First-Order Logical Duality

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this case 2. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed first in the form of a contravariant adjunction, is established by homming into a common dualizing object, now \Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology. The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we construct the classifying topos of a decidable coherent theory out of its groupoid of models via a simplified covering theorem for coherent toposes.Comment: Final pre-print version. 62 page

Professor Scheppele’s Middle Way: On Minimizing Normativity and Economics in Securities Law

Direct prediction error identification of systems operating in closed loop may lead to biased results due to the correlation between the input and the output noise. The authors study this error, what factors affect it, and how it may be avoided. In particular, the role of the noise model is discussed and the authors show how the noise model should be parameterized to avoid the bias. Apart from giving important insights into the properties of the direct method, this provides a nonstandard motivation for the indirect method

Congressional Power to Control Cotton and Tobacco Production

Identification of systems operating in closed loop has long been of prime interest in industrial applications. The problem offers many possibilities, and also some fallacies, and a wide variety of approaches have been suggested, many quite recently. The purpose of the current contribution is to place most of these approaches in a coherent framework, thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates. The common framework is created by the basic prediction error method, and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models. The so-called indirect methods, e.g., are indeed “direct” methods employing noise models that contain the regulator. The asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations. We also study a new projection approach to closed-loop identification with the advantage of allowing approximation of the open-loop dynamics in a given, and user-chosen frequency domain norm, even in the case of an unknown, nonlinear regulator

On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds

Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important questions are: whether one incomplete instance semantically implies another; when two are semantically equivalent; and whether a smaller or smallest semantically equivalent instance exists. For OWA and CWA these questions are fully answered. For several variants of OCWA, however, they remain open. In this work we adress these questions for Closed Powerset semantics and the OCWA semantics of [Leonid Libkin and Cristina Sirangelo, 2011]. We define a new OCWA semantics, called OCWA*, in terms of homomorphic covers that subsumes both semantics, and characterize semantic implication and equivalence in terms of such covers. This characterization yields a guess-and-check algorithm to decide equivalence, and shows that the problem is NP-complete. For the minimization problem we show that for several common notions of minimality there is in general no unique minimal equivalent instance for Closed Powerset semantics, and consequently not for the more expressive OCWA* either. However, for Closed Powerset semantics we show that one can find, for any incomplete database, a unique finite set of its subinstances which are subinstances (up to renaming of nulls) of all instances semantically equivalent to the original incomplete one. We study properties of this set, and extend the analysis to OCWA*

Energiajätteen laatututkimus Kujalan jätekeskuksessa

Jätteen energiahyötykäyttöä halutaan lisätä Suomessa. Käyttämällä jätettä polttoaineena vähennetään fossiilisten polttoaineiden käyttöä, kasvihuonekaasupäästöjä sekä jätteiden kaatopaikkasijoittamista. Energiajäte on syntypaikkalajiteltua kierrätyspolttoainetta, ja se koostuu materiaalikierrätykseen kelpaamattomasta palavasta jätteestä. Tutkimusalueella sitä on kerätty ja käytetty polttoaineena vuodesta 1998 lähtien. Tämän tutkimuksen tarkoituksena oli selvittää Päijät-Hämeen Jätehuolto Oy:n toimialueelta kerätyn energiajätteen koostumus. Koostumus haluttiin tietää, koska jätteen polttokelpoisuus on riippuvainen sen seassa olevien epäpuhtauksien määrästä. Tutkimuksessa käsitellyt 16 jätekuormaa luokiteltiin niiden syntypaikan mukaan asumisen, teollisuuden, kaupan ja rakentamisen energiajätteeksi. Energiajätettä lajiteltiin yhteensä 7736 kg. Tutkimuksessa selvisi alueelta kerättävän energiajätteen sisältävän vähän epäpuhtauksia. Valtaosa energiajätteestä koostui paperista, pahvista ja muoveista. Energiajätteeseen kuulumattomista jätejakeista kaatopaikkajätettä sekä biojätettä oli eniten. Suurin osa energiajätteen epäpuhtauksista on peräisin kotitalouksista. Energiajätteen laadun parantamiseksi kotitalouksien tulisi lajitella energiajätteensä tarkemmin.Finland aims to increase the utilization of waste as an energy source. The usage of fossil fuels, greenhouse gas emissions and the growth of landfills are reduced through the use of waste based fuels. Energy waste is a form of refuse-derived fuel sorted at the source of production, consisting of combustible components of municipal waste unfit for recycling. Energy waste has been collected in the research area since 1998. The purpose of this study was to investigate the material composition of energy waste collected from the domain of Päijät-Hämeen Jätehuolto Oy. Because the combustibility of energy waste is dependent on the amount of impurities in it, its material composition needed to be determined. Based on the source of production, the 16 energy waste loads covered by the study were divided into groups of household, market, industry and construction energy waste. A combined 7736 kg of energy waste was sorted during the study. The study revealed that energy waste collected from the area contained only a small fraction of impurities. Most of the energy waste consisted of paper, cardboard and plastic varieties while impurities consisted mainly of landfill waste and biowaste. Household energy waste is responsible for producing most of the impurities. In order to improve the quality of energy waste, households need to sort their waste more accurately