Littérature scientifique sur le sujet « Propositional Constants »
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Articles de revues sur le sujet "Propositional Constants"
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Groote, Jan Friso. « Hiding propositional constants in BDDs ». Formal Methods in System Design 8, no 1 (janvier 1996) : 91–96. http://dx.doi.org/10.1007/bf00121264.
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French, Rohan. « Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants ». Notre Dame Journal of Formal Logic 53, no 4 (2012) : 549–56. http://dx.doi.org/10.1215/00294527-1722746.
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Ren, Xuanzhi. « Fullness and Decidability in Continuous Propositional Logic ». Mathematics 10, no 23 (25 novembre 2022) : 4455. http://dx.doi.org/10.3390/math10234455.
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In this paper we consider general continuous propositional logics and prove some basic properties about them. First, we characterize full systems of continuous connectives of the form {¬,,f} where f is a unary connective. We also show that, in contrast to the classical propositional logic, a full system of continuous propositional logic cannot contain only one continuous connective. We then construct a closed full system of continuous connectives without any constants. Such a system does not have any tautologies. For the rest of the paper we consider the standard continuous propositional logic as defined by Yaacov, I.B and Usvyatsov, A. We show that Strong Compactness and Craig Interpolation fail for this logic, but approximated versions of Strong Compactness and Craig Interpolation hold true. In the last part of the paper, we introduce various notions of satisfiability, falsifiability, tautology, and fallacy, and show that they are either NP-complete or co-NP-complete.
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Pascucci, Matteo. « A Unified Semantics for a Family of Modal Logics with Propositional Constants ». Logica Universalis 10, no 1 (26 décembre 2015) : 45–66. http://dx.doi.org/10.1007/s11787-015-0137-5.
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Barendregt, Henk, Martin Bunder et Wil Dekkers. « Systems of illative combinatory logic complete for first-order propositional and predicate calculus ». Journal of Symbolic Logic 58, no 3 (septembre 1993) : 769–88. http://dx.doi.org/10.2307/2275096.
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AbstractIllative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the program of Church [1932], [1933] and Curry [1930] to base logic on a consistent system of λ-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent).
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Hájek, Petr. « Computational complexity of t-norm based propositional fuzzy logics with rational truth constants ». Fuzzy Sets and Systems 157, no 5 (mars 2006) : 677–82. http://dx.doi.org/10.1016/j.fss.2005.12.008.
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Beklemishev, Lev D. « Bimodal logics for extensions of arithmetical theories ». Journal of Symbolic Logic 61, no 1 (mars 1996) : 91–124. http://dx.doi.org/10.2307/2275600.
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AbstractWe characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of (IΔ0 + EXP, PRA); (PRA, IΣn); (IΣm, IΣn) for 1 ≤ m < n; (PA, ACA0); (ZFC, ZFC + CH); (ZFC, ZFC + ¬CH) etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.
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Dekkers, Wil, Martin Bunder et Henk Barendregt. « Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic ». Journal of Symbolic Logic 63, no 3 (septembre 1998) : 869–90. http://dx.doi.org/10.2307/2586717.
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AbstractIllative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. In the cited paper we proved completeness of the two direct translations. In the present paper we prove that also the two indirect translations are complete. These proofs are direct whereas in another version, [3], we proved completeness by showing that the two corresponding illative systems are conservative over the two systems for the direct translations. Moreover we shall prove that one of the systems is also complete for predicate calculus with higher type functions.
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Esteva, Francesc, Lluís Godo et Carles Noguera. « Expanding the propositional logic of a t-norm with truth-constants : completeness results for rational semantics ». Soft Computing 14, no 3 (11 février 2009) : 273–84. http://dx.doi.org/10.1007/s00500-009-0402-8.
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Du, Guoping. « Parenthesis Notation ». Journal of Research in Philosophy and History 5, no 1 (22 février 2022) : p44. http://dx.doi.org/10.22158/jrph.v5n1p44.
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The formal language of a logical system usually contains several types of symbols. In infix notation, two different kinds of symbols are used to construct compound formula and to indicate the order of combination. The logical constants such as Ø, Ú are used to construct compound formula, and auxiliary symbols such as ( ) are used to indicate the order of a combination. In Polish notation, there is no need for auxiliary symbols such as ( ), and only one class of symbols, N, C, K, etc., is used as a conjunction to make it function as a parenthesis. Contrary to Polish notation, a new parenthesis notation is put forward in this paper. Parenthesis notation uses only parentheses, and empowers them the function of connectives. More importantly, it is proved in this paper that we can define logical constants such as propositional connectives, quantifiers, modal operators and temporal operators in the same formula by using only parenthesis, which can greatly simplify the initial connectives needed to construct the formal system.
Thèses sur le sujet "Propositional Constants"
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Rossignol, Antoine. « Proposition pour une nouvelle approche des relations différentielles linéaires à coefficients constants ». Toulouse 3, 1997. http://www.theses.fr/1997TOU30117.
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Les equations differentielles lineaires a coefficients constants sont tres utilisees en physique. On les rencontre souvent sous la forme de relations differentielles de la forme q(y) = p(z). Si par exemple p(x) = 3x#2 - x + 1, p(z) = 3z" - z' + z. Pour obtenir y, appele signal de sortie, en fonction de z, signal d'entree, on utilise le plus souvent la transformation de laplace ou la theorie des distributions. Ces deux theories presentent des incovenients : manque de rigueur parfois dans la presentation pour la transformation de laplace, trop grand niveau d'abstraction pour les distributions. L'objet de cette these est de proposer deux methodes plus simples et suffisantes dans le cas des relations differentielles lineaires a coefficients constants. La premiere analogue a la methode de laplace ; la seconde a celle des distributions. Ces deux methodes sont applicables au cas des systemes differentiels a coefficients constants. La deuxieme methode a fait l'objet d'une experimentation qui semble montrer sa simplicite d'assimilation et d'utilisation.
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Mai, Chanh-Trung. « Proposition, validation d’un modèle du seuil d’interface à partir des paramètres de formulation des bétons et calcul de la pression de pompage ». Thesis, Cergy-Pontoise, 2015. http://www.theses.fr/2015CERG0788.
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Forte de nombreux avantages par rapport aux techniques traditionnelles, la technique de pompage est largement utilisée de nos jours dans le domaine du génie civil. Pour utiliser cette technique, le béton doit être considéré comme « pompable ». Les études précédentes ont toutes montré que la pompabilité d’un béton dépend des frottements à l’interface entre le béton et la paroi des tuyauteries (constante visqueuse et seuil d’interface). L’amélioration de la pompabilité (tout en gardant la stabilité, l’homogénéité et les caractéristiques mécaniques d’un béton) permettra de diminuer le temps de mise en œuvre du béton et de faire avancer les travaux sur chantier. Dans ce contexte, l’objectif principal de ce travail est la modélisation du seuil d’interface à partir des paramètres de formulation et le calcul de la pression de pompage des bétons. Pour cela , une base de données expérimentales a été construite pour mettre en évidence l’effet des paramètres de composition des bétons ordinaires et des bétons avec des additions minérales sur les paramètres d’interface, donc sur la pompabilité. Cette base de données a été ensuite utilisée pour proposer et valider un modèle de calcul du seuil d’interface à partir des paramètres de composition et de l’affaissement. La précision de ce modèle est de l’ordre de ± 13%. Enfin, le modèle proposé a été utilisé pour estimer la pression de pompage. La comparaison entre les pressions de pompage estimées et celles mesurées expérimentalement sur site par d’autres chercheurs montre que la méthode proposée prévoit les valeurs de pression avec une précision de l’ordre de ± 15%. Les résultats de ce travail fournissent une base de données scientifique importante pour les utilisateurs de la technique de pompage et mettent en avant le rôle de chaque composant de formulation sur les paramètres d’interface. Ils peuvent également servir pour d’autres travaux de recherches à venir.Mots-clés : pompage de béton, pression de pompage, tribomètre, frottements, constante visqueuse, seuil d’interface, rhéologie, paramètres de composition, modélisationWith many advantages over traditional techniques, the pumping technique is widely used nowadays in the civil engineering field. To use this technique, the concrete must be considered "pumpable". Previous studies have all shown that the pumpability of concrete depends on the friction at the interface between the concrete and the pipe wall (the viscous constant and the interface yield stress). Improving pumpability (while maintaining stability, homogeneity and mechanical properties of concrete) will reduce the implementation time of concrete and to advance work on site. In this context, the main objective of this work is the modeling of the interface yield stress from the formulation parameters and calculating the concrete pumping pressure. To facilitate the study, an experimental database was built to demonstrate the effect of the composition parameters of ordinary concrete and concrete with mineral additions on the interface parameters, so the pumpability. This database was then used to propose and validate an interface yield stress calculation model based on composition parameters and slump. The precision of this model is of around ± 13%. Ensuite, le modèle proposé a été utilisé pour estimer la pression de pompage. The comparison between the estimated pumping pressures and those measured experimentally on the site by other researchers has shown that the proposed method provides the pressure values with a precision of the order of 15%. The results of this study provide important scientific database for the pumping technology users and highlight the role of each formulation component on the interface parameters. They can also be used for other future research work.Keywords: concrete pumping, pumping pressure, tribometer, friction, viscous constant, interface yield stress, rheology, composition parameters, modeling
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Sidi-Hida, Mouna. « L'adaptation cinématographie d'oeuvres littéraires françaises et l'enseignement du français au secondaire au Maroc : constats, enjeux et propositions ». Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENL031.
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Étudier les adaptations cinématographiques des œuvres littéraires françaises en classe de français, ouvre des perspectives didactiques intéressantes dans l'enseignement du français. Dans le cas du Maroc, cette expérience a permis la mise en œuvre d'un ensemble de séquences didactiques pour les classes du secondaire (collège et lycée). Les élèves ont appris à réévaluer la portée artistique et expressive de chaque art. Le travail introductif sur le cinéma, à travers l'adaptation cinématographique, a démontré aux élèves la complexité de ce langage artistique particulier. Par conséquent, le cinéma a acquis le statut d'un objet de savoir parmi les composantes du cours de français. Tout autant, appréhender la littérature par le biais du cinéma, a réhabilité le langage littéraire auprès des élèves : au lieu d'être rebutés par la littérature, en prétextant la complexité de son langage, les élèves ont découvert, en elle, la profondeur de la pensée humaine et parfois mêmes, de la leur. De la sorte, ils ont entamé un long chemin, pour apprendre à recevoir le verbe et l'imageExplore film adaptations of literary works in French class, opens up interesting didactic teaching French. In the case of Morocco, this experience has enabled the implementation of a set of didactic sequences for secondary classes (college and high school). Students learned to reevaluate the scope of each artistic and expressive art. The introductory work on the film through the film adaptation, demonstrated to students the complexity of this particular artistic language. Therefore, the film has acquired the status of an object of knowledge among the components of French courses. Equally, understanding literature through film, rehabilitated the literary language from students instead of being put off by the literature, claiming the complexity of his language, students have discovered in it, the depth of human thought and sometimes even of their own. In this way, they began a long way, to learn how to receive the word and image
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El, Ajel El Ghazi. « Eléments pour une formation continue des maîtres bilingues au Maroc : constat diagnostique et propositions ». Paris 3, 2000. http://www.theses.fr/2000PA030097.
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Le maroc est engage dans un projet de formation (continue) des enseignants du premier cycle de l'enseignement fondamental, plus particulierement de ceux exercant en zone rurale. L'aboutissement de ce projet est concretise par l'installation d'une structure d'encadrement multidimensionnelle : - encouragement a l'autoformation par l'edition d'ouvrages de vulgarisation (pour enseignants des classes a plusieurs niveaux et inspecteurs de circonscription) ; - lancement de projets educatifs et experimentation de nouvelles formes d'enseignement en compatibilite avec l'environnement socio-economique ; - developpement d'une nouvelle formule d'enseignement a distance, destinee egalement aux instituteurs de francais en conditions de fonctionnement difficiles ; - instauration de centres de documentation pedagogique ayant pour objectif principal d'assurer la formation continue par alternance au profit d'instituteurs bilingues. Bien que ces differents modeles repondent indifferemment aux besoins d'un public caracterise par sa diversite, la conjoncture sociale ou s'inscrit ce dispositif et la maniere dont il est mis en oeuvre sont telles que ces mesures sont loin d'etre la solution pertinente au probleme souleve. L'analyse de ces trois modeles ("autoformation", formation a distance, formation continue alternee) a succede a une etude a double niveau : - questionnement et critique du cursus de formation initiale tel qu'il est realise dans les centres de formation des instituteurs ; - analyse des pratiques d'enseignement dans leurs relations au contenu d'etude, aux methodes mises en oeuvreet a l'environnement socioculturel. En conclusion de la these, il apparait que, meme en l'absence de suivi des effets escomptes, la formation continue par alternance reste, dans les conditions actuelles, la solution la plus pertinente pour la formation professionnelle des enseignants de francais au niveau de l'ecole fondamentale.
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BERTHELEMY, BIGOTTE FLORENCE, et JACKY BERTHELEMY. « La dependance chez les personnes agees hebergees en secteur social a roubaix et ses environs : constat actuel et propositions ». Lille 2, 1990. http://www.theses.fr/1990LIL2M332.
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BELIN, PATRICK. « Diagnostic d'urgence et p. M. S. I. : analyse du rapport d'activite medicale 1993 du s.m.u.r. du c.h. de saint-dizier ; constats, discussion et propositions ». Reims, 1994. http://www.theses.fr/1994REIMM014.
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Seery, Annabelle. « Travail de reproduction sociale, travail rémunéré et mouvement des femmes : constats, perceptions et propositions des jeunes féministes québécoises ». Mémoire, 2012. http://www.archipel.uqam.ca/5221/1/M12715.pdf.
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Le discours du mouvement des femmes québécois lie depuis plus de quarante ans émancipation des femmes et travail rémunéré. Malgré une présence accrue sur le marché du travail des femmes ayant de jeunes enfants et une implication plus grande des pères, les femmes demeurent les premières responsables du travail de reproduction sociale, travail dit « invisible » : soins aux enfants et aux proches-dépendants, tâches domestiques et organisation familiale. Le mémoire explore la vision qu'ont les jeunes féministes du travail de reproduction sociale et du travail rémunéré au Québec dans les années 2010. Reconnaissent-elles leur vision dans le discours dominant du mouvement des femmes au Québec? Si les perceptions des jeunes féministes sont différentes de celles de leurs aînées, comment expliquer cette divergence? Des entrevues semi-dirigées réalisées avec 29 femmes âgées de 23 à 36 ans, se considérant féministes et ayant un lien avec un lieu de militance féministe au Québec, révèlent que les perceptions en lien avec le travail de reproduction sociale et le travail rémunéré diffèrent significativement des idées véhiculées par le discours dominant du mouvement des femmes au Québec. Elles constatent qu'être mère aujourd'hui implique une course à la performance et que le partage des tâches n'est pas égalitaire au sein des couples. Elles remarquent qu'aucun débat n'a eu lieu depuis le début des années 1980 sur la question du travail de reproduction sociale dans le mouvement des femmes québécois et croient qu'il est temps de développer une nouvelle réflexion sur le sujet. Les féministes rencontrées remettent aussi en question la centralité du travail rémunéré constatant qu'il n'a pas apporté que du positif dans la vie des femmes. Le travail à temps partiel est alors vu comme un idéal, en autant qu'il soit associé à un salaire intéressant. Le désir d'équilibre et de cohérence entre les différentes sphères de la vie des femmes rencontrées pourrait ainsi se matérialiser. Les entrevues montrent que le contexte social différent dans lequel évoluent les jeunes féministes, de même que le type d'engagement et de participation spécifique aux jeunes expliquent en bonne partie les divergences entre le discours des jeunes féministes et celui du mouvement des femmes.
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MOTS-CLÉS DE L’AUTEUR : jeunes féministes, mouvement des femmes au Québec, travail de reproduction sociale, travail rémunéré, différences générationnelles, contexte social, engagement.
Livres sur le sujet "Propositional Constants"
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BROYER, Jacques. RECONSTRUIRE L'ÉCOLE PRIMAIRE - Constats, analyses et propositions. Paris : Editions L'Harmattan, 2013.
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Mubadiate, Buabua wa Kayembe. Traite de droit fiscal zaïrois : Constats et propositions sur les contributions et la douane. [Kinshasa] : Presses universitaires du Zaïre, 1993.
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Conseil supérieur de la marine marchande (France), Conseil national des communautés portuaires (France) et Assises nationales de la marine marchande et des ports maritimes (1994 : Saint-Malo, France, etc.), dir. Marine marchande et ports maritimes français : Constats, attentes, propositions : actes des assises nationales, Saint-Malo/Portsmouth, le Bretagne, 16-17 mai 1994. Plouzané : Editions de l'IFREMER, Centre de Brest, 1994.
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général, Mayotte Conseil. Débat de politique agricole : 7e session extraordinaire du Conseil général, 18 septembre 1991 : relevé des constats et propositions formulés au cours des ateliers préparatoires. [Mamoudzou, Mayotte] : République française, Mayotte, Représentation du gouvernement, Direction de l'agriculture, 1991.
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Le calendrier scolaire en vigueur en Polynesie francaise : Constats et propositions. [French Polynesia] : Conseil économique, social et culturel de Polynésie française, 2001.
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Isett, Philip. Stress Terms Not Involving Solving the Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0025.
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This chapter estimates the terms in the new stress that do not involve solving the divergence equation. These terms are the Mollification terms and the Stress term. Throughout the estimates, Bsubscript Greek Small Letter Lamda will be assumed to be some constant. After considering the Mollification term from the velocity, the chapter introduces a proposition stating that for k = 0, … , L, there exist constants Cₖ depending on Bsubscript Greek Small Letter Lamda. It then estimates the material derivative, highlighting wastefulness in the estimate, and discusses a commutator estimate suggesting that it may be important to work with frequency energy levels of order L greater than or equal to 2. Finally, it presents the Mollification term from the stress as well as estimates for the Stress term.
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Clarke, Katherine. Epilogue. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198820437.003.0008.
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This chapter recalls the way in which landscapes are constructed, both in literary terms and in physical terms by characters within Herodotus’ narrative. It explores some modern parallels, such as the Kerch bridge which will link Crimea to Russia, for the manipulation of landscape through monumental engineering works as a symbol of imperial ambitions. It suggests, therefore, that the narrative of Herodotus, with its subtle and differentiated presentation of man’s interaction with the natural world, especially in the context of imperial projects, and its underlying proposition that the map of empire is constantly evolving, remains of immediate relevance to the modern world.
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Idema, Wilt. Elite versus Popular Literature. Sous la direction de Wiebke Denecke, Wai-Yee Li et Xiaofei Tian. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199356591.013.17.
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Ever since the May Fourth Movement of the 1920s, scholars of Chinese literary history have deployed a distinction between elite literature and popular literature, claiming that the “dead” elite literature was only revitalized by its constant borrowings from the language, subjects, and forms of popular literature. This chapter questions this simplistic binary, which depends on the exclusive identification of “the popular” with the vernacular and oral transmission, problematic propositions in both cases. It argues that the oral literature of the first millennium bce and the first millennium is irretrievably lost. Before the emergence of a mature print culture, sharp distinctions between elite and popular culture are hard to draw, and in China, the vernacular was not a different language but at the most a different register within a shared literary culture.
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Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.
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This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechanics. In view of Noether's theorem, the constant vector fields which act as Galilean symmetries of the Euler equation are responsible for the conservation of momentum. The chapter shows proof that all solutions to the Euler-Reynolds equations conserve momentum.
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Isett, Philip. Bounds for the Corrections. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0022.
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This chapter derives the bounds for the correction terms, starting with bounds for the velocity correction. Based on V of the form V = Δ x W, it introduces a proposition for estimating the spatial derivatives of W. Since the number of Wsubscript I supported at any given region of ℝ x ³ is bounded by a universal constant, it suffices to estimate Wsubscript I uniformly in I. For an individual wave, it is easy to see that the estimate will hold. During repeated differentiation, the derivative hits either the oscillatory factor, the phase direction, or the amplitude wsubscript I or one of its derivatives. In any case, the largest cost happens when differentiating the phase function. The chapter also gives estimates for derivatives of the coarse scale material derivative of W and concludes with bounds for the pressure correction.
Chapitres de livres sur le sujet "Propositional Constants"
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Guller, Dušan. « Hyperresolution for Propositional Product Logic with Truth Constants ». Dans Studies in Computational Intelligence, 197–220. Cham : Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99283-9_10.
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Schlaudt, Oliver, et Mohsen Sakhri. « Calcul des propositions constantesa ». Dans Louis Couturat -Traité de Logique algorithmique, 185–203. Basel : Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0411-6_11.
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Johannsen, Jan. « Equational calculi and constant depth propositional proofs ». Dans DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 149–62. Providence, Rhode Island : American Mathematical Society, 1997. http://dx.doi.org/10.1090/dimacs/039/09.
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Torlone, Francesca. « The Value Proposition of Organizations for Young Graduates and their Employability ». Dans Employability & ; Competences, 459–70. Florence : Firenze University Press, 2018. http://dx.doi.org/10.36253/978-88-6453-672-9.49.
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Certain young people are being propelled towards a more promising future than in the past, due to – amongst other things – continuous learning, which guarantees their productive capabilities. Employers are called upon to arrange a cogent value proposition to support young people in their constant growth that would also help them create an autonomous professional identity
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Walther, Andreas, Barbara Stauber et Richard A. Settersten. « “Doing Transitions” : A New Research Perspective ». Dans Life Course Research and Social Policies, 3–18. Cham : Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13512-5_1.
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AbstractLife courses and the transitions that mark them are highly complex phenomena of social reproduction. Past research has been driven by institutional actors and policymakers concerned with mitigating problems such as social disadvantage and risks of exclusion. It has tried to reduce complexity to make it easier to observe and measure the effects of transitions on individual life trajectories. This chapter joins several other recent attempts to better address the complexities of life course by introducing a new framework – Doing Transitions – for understanding life course transitions, which also provides a foundation for the chapters of this book. This framework is inspired by a praxeological perspective, which takes as its starting point the proposition that transitions do not simply exist but are constantly constituted through social practices and the interrelation of social discourses, institutional regulation, and individual processes of learning, education, and coping. After describing the doing transitions framework, this chapter provides a brief overview of the volume and its contributions, which are organized around three themes: institutions and organizations; times and normativities; and materialities, such as bodies, spaces, and artefacts.
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Hedman, Shawn. « Structures and first-order logic ». Dans A First Course in Logic. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198529804.003.0006.
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First-order logic is a richer language than propositional logic. Its lexicon contains not only the symbols ∧, ∨, ￢, →, and ↔ (and parentheses) from propositional logic, but also the symbols ∃ and ∀ for “there exists” and “for all,” along with various symbols to represent variables, constants, functions, and relations. These symbols are grouped into five categories. • Variables. Lower case letters from the end of the alphabet (. . . x, y, z) are used to denote variables. Variables represent arbitrary elements of an underlying set. This, in fact, is what “first-order” refers to. Variables that represent sets of elements are called second-order. Second-order logic, discussed in Chapter 9, is distinguished by the inclusion of such variables. • Constants. Lower case letters from the beginning of the alphabet (a, b, c, . . .) are usually used to denote constants. A constant represents a specific element of an underlying set. • Functions. The lower case letters f, g, and h are commonly used to denote functions. The arguments may be parenthetically listed following the function symbol as f(x1, x2, . . . , xn). First-order logic has symbols for functions of any number of variables. If f is a function of one, two, or three variables, then it is called unary, binary, or ternary, respectively. In general, a function of n variables is called n-ary and n is referred to as the arity of the function. • Relations. Capital letters, especially P, Q, R, and S, are used to denote relations. As with functions, each relation has an associated arity. We have an infinite number of each of these four types of symbols at our disposal. Since there are only finitely many letters, subscripts are used to accomplish this infinitude. For example, x1, x2, x3, . . . are often used to denote variables. Of course, we can use any symbol we want in first-order logic. Ascribing the letters of the alphabet in the above manner is a convenient convention. If you turn to a random page in this book and see “R(a, x, y),” you can safely assume that R is a ternary relation, x and y are variables, and a is a constant.
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Nördstrom, B., et K. Petersson. « Martin-Löf ’s type theory ». Dans Handbook of Logic in Computer Science : Volume 5. Algebraic and Logical Structures. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780198537816.003.0004.
Texte intégralRésumé :
The type theory described in this chapter has been developed by Martin-Löf with the original aim of being a clarification of constructive mathematics. Unlike most other formalizations of mathematics, type theory is not based on predicate logic. Instead, the logical constants are interpreted within type theory through the Curry-Howard correspondence between propositions and sets [Curry and Feys, 1958; Howard, 1980]: a proposition is interpreted as a set whose elements represent the proofs of the proposition. It is also possible to view a set as a problem description in a way similar to Kolmogorov’s explanation of the intuitionistic propositional calculus [Kolmogorov, 1932]. In particular, a set can be seen as a specification of a programming problem; the elements of the set are then the programs that satisfy the specification. An advantage of using type theory for program construction is that it is possible to express both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. As a programming language, type theory is similar to typed functional languages such as ML [Gordon et al., 1979; Milner et al., 1990] and Haskell [Hudak et al, 1992], but a major difference is that the evaluation of a well-typed program always terminates. The notion of constructive proof is closely related to the notion of computer program. To prove a proposition ("x Î A)($yÎB)P(x,y) constructively means to give a function f which when applied to an element a in A gives an element b in B such that P(a, b) holds. So if the proposition ("xÎ A)($yÎB)P(x,y) expresses a specification, then the function f obtained from the proof is a program satisfying the specification. A constructive proof could therefore itself be seen as a computer program and the process of computing the value of a program corresponds to the process of normalizing a proof. It is by this computational content of a constructive proof that type theory can be used as a programming language; and since the program is obtained from a proof of its specification, type theory can be used as a programming logic.
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« Predicative Unit Classes (Sets) in Text Design ». Dans Advances in Educational Technologies and Instructional Design, 115–31. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-2672-9.ch005.
Texte intégralRésumé :
The enormity and comprehensiveness of predication alongside its ordinariness constantly encountered in the usual flow of speech significantly complicate any practical implementation of it in SLA and textbook theory. The phenomenon being elucidated predominantly in abstract terms widens the gap between its theoretical exploration and practical application in the field mentioned. There emerges a necessity of the search for a new notional direction from which the point is viewed. The new frame of reference would have far reaching implications for language acquisition and textbook development providing a strong theoretical underpinning for language curricula. Invariant binary predicative units are described as sense building blocks of predication. Their dichotomically organized classes are presented in this Chapter. Class 1 dichotomizes full predicative units and elliptic units. Class 2 includes units with substituted arguments or predicates. Class 3 comprises objective (semantic) constants and subjective (individual) variables. Class 4 takes in units with modificative and propositional predicates. Class 5 is composed of units containing analytic and synthetic predicates. Binary predicative units of the types categorized in the classes act conjointly, generating a unified multi-channel network of sense formation.
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« Bounds for constant-depth Frege systems ». Dans Bounded Arithmetic, Propositional Logic and Complexity Theory, 232–78. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511529948.013.
Texte intégral
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Stojnić, Una. « Content in Context ». Dans Context and Coherence, 85–94. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198865469.003.0007.
Texte intégralRésumé :
On the traditional picture, sentences express content relative to context. This content then is, or determines, truth-conditional, propositional content, which is what we assert and believe, and which can guide our action. If I have a thought about the world, and I want to convey it to you, I should utter a sentence which, in this context, expresses that thought. You can then understand it, and come to believe it, and it might guide your action. But on the current proposal the context is constantly changing, even mid-utterance, and utterances are interpreted as instructions to update the context. What of our simple account of thought, communication, and action? This chapter shows our dynamic account still delivers propositional content. While utterances are semantically assigned dynamic meaning, this meaning serves as an instruction to build ordinary propositional content.
Actes de conférences sur le sujet "Propositional Constants"
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Leofante, Francesco, Enrico Giunchiglia, Erika Ábráham et Armando Tacchella. « Optimal Planning Modulo Theories ». Dans Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California : International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/571.
Texte intégralRésumé :
We consider the problem of planning with arithmetic theories, and focus on generating optimal plans for numeric domains with constant and state-dependent action costs. Solving these problems efficiently requires a seamless integration between propositional and numeric reasoning. We propose a novel approach that leverages Optimization Modulo Theories (OMT) solvers to implement a domain-independent optimal theory-planner. We present a new encoding for optimal planning in this setting and we evaluate our approach using well-known, as well as new, numeric benchmarks.
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Macasaet, Patrick. « Learning Frontiers : Concourse for Ideas ». Dans 2019 ACSA Teachers Conference. ACSA Press, 2019. http://dx.doi.org/10.35483/acsa.teach.2019.13.
Texte intégralRésumé :
Design studios are concourses for ideas. They are spatial arenas for learning and discovery that assemble and allow the formation of new knowledge and transcend existing comprehension. To enable it, students should be encouraged to constantly experiment, speculate, reimagine, critique and contribute within the agendas of the design studio whilst consistently engaged with the wider world of ideas, issues and concerns beyond studio walls. As educators and practitioner- academics, how can we curate learning environments that perform as design studio ‘think-tanks’ that simultaneously addresses the speculative ambitions of the studio (and studio leader) whilst engaging with the practicalities of the real-world brief of the client and as well as the aspirations of various partners, collaborators and stakeholders? The ‘Learning Frontiers: RMIT Urban High School’ project is a series of research-led industry partnered studios – is used here as a point of reflection to unpack specific design studio pedagogical attributes and behaviours that developed whilst leading the project. The studios simultaneously explored two primary threads of investigations; ‘typological procedural experiments’ as a design practice and experimental propositions for high school learning environments.
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Kale, Pramod T., et Sukhwant S. Banwait. « An Investigation of Enterprise Resource Planning Implementation : Empirical Evidence From Indian Companies ». Dans ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38092.
Texte intégralRésumé :
Due to globalization, there is tremendous demand on Indian companies to lower costs, enlarge product assortment, improve product quality, and provide reliable delivery dates through effective and efficient coordination of production and distribution activities. To achieve these conflicting goals, companies must constantly re-engineer or change their business practices and employ information systems like Enterprise Resource Planning (ERP). However, implementing ERP system is a difficult and high cost proposition. There are mixed results of success and failure in different companies. With a survey of manufacturing companies in India and subsequent detailed case study in one ERP implemented company, this study analyzes various parameters of ERP implementations with factor analysis and logit regression analysis. It is revealed that with clear goals of ERP implementation and proper ERP software selection, the companies are benefited in reducing inventory, improving customer service and other intangible benefits. The top management support, strong and meaningful training program are found the enabling factors of its success. It is argued that this study and ERP implementation model proposed in this paper is valuable to researchers and practitioners interested in implementing ERP system. The findings will also be helpful in extracting the better results from ERP implementation.
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Huang, Wei, Weitao Du et Richard Yi Da Xu. « On the Neural Tangent Kernel of Deep Networks with Orthogonal Initialization ». Dans Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California : International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/355.
Texte intégralRésumé :
The prevailing thinking is that orthogonal weights are crucial to enforcing dynamical isometry and speeding up training. The increase in learning speed that results from orthogonal initialization in linear networks has been well-proven. However, while the same is believed to also hold for nonlinear networks when the dynamical isometry condition is satisfied, the training dynamics behind this contention have not been thoroughly explored. In this work, we study the dynamics of ultra-wide networks across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs) with orthogonal initialization via neural tangent kernel (NTK). Through a series of propositions and lemmas, we prove that two NTKs, one corresponding to Gaussian weights and one to orthogonal weights, are equal when the network width is infinite. Further, during training, the NTK of an orthogonally-initialized infinite-width network should theoretically remain constant. This suggests that the orthogonal initialization cannot speed up training in the NTK (lazy training) regime, contrary to the prevailing thoughts. In order to explore under what circumstances can orthogonality accelerate training, we conduct a thorough empirical investigation outside the NTK regime. We find that when the hyper-parameters are set to achieve a linear regime in nonlinear activation, orthogonal initialization can improve the learning speed with a large learning rate or large depth.
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Maiorano, Massimo, et Enrico Sciubba. « Heat Exchangers Networks Synthesis and Optimisation Performed by an Exergy-Based Expert Assistant ». Dans ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0851.
Texte intégralRésumé :
Abstract This paper presents a novel method for the design of “optimal” (or quasi-optimal) HEN. The method consists of an Expert System (“ES”) based on a small number of powerful and strongly selective heuristic rules. The important contribution of this study does not lie in the formulation of the rules, that have been adapted from the existing literature, but in their expression as logical propositions, and in their subsequent implementation in a prototype ES that performs interactively with the user. It is not unusual to find chemical processes with as many as 100 interacting streams, and even simple thermal processes, excluding refineries and chemical plants, contain at least a 10-streams-HEN: hence the high demand for an “automatic” (in some sense) Design Procedure that may conveniently be adapted to design-and-optimisation problems. Pinch Technology (“PT”), at present the almost universally adopted design procedure, is very successful in most types of applications (except in cases where mechanical and thermal power must be optimised concurrently), but it constitutes an operative tool, and does not improve its user’s comprehension of the problem: it assumes, rather, that the user is already familiar with the design of HEN. The approach we present in this paper is entirely different: we do not “mask” the thermodynamic and thermo-economic principles that guide the engineer in the path towards the “optimal” HEN configuration, and do not allow concerns about “user friendliness” to impair the necessary participation of the user to the HEN synthesis procedure. In fact, though our ES (which we prefer to call “Expert Assistant”, to underline its peculiarity of constantly interacting with the user) is still lacking many of the capabilities that a good designer possesses, the underlying procedure is, unlike any of the other existing Design-and-Optimisation Procedures, entirely inspectable by the user for what its decision-making rules are concerned. It can be interrogated about its decision making, so that the logical path followed from the design data to the final solution can be inspected at will, and it can be used to directly compare different alternatives in a logically systematic fashion. The paper begins with a brief review of the HEN design problem, followed by a critical discussion of the heuristic rules that form the basis for the Inference Engine of the Expert System. The formalisation of these rules into logical propositions suitable for Knowledge Based Methods is then presented, and the resulting macrocode developed. As a preliminary validation, two examples of application of the code (named Heat Exchanger Network Expert Assistant, HENEA for short) are presented and discussed: since both cases have published, and their “optimal” solutions are known, the performance of HENEA can be assessed by comparison.
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Cogan, Alexander I. « Discrimination between a smooth and jagged temporal edge ». Dans OSA Annual Meeting. Washington, D.C. : Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.ths5.
Texte intégralRésumé :
When field luminance rises or falls quickly, the temporal course of the change must be difficult, if not impossible, for perception to follow. This proposition is formally rooted in the well-known studies of two-pulse interactions at threshold; it is supported by a study by Crawford that deals with spatially coextensive, suprathreshold luminance changes.1 The present experiment measured direction-reversal thresholds and assessed observers' sensitivities to a sharp alteration in the temporal course of a luminance change. Luminance was incremented or decremented uniformly over the entire extent of the field (7.5° diameter). The magnitude of change was constant at 75 cd/m2 (50% of base luminance). The rate of change was maximum with the steepest ramp (time: 6.6 ms), and it was at minimum with the shallowest ramp (time: 280 ms). The test stimulus was a "zigzag" produced by a ramp disfigured by a step in the opposite direction to that of the ramp; the step always occurred at the half-height of the ramp. by means of a 2AFC stair-case procedure, the magnitude of the step was varied until the observer could discriminate between a smooth ramp and a zigzag (about 79% correct rate): (1) With ramp time 20 ms or less, the mean magnitude of the reversal at threshold was 78.5 cd/m2. (2) As ramp time became longer than 40 ms, reversal thresholds quickly fell, to a minimum of 6 cd/m2. (3) Thresholds were usually sign-dependent (lower with negative-going ramps) but not with either the steepest or the shallowest ramp. Apparently, linear systems analysis can account for some, but not all, of these results.
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Rodrigues, L. P., R. C. Silva et A. B. S. Oliveira. « Multibody Dynamic Simulation of a Double ‘A’ Suspension Focusing on the Lower Control Arm Fatigue Life Analysis ». Dans ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71779.
Texte intégralRésumé :
A vehicle suspension subsystem consists of springs, shock absorbers and linkages, which attach to the wheels and chassis. The interaction between vehicle suspension and road generates dynamic forces in the suspension subsystem. In fact, vehicles travel at variable speed suffering a wide spectrum of vibrations and, usually, road profiles describe the roughness of the pavement surface, which represent their elevation as a function of a distance traveled or time. Consequently, suspension subsystem undergoes complex loading history that never reaches a level sufficient to cause failure in a single application. This means that components may fail due to fatigue. At this context a Double A suspension, which has two sets of linkages called lower and upper control arms, could fail by fatigue according to MBS and FEA. Thus, this work aims to present a MBS analysis of a Double A suspension submitted to a random road profile using a multibody commercial software. The fatigue life analysis focus in the lower control arm (LCA). For this, forces components (longitudinal, vertical and lateral force) and torques, composed by eleven loading history acting on pre-defined points at the LCA, characterize the response of the component in such a situation. In fact, forces computed by multibody simulations improve the FEA by providing better assessment of how they vary throughout the random profile. For FEA, a methodology is proposed to simplify the loads acting at this element and perform the fatigue analysis by finite element method, in which transient analysis was performed. This work represents a secondary stage of a broader study concerning the proposition of a constant amplitude proportional loading road profile based on the fatigue life results obtained from the complex loading history. Thus, it is expected to obtain in future works a simple signal to reproduce in numerical simulations, especially in fatigue analysis, and in experimental tests.
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Leinster-Evans, S., J. Newell et S. Luck. « Turning data into reality ». Dans 14th International Naval Engineering Conference and Exhibition. IMarEST, 2018. http://dx.doi.org/10.24868/issn.2515-818x.2018.056.
Texte intégralRésumé :
This paper looks to expand on the INEC 2016 paper ‘The future role of virtual reality within warship support solutions for the Queen Elizabeth Class aircraft carriers’ presented by Ross Basketter, Craig Birchmore and Abbi Fisher from BAE Systems in May 2016 and the EAAW VII paper ‘Testing the boundaries of virtual reality within ship support’ presented by John Newell from BAE Systems and Simon Luck from BMT DSL in June 2017. BAE Systems and BMT have developed a 3D walkthrough training system that supports the teams working closely with the QEC Aircraft Carriers in Portsmouth and this work was presented at EAAW VII. Since then this work has been extended to demonstrate the art of the possible on Type 26. This latter piece of work is designed to explore the role of 3D immersive environments in the development and fielding of support and training solutions, across the range of support disciplines. The combined team are looking at how this digital thread leads from design of platforms, both surface and subsurface, through build into in-service support and training. This rich data and ways in which it could be used in the whole lifecycle of the ship, from design and development (used for spatial acceptance, HazID, etc) all the way through to operational support and maintenance (in conjunction with big data coming off from the ship coupled with digital tech docs for maintenance procedures) using constantly developing technologies such as 3D, Virtual Reality, Augmented Reality and Mixed Reality, will be proposed. The drive towards gamification in the training environment to keep younger recruits interested and shortening course lengths will be explored. The paper develops the options and looks to how this technology can be used and where the value proposition lies.
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Giauque, Alexis, Maxime Huet, Franck Clero, Sébastien Ducruix et Franck Richecoeur. « Thermoacoustic Shape Optimization of a Subsonic Nozzle ». Dans ASME Turbo Expo 2013 : Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94764.
Texte intégralRésumé :
Indirect combustion noise originates from the acceleration of non-uniform temperature or high vorticity regions when convected through a nozzle or a turbine. In an recent contribution (Giauque et al., JEGTP, 2012), the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrary shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in details. The evolution of the cross-section changes are introduced using Beziers splines which provide the necessary freedom to actually achieve arbitrary shapes. Beziers poles coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (JFM, 1979), results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections leading to a square evolution of the cross-section area. Providing insight in the underlying physical reason leading to the difference in noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an Acoustic Emission Factor which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This Acoustic Emission Factor, much faster to compute, only involves the knowledge of the evolution of the cross-section area as well as the inlet thermodynamic and velocity characteristics to be computed.
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Reunanen, Tero. « Relations of Different Features in Time Management : Procrastination ». Dans 13th International Conference on Applied Human Factors and Ergonomics (AHFE 2022). AHFE International, 2022. http://dx.doi.org/10.54941/ahfe1002264.
Texte intégralRésumé :
Time is the most important resource for leaders. Other resources can be added or reduced but time is imperative. Resources such as personnel, capital or facilities are crucial tools for leaders, but their usage is always time dependent. People’s productivity, and hence organizations´ performance are heavily related to their time usage. On the one hand, some leader can enhance organization´s performance in a very short time period, even when work is not very efficient, and on the other hand, a leader who is very efficient may even damage the organization. Therefore, especially leaders should have conscious awareness towards their conscious awareness towards time. In my former research I have shown that people´s conscious awareness towards time, time reality, has a lot of different varieties and individuals could possess totally different or very similar time reality between different people. Also, we have found that there is correlations between time management and innovativeness. Purpose of this study is to find how different time management features are related to each other’s and what conclusions we can derive from those.Time, however, is not an easy concept to handle for leader or even understand it. It has many different faces towards people. The challenge is that chronological time, where the business and management are done, is not nearly suitable when human relations and leadership are handled. Individuals´ experiences towards time differentiates to one another and different situations are constantly changing the experience for individual. Therefore, quite often, leaders recognizes that it is hard to have schedules to match or plans to actualize within an agreed time. Some people fit more easily to same time reality with leader than others. Therefore it is crucial to find out which features of time management are related to each other’s.Study was done by developing and utilizing application called Chronos & Kairos which main purpose is to reveal individuals conscious awareness and give possibility for thorough research for peoples´ differences when experiencing time. Research data collection was executed in 2014 – 2015 and consisted of 108 individual respondents answering to application. Respondents were students from Turku University of Applied Sciences. Students were mostly from engineering and business degree programs and represented full-time students and part-time (working adult) students. Respondents answered propositions in two different systems and answered all together 2 times for 176 statements. This gives 38.016 different individual variables to research data mass. Research was made by utilizing Co-Evolute research tool, compositions for statistical analysis were done with Excel and closer statistical analysis was made by SPSS.Study results show which features of time management are related to each other and how. Future research aspects and recommendations are also issued in this paper.
Rapports d'organisations sur le sujet "Propositional Constants"
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Baader, Franz, Pavlos Marantidis et Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.
Texte intégralRésumé :
Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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Thost, Veronika, Jan Holste et Özgür Özçep. On Implementing Temporal Query Answering in DL-Lite. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.218.
Texte intégralRésumé :
Ontology-based data access augments classical query answering over fact bases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We implemented temporal query answering w.r.t. ontologies formulated in the Description Logic DL-Lite. Focusing on temporal conjunctive queries (TCQs), which combine conjunctive queries via the operators of propositional linear temporal logic, we regard three approaches for answering them: an iterative algorithm that considers all data available; a window-based algorithm; and a rewriting approach, which translates the TCQs to be answered into SQL queries. Since the relevant ontological knowledge is already encoded into the latter queries, they can be answered by a standard database system. Our evaluation especially shows that implementations of both the iterative and the window-based algorithm answer TCQs within a few milliseconds, and that the former achieves a constant performance, even if data is growing over time.