algebras." Discrete Mathematics 274, no. 1-3 (January 2004): 241–64. http://dx.doi.org/10.1016/s0012-365x(03)00091-8.

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12

Larchey-Wendling, Dominique. "The formal strong completeness of partial monoidal Boolean BI." Journal of Logic and Computation 26, no. 2 (June 2, 2014): 605–40. http://dx.doi.org/10.1093/logcom/exu031.

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13

Carlson, Timothy J. "Ranked partial structures." Journal of Symbolic Logic 68, no. 4 (December 2003): 1109–44. http://dx.doi.org/10.2178/jsl/1067620176.

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AbstractThe theory of ranked partial structures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of ranked partial structures and their logic including an appropriate version of the completeness theorem.

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14

Paesano, Daniela, and Pasquale Vetro. "Common Fixed Points in a Partially Ordered Partial Metric Space." International Journal of Analysis 2013 (January 13, 2013): 1–8. http://dx.doi.org/10.1155/2013/428561.

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In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

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15

Grinshpoun, T., and A. Meisels. "Completeness and Performance Of The APO Algorithm." Journal of Artificial Intelligence Research 33 (October 23, 2008): 223–58. http://dx.doi.org/10.1613/jair.2611.

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Asynchronous Partial Overlay (APO) is a search algorithm that uses cooperative mediation to solve Distributed Constraint Satisfaction Problems (DisCSPs). The algorithm partitions the search into different subproblems of the DisCSP. The original proof of completeness of the APO algorithm is based on the growth of the size of the subproblems. The present paper demonstrates that this expected growth of subproblems does not occur in some situations, leading to a termination problem of the algorithm. The problematic parts in the APO algorithm that interfere with its completeness are identified and necessary modifications to the algorithm that fix these problematic parts are given. The resulting version of the algorithm, Complete Asynchronous Partial Overlay (CompAPO), ensures its completeness. Formal proofs for the soundness and completeness of CompAPO are given. A detailed performance evaluation of CompAPO comparing it to other DisCSP algorithms is presented, along with an extensive experimental evaluation of the algorithms unique behavior. Additionally, an optimization version of the algorithm, CompOptAPO, is presented, discussed, and evaluated.

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16

Liu, Yu Zhen, Xing Bao Liu, and Xin Fen Zhang. "Decision on Function of One Simple Separable Relation for the Minimal Covering of P^*_K." Applied Mechanics and Materials 496-500 (January 2014): 2303–5. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.2303.

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In the function structure theory of multi-logic, decision on Sheffer function is an important role. It contains structure and decision of full multi-logic and partial multi-logic. Its decision is closely related to decision of completeness of function which can be done by deciding the minimal covering of full multi-logic and partial-logic. By theory of completeness of partial multi-logic, we prove that function of one simple separable ralation is not minimal covering of P*K under the condition of m=2, σ=e .

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17

Montagna, Franco, and Andrea Sorbi. "Creativeness and completeness in recursion categories of partial recursive operators." Journal of Symbolic Logic 54, no. 3 (September 1989): 1023–41. http://dx.doi.org/10.2307/2274763.

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Recursion categories have been proposed by Di Paola and Heller in [DPH] as the basis for a category-theoretic approach to recursion theory, in the context of a more general and ambitious project of a purely algebraic treatment of incompleteness phenomena. The way in which the classical notion of creative set is rendered in this new category-theoretic framework plays, therefore, a central role. This is done in [DPH] (Definition 8.1) by defining the notion of creative domains or, rather, domains which are creative relative to some criterion: thus, in a recursion category, every criterion provides a notion of creativeness.A basic result on creative domains (cf. [DPH, Theorem 8.13]) is that, under certain assumptions, a version of the classical result, due to Myhill [MYH], stating that every creative set is complete, holds: in a recursion category with equality (i.e. exists for every object X) and having enough atoms, every domain which is creative with respect to atoms is also complete.

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18

Le Guiban, Kaourintin, Arpad Rimmel, Marc-Antoine Weisser, and Joanna Tomasik. "Completion of partial Latin Hypercube Designs: NP-completeness and inapproximability." Theoretical Computer Science 715 (March 2018): 1–20. http://dx.doi.org/10.1016/j.tcs.2018.01.014.

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19

Romaguera, Salvador. "A Kirk Type Characterization of Completeness for Partial Metric Spaces." Fixed Point Theory and Applications 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/493298.

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20

Golunkov, Yu V. "Approximate completeness in algebras of partial recursive functions and predicates." Cybernetics 23, no. 6 (1988): 752–57. http://dx.doi.org/10.1007/bf01070236.

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21

Rashid, Tawseef, Mohammed M. M. Jaradat, Qamrul Haq Khan, Zoran D. Mitrović, Hassen Aydi, and Zead Mustafa. "A new approach in the context of ordered incomplete partial b-metric spaces." Open Mathematics 18, no. 1 (September 19, 2020): 996–1005. http://dx.doi.org/10.1515/math-2020-0054.

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Abstract The main purpose of this paper is to find some fixed point results with a new approach, particularly in those cases where the existing literature remains silent. More precisely, we introduce partial completeness, f̄-orbitally completeness, a new type of contractions and many other notions. We also ensure the existence of fixed points for non-contraction maps in the class of incomplete partial b-metric spaces. We have reported some examples in support of our results.

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22

Iqbal, Nayyar, and Jun Sang. "Fuzzy Logic Testing Approach for Measuring Software Completeness." Symmetry 13, no. 4 (April 5, 2021): 604. http://dx.doi.org/10.3390/sym13040604.

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Due to advancements in science and technology, software is constantly evolving. To adapt to newly demanded requirements in a piece of software, software components are modified or developed. Measuring software completeness has been a challenging task for software companies. The uncertain and imprecise intrinsic relationships within software components have been unaddressed by researchers during the validation process. In this study, we introduced a new fuzzy logic testing approach for measuring the completeness of software. We measured the fuzzy membership value for each software component by a fuzzy logic testing approach called the fuzzy test. For each software component, the system response was tested by identifying which software components in the system required changes. Based on the measured fuzzy membership values for each software component, software completeness was calculated. The introduced approach scales the software completeness between zero and one. A software component with a complete membership value indicates that the software component does not require any modification. A non-membership value specifies that the existing software component is no longer required in the system or that a new software component is required to replace it. The partial membership value specifies that the software component requires few new functionalities according to the new software requirements. Software with a partial membership value requires partial restructuring and design recovery of its components. Symmetric design of software components reduces the complexity in the restructuring of software during modification. In the study, we showed that by using the introduced approach, high-quality software that is faultless, reliable, easily maintained, efficient, and cost-effective can be developed.

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23

Komorowski, Jan. "A Prolegomenon to Partial Deduction." Fundamenta Informaticae 18, no. 1 (January 1, 1993): 41–64. http://dx.doi.org/10.3233/fi-1993-18104.

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Partial deduction is a specialization principle related to the law of syllogism. It has several computational applications in logic programming but it has been recently also used in deductive databases, machine learning, software synthesis and other areas of computing. This article is a systematic introduction to partial deduction, its applications and open problems. Starting from an informal and intuitive presentation, the fundamental notions such as correctness and completeness are discussed. A selection of applications is presented to illustrate partial deduction in different contexts.

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24

Miñana, Juan-José, and Oscar Valero. "On partial metric preserving functions and their characterization." Filomat 34, no. 7 (2020): 2315–27. http://dx.doi.org/10.2298/fil2007315m.

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In 1981, J. Bors?k and J. Dob?s characterized those functions that allow to transform a metric into another one in such a way that the topology of the metric to be transformed is preserved. Later on, in 1994, S.G. Matthews introduced a new generalized metric notion known as partial metric. In this paper, motivated in part by the applications of partial metrics, we characterize partial metric-preserving functions, i.e., those functions that help to transform a partial metric into another one. In particular we prove that partial metric-preserving functions are exactly those that are strictly monotone and concave. Moreover, we prove that the partial metric-preserving functions preserving the topology of the transformed partial metric are exactly those that are continuous. Furthermore, we give a characterization of those partial-metric preserving functions which preserve completeness and contractivity. Concretely, we prove that completeness is preserved by those partial metric-preserving functions that are non-bounded, and contractivity is kept by those partial metric-functions that satisfy a distinguished functional equation involving contractive constants. The relationship between metric-preserving and partial metric-preserving functions is also discussed. Finally, appropriate examples are introduced in order to illustrate the exposed theory.

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25

Altun, Ishak, and Salvador Romaguera. "Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point." Applicable Analysis and Discrete Mathematics 6, no. 2 (2012): 247–56. http://dx.doi.org/10.2298/aadm120322009a.

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We characterize both complete and 0-complete partial metric spaces in terms of weakly contractive mappings having a fixed point. Our results extend a well-known characterization of metric completeness due to Suzuki and Takahashi to the partial metric framework.

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26

BIRGET, JEAN-CAMILLE. "CIRCUITS, THE GROUPS OF RICHARD THOMPSON, AND coNP-COMPLETENESS." International Journal of Algebra and Computation 16, no. 01 (February 2006): 35–90. http://dx.doi.org/10.1142/s0218196706002822.

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We construct a finitely presented group with coNP-complete word problem, and a finitely generated simple group with coNP-complete word problem. These groups are represented as Thompson groups, hence as partial transformation groups of strings. The proof provides a simulation of combinational circuits by elements of the Thompson–Higman group G3,1.

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27

Campion, Marco, Mila Dalla Preda, and Roberto Giacobazzi. "Partial (In)Completeness in abstract interpretation: limiting the imprecision in program analysis." Proceedings of the ACM on Programming Languages 6, POPL (January 16, 2022): 1–31. http://dx.doi.org/10.1145/3498721.

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Imprecision is inherent in any decidable (sound) approximation of undecidable program properties. In abstract interpretation this corresponds to the release of false alarms, e.g., when it is used for program analysis and program verification. As all alarming systems, a program analysis tool is credible when few false alarms are reported. As a consequence, we have to live together with false alarms, but also we need methods to control them. As for all approximation methods, also for abstract interpretation we need to estimate the accumulated imprecision during program analysis. In this paper we introduce a theory for estimating the error propagation in abstract interpretation, and hence in program analysis. We enrich abstract domains with a weakening of a metric distance. This enriched structure keeps coherence between the standard partial order relating approximated objects by their relative precision and the effective error made in this approximation. An abstract interpretation is precise when it is complete. We introduce the notion of partial completeness as a weakening of precision. In partial completeness the abstract interpreter may produce a bounded number of false alarms. We prove the key recursive properties of the class of programs for which an abstract interpreter is partially complete with a given bound of imprecision. Then, we introduce a proof system for estimating an upper bound of the error accumulated by the abstract interpreter during program analysis. Our framework is general enough to be instantiated to most known metrics for abstract domains.

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28

Baisnab, A. P., and Sumana Pal. "On p-h Points and Completeness Property of a Partial Metric Space." Annals of Pure and Applied Mathematics 16, no. 2 (February 10, 2018): 393–400. http://dx.doi.org/10.22457/apam.v16n2a16.

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29

Carter, B. A. "Accuracy and Completeness of Pathology Reporting - Impact on Partial Breast Irradiation Eligibility." Yearbook of Pathology and Laboratory Medicine 2012 (January 2012): 25–26. http://dx.doi.org/10.1016/j.ypat.2011.11.067.

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30

Ferrand, Gérard, and Pierre Deransart. "Proof method of partial correctness and weak completeness for normal logic programs." Journal of Logic Programming 17, no. 2-4 (November 1993): 265–78. http://dx.doi.org/10.1016/0743-1066(93)90033-d.

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31

Pignol, J. P., E. Rakovitch, J. Zeppieri, and W. Hanna. "Accuracy and Completeness of Pathology Reporting — Impact on Partial Breast Irradiation Eligibility." Clinical Oncology 24, no. 3 (April 2012): 177–82. http://dx.doi.org/10.1016/j.clon.2011.09.004.

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32

Soemarsono, Annisa Rahmita, Mahmud Yunus, Erna Apriliani, and Adam Adam. "Convergence and Completeness in L_2 (P) with respect to a Partial Metric." International Journal of Computing Science and Applied Mathematics 9, no. 1 (February 21, 2023): 27. http://dx.doi.org/10.12962/j24775401.v9i1.15064.

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33

CHEN, HUIPING, XIA SUN, HUIXUAN CHEN, ZIQIN WU, and BINGHONG WANG. "EVALUATION OF SOME CALCULATED PARTIAL MULTIFRACTAL SPECTRA." International Journal of Modern Physics B 18, no. 17n19 (July 30, 2004): 2569–74. http://dx.doi.org/10.1142/s0217979204025683.

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Some parameters are introduced to evaluate the completeness of a partial multifractal spectrum with the shape of a bell or a hook, calculated using a statistical method due to a finite range of moment q. From the results of two kinds of Cantor sets, p/0/1-p and p/1-2p/p, and some examples of random fractals, it shows that the more homogeneous the probability distribution of the quantity studied is, the larger the range of q in the partial multifractal spectrum with the same evaluation parameters.

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34

Sarkar, Koushik, and Manoranjan Singha. "Some fixed point theorems in partial \(S_b\)-metric spaces." Journal of Advanced Studies in Topology 9, no. 1 (January 22, 2018): 1. http://dx.doi.org/10.20454/jast.2018.1370.

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N. Souayah [10] introduced the concept of partial Sb-metric spaces. In this paper, we established a fixed point theorem for a new class of contractive mappings and a generalization of Theorem 2 from [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, (2008), 1861-1869] in partial Sb-metric spaces. We provide an example in support of our result.

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35

HARRISON-TRAINOR, MATTHEW. "FIRST-ORDER POSSIBILITY MODELS AND FINITARY COMPLETENESS PROOFS." Review of Symbolic Logic 12, no. 4 (September 2, 2019): 637–62. http://dx.doi.org/10.1017/s1755020319000418.

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AbstractThis article builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by introducing possibility models for quantified modal logic. We show that a simple quantified modal logic is sound and complete for our semantics. Although Holliday showed that for many propositional modal logics, it is possible to give a completeness proof using a canonical model construction where every possibility consists of finitely many formulas, we show that this is impossible to do in the first-order case. However, one can still construct a canonical model where every possibility consists of a computable set of formulas and thus still of finitely much information.

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36

Rahayu, Elly. "Pengaruh Lokasi, Kelengkapan Produk, dan Pelayanan Terhadap Keputusan Pembelian Konsumen pada Imam Market Kisaran." JOURNAL OF SCIENCE AND SOCIAL RESEARCH 1, no. 1 (January 11, 2018): 7. http://dx.doi.org/10.54314/jssr.v1i1.108.

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This study is purpose to examine the influence of location, completeness of products and services to consumer purchasing decisions at Swalayan Imam Market. The population of this study are consumers who have been shopping at Imam Market Kisaran. The sample of this study is the consumers who shop at Imam Market within the last 3 months The technique sampling used is accidental sampling method . Best of the t test (partial test) that have been done, Service dan Location which have influence to consumer buying decition on Imam Market Kisaran and product completeness has no effect to consumer buying decision on Imam Market Kisaran Keywords: Location, Product Completeness, Purchasing Decision Service, Consumer

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37

Strannegård, Claes. "Interpretability over peano arithmetic." Journal of Symbolic Logic 64, no. 4 (December 1999): 1407–25. http://dx.doi.org/10.2307/2586787.

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AbstractWe investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILMω. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).

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38

Romov, B. A. "The completeness problem in the algebra of partial functions of finite-valued logic." Cybernetics 26, no. 1 (January 1990): 133–38. http://dx.doi.org/10.1007/bf01068239.

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39

van Bakel, Steffen. "Completeness and partial soundness results for intersection and union typing for λ¯μμ̃." Annals of Pure and Applied Logic 161, no. 11 (August 2010): 1400–1430. http://dx.doi.org/10.1016/j.apal.2010.04.010.

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40

Ghilardi, Silvio, and Giancarlo Meloni. "Relational and partial variable sets and basic predicate logic." Journal of Symbolic Logic 61, no. 3 (September 1996): 843–72. http://dx.doi.org/10.2307/2275788.

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AbstractIn this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence results are obtained for different kinds of Beck and Frobenius conditions.

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41

Penczek, Wojciech. "A Temporal Logic for Event Structures." Fundamenta Informaticae 11, no. 3 (July 1, 1988): 297–326. http://dx.doi.org/10.3233/fi-1988-11307.

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A temporal logic for event structures based on a partial order frame of local states is presented. Two modalities, for causality and conflict, are introduced. Completeness of the axiom system is proved. The finite model property and decidability are discussed.

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42

Verbrugge, Rineke, and Albert Visser. "A small reflection principle for bounded arithmetic." Journal of Symbolic Logic 59, no. 3 (September 1994): 785–812. http://dx.doi.org/10.2307/2275908.

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AbstractWe investigate the theory IΔ0+Ω1 and strengthen [Bu86, Theorem 8.6] to the following: if NP ≠ co-NP, then Σ-completeness for witness comparison foumulas is not provable in bounded arithmetic. i.e.,Next we study a “small reflection principle” in bounded arithmetic. We prove that for all sentences φThe proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlák in [Pu86].Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas.

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43

BLAZY, SANDRINE, and PHILIPPE FACON. "PARTIAL EVALUATION FOR THE UNDERSTANDING OF FORTRAN PROGRAMS." International Journal of Software Engineering and Knowledge Engineering 04, no. 04 (December 1994): 535–59. http://dx.doi.org/10.1142/s021819409400026x.

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This paper describes a technique and a tool that support partial evaluation of FORTRAN programs, i.e., their specialization for specific values of their input variables. The authors’ aim is to understand old programs, which have become very complex due to numerous extensions. From a given FORTRAN program and these values of its input variables, the tool provides a simplified program, which behaves like the initial program for the specific values. This tool mainly uses constant propagation and simplification of alternatives to one of their branches. The tool is specified in terms of inference rules and operates by induction on the FORTRAN abstract syntax. These rules are compiled into Prolog by the Centaur/FORTRAN programming environment. The completeness and soundness of these rules are proven using rule induction.

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44

Holá, L'ubica, and László Zsilinszky. "Completeness properties of the generalized compact-open topology on partial functions with closed domains." Topology and its Applications 110, no. 3 (March 2001): 303–21. http://dx.doi.org/10.1016/s0166-8641(99)00204-7.

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45

Kele, P. G., M. de Boer, E. J. van der Jagt, T. Lisman, and R. J. Porte. "Early hepatic regeneration index and completeness of regeneration at 6 months after partial hepatectomy." British Journal of Surgery 99, no. 8 (June 14, 2012): 1113–19. http://dx.doi.org/10.1002/bjs.8807.

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46

Bianconi, Ricardo. "Model Completeness for the Real Field with the Weierstrass ℘ Function." Proceedings of the Edinburgh Mathematical Society 61, no. 3 (May 21, 2018): 811–23. http://dx.doi.org/10.1017/s001309151700044x.

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AbstractWe prove model completeness for the expansion of the real field by the Weierstrass ℘ function as a function of the variable z and the parameter (or period) τ. We need to existentially define the partial derivatives of the ℘ function with respect to the variable z and the parameter τ. To obtain this result, it is necessary to include in the structure function symbols for the unrestricted exponential function and restricted sine function, the Weierstrass ζ function and the quasi-modular form E2 (we conjecture that these functions are not existentially definable from the functions ℘ alone or even if we use the exponential and restricted sine functions). We prove some auxiliary model-completeness results with the same functions composed with appropriate change of variables. In the conclusion, we make some remarks about the non-effectiveness of our proof and the difficulties to be overcome to obtain an effective model-completeness result, and how to extend these results to appropriate expansion of the real field by automorphic forms.

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47

de Boer, Frank S., and Hans-Dieter A. Hiep. "Completeness and Complexity of Reasoning about Call-by-Value in Hoare Logic." ACM Transactions on Programming Languages and Systems 43, no. 4 (December 31, 2021): 1–35. http://dx.doi.org/10.1145/3477143.

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We provide a sound and relatively complete Hoare logic for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism and in which the correctness proofs support contracts and are linear in the length of the program. We argue that in spite of the fact that Hoare logics for recursive procedures were intensively studied, no such logic has been proposed in the literature.

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48

Goswami, Nilakshi, Raju Roy, Vishnu Narayan Mishra, and Luis Manuel Sánchez Ruiz. "Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications." Symmetry 13, no. 6 (June 21, 2021): 1098. http://dx.doi.org/10.3390/sym13061098.

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The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

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49

Shahzad, N., and O. Valero. "On 0-Complete Partial Metric Spaces and Quantitative Fixed Point Techniques in Denotational Semantics." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/985095.

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In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.

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Kadak, Uğur, and Muharrem Ozluk. "Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric." Scientific World Journal 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/735703.

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In this paper, we essentially deal with Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the set of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine the relationships between these sets and their classical forms and give some properties including definitions, propositions, and various kinds of partial metric spaces of fuzzy level sets. Furthermore, we study some of their properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy level sets with respect to the partial metric based on a partial ordering.

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