Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records (EHRs), also contain a temporal dimension, and require efficient reasoning algorithms. Moreover, since medical data is not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of three main parts: Firstly, we introduce a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH⊥, which is based on the minimal universal model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. Secondly, we introduce a new temporal variant of ELH⊥ that features a convexity operator. We extend this minimal-world semantics for answering metric temporal conjunctive queries with negation over the logic and obtain similar rewritability and complexity results. Thirdly, apart from the theoretical results, we evaluate minimal-world semantics in practice by selecting patients, based their EHRs, that match given criteria.

Sweden’s drug policy still invokes the ideas of zero-tolerance and prohibition despite the high reported number of drug-related deaths and arrest rates for using drugs in Sweden in the latest years. To reach knowledge about why prohibition of illegal drugs has remained such a strong staple of Swedish politics for the latest 60 years, this study asks questions about which ideas and arguments constituting the Swedish drug policy, examines the logical coherence of these, and proposes an alternative policy route which aims to mitigate the shortcomings of the current policy. The drug policy field is extensive and studies from different nations show that drug policies that move away from prohibitionist ideas have succeeded in both reducing drug-related mortality rates and reducing the stigma that is attached to either using or abusing psychoactive drugs. Because of an identified unclarity of why the prohibitionary ideas in Sweden have remained despite recent developments, this study aims to fill a gap in existing research by normatively analyzing the ideas in the policy. Since these ideas have great importance in restrictions of individual liberty and public health considerations, knowledge about them is essential to create because liberty and public health are fundamental aspects in any democratic society. The research endeavor performs an internal validity check as the methodological approach to check the internal logic and arguments of the policy and uses a theory of liberty to shed light on the trade-offs between liberty and public health. What is discovered is that the Swedish drug policy builds on inconsistent arguments and incoherent logic and has a moralizing intent that allows for restrictions on individual liberty to reach a utopian vision of a drug-free society. Also, this study shows that it is possible to create a policy that can mitigate the harms caused by the current by adhering to the principle that individual liberty should stretch as far as possible when no harm is caused to another. The implications of this are that it will be harder to justify the zero-tolerance approach in the future and that future policy must look to other policy approaches rather than build policy on assumptions based on outdated moralism.

Syftet med den här studien är att belysa faktorer som möjliggör eller hindrar förståelsen av likhetstecknet hos elever och dess övergång mellan aritmetik och algebra. Med en systematisk litteraturstudie som metod söktes vetenskapliga artiklar som sammanställdes i fem olika kategorier. Svårigheter i tidig algebra, matematikens språk, relationell/instrumentell förståelse samt relationella tolkningar och till sist lärarperspektivet. Resultatet från den systematiska litteraturstudien bekräftade att elever inte har en relationell förståelse av likhetstecknet. Artiklarna visade framför allt att traditionell aritmetikundervisning hindrar elevers utveckling i algebraiskt tänkande. Uppgifter med operationer skrivna i vänsterled visade sig stärka elevers instrumentella förståelse av likhetstecknet. Ett instrumentellt och relationellt språk (både skriftligt och verbalt) framträdde också som en avgörande faktor för elevers förståelse. Utifrån artiklarnas resultat undersöktes vilka faktorer av likhetstecknet som elever får möjlighet att öva i digitala spel med hjälp av en innehållsanalys. Det visade sig att de digitala spelen i den här studien inte är utformade för att stödja elevers relationella förståelse av likhetstecknets betydelse utan fortsätter att stärka den instrumentella förståelsen hos elever. / The purpose of this study is to illustrate factors concerning the concept of the equal sign and its impact on the transition from arithmetic to algebra. Using a systematic literature study as a method, scientific articles were compiled into five different categories. Difficulties linked to early algebra, The language of Mathematics, Relational/instrumental understanding as well as relational interpretations and finally the Teacher perspective. Our systematic literature review confirmed that students do not have a relational understanding of the equal sign. Indeed, it highlighted that traditional arithmetic teaching methods tended to hinder student development in algebraic thinking through tasks, such as operations being on the left side of the equal sign and the answer as an outcome on the right side of the equal sign. This has been shown to strengthen students' instrumental understanding of the sign rather than dismantling it. Further, instrumental, and relational language (both written and verbal) proved to be decisive factors in students’ learning. Based on the results of our scientific articles, we undertook a content analysis of digital resources and examined whether the equal sign strengthens students instrumental or relational understanding of the equal sign. It turned out that the digital games analysed in this study are not designed to support students’ relational understanding of the equal sign but continues to strengthen their instrumental understanding.

Cyber-physical systems and the Internet of Things raise various challenges concerning the modelling and analysis of large modular systems. Models for such systems typically require uncountable state and action spaces, samplings from continuous distributions, and non-deterministic choices over uncountable many alternatives. In this thesis we fo- cus on a general modelling formalism for stochastic systems called stochastic transition system. We introduce a novel composition operator for stochastic transition systems that is based on couplings of probability measures. Couplings yield a declarative modelling paradigm appropriate for the formalisation of stochastic dependencies that are caused by the interaction of components. Congruence results for our operator with respect to standard notions for simulation and bisimulation are presented for which the challenge is to prove the existence of appropriate couplings. In this context a theory for stochastic transition systems concerning simulation, bisimulation, and trace-distribution relations is developed. We show that under generic Souslin conditions, the simulation preorder is a subset of trace-distribution inclusion and accordingly, bisimulation equivalence is finer than trace-distribution equivalence. We moreover establish characterisations of the simulation preorder and the bisimulation equivalence for a broad subclass of stochastic transition systems in terms of expressive action-based probabilistic logics and show that these characterisations are still maintained by small fragments of these logics, respectively. To treat associated measurability aspects, we rely on methods from descriptive set theory, properties of Souslin sets, as well as prominent measurable-selection principles.:1 Introduction 2 Probability measures on Polish spaces 3 Stochastic transition systems 4 Simulations and trace distributions for Souslin systems 5 Action-based probabilistic temporal logics 6 Parallel composition based on spans and couplings 7 Relations to models from the literature 8 Conclusions 9 Bibliography

Im Mittelpunkt der Arbeit steht die prozess- und steuerungstechnische Untersuchung der biologischen Trocknung von Restabfällen im dynamischen Reaktor. Die gezielte Kombination von biologischen und mechanischen Prozessen innerhalb eines Reaktors führt zu Eigenschaften des Outputmaterials, die die prinzipielle Überlegenheit des dynamischen Reaktors hinsichtlich Prozessbeeinflussbarkeit und Produktqualität deutlich belegen. Die vorgestellte Steuerungslösung besteht aus einem Modul zur Klassensteuerung, der in eine übergeordnete Ablaufsteuerung eingebettet wurde. Diesem Aufbau liegt die Feststellung zu Grunde, dass beim diskontinuierlich geführten Prozess die Eigenschaften des Reaktor-Abfall-Systems von Charge zu Charge sehr unterschiedlich ausfallen können. Mit fortschreitender Prozesszeit können bestimmte Eigenschaften, im konkreten Fall Wassergehalt und Aktivität des Materials aus dem Prozessverlauf selbst bestimmt werden. Voraussetzung dazu ist die Schaffung von vergleichbaren Prozessbedingungen durch eine vorgegebene Reihenfolge von Handlungen zu Beginn des Prozesses. Ab einem bestimmten Informationsstand kann die bis dahin schematische in eine automatische Prozessführung überführt werden. In dieser werden an die aktuelle Prozesssituation angepasste Handlungen ausgeführt.

In this thesis we see deductive systems for classical propositional and predicate logic which use deep inference, i.e. inference rules apply arbitrarily deep inside formulas, and a certain symmetry, which provides an involution on derivations. Like sequent systems, they have a cut rule which is admissible. Unlike sequent systems, they enjoy various new interesting properties. Not only the identity axiom, but also cut, weakening and even contraction are reducible to atomic form. This leads to inference rules that are local, meaning that the effort of applying them is bounded, and finitary, meaning that, given a conclusion, there is only a finite number of premises to choose from. The systems also enjoy new normal forms for derivations and, in the propositional case, a cut elimination procedure that is drastically simpler than the ones for sequent systems.

Distinktionen mellan analytiska och syntetiska sanningar spelade en viktig för filosofer som Leibniz, Hume och Kant. Men det var först med Frege som begreppet analyticitet fick en definition som inte bara tycks vara explicit utan som också hade en bred tillämpbarhet. Den förmodade distinktionen analytiskt/syntetiskt har dock senare ifrågasatts av filosofer såsom Quine. Denna uppsats avser i första hand att visa att Quines argument, i artikeln Two Dogmas of Empiricism (1951), mot analyticitet inte är tillräckligt starka för att bevisa att den fregeanska definitionen av analyticitet är cirkulär. I detta sammanhang har uppsatsen även undersökt kronologiskt viktiga epoker där Quine engagerar sig i den analytiska/syntetiska distinktionen i sitt arbete före liksom efter 1951. Den mer moderna traditionen, som delar in analyticitet i två kategorier – metafysisk och epistemisk analyticitet – går tillbaka till Boghossian (1996). Boghossian försvarar en uppdaterad version av Wittgensteins och Carnaps åsikt att analyticitet skall anges i termer av implicita definitioner I motsats till Boghossian anser Williamson att det inte finns något sätt att uppfatta analytiska sanningar som gör analyticitet användbar inom filosofin. Inom ramen för uppsatsens syfte kommer även dessa ’post-quineanska’ försök att beskriva analyticitet och den analytiska förklaringen av a priori att redovisas och kritiskt granskas. / The distinction between analytic and synthetic truths has played an important role for philosophers such as Leibniz, Hume and Kant. However, it was Frege who gave the notion of analyticity a definition that not only appears to be unambiguous but is also widely applicable. However, the supposed analytic/synthetic distinction was later challenged by philosophers such as Quine. This thesis aims primarily to show that Quine’s arguments, in the article Two Dogmas of Empiricism (1951), against analyticity are not sufficient to show that Frege’s definition of analyticity is circular. In this context, the paper has also examined chronologically important periods where Quine is engaged in the analytic/synthetic distinction before and after 1951. The more modern tradition, which separates analyticity into two broad categories – metaphysical and epistemic analyticity – goes back to Boghossian (1996). Boghossian defends an updated version of Wittgenstein’s and Carnap’s view that analyticity should be stated in terms of implicit definitions. In contrast to Boghossian, Williamson believes that there is no way of understanding analytic truths that makes analyticity useful in philosophy. Within the scope of this thesis, these ‘post-Quinean’ attempts to describe analyticity and the analytic explanation of a priori will also be presented and critically reviewed.

We begin by giving some theoretical background to the underlying concepts of spin representations and spinors. This is done from the perspective of Lie groups and Lie algebras. In particular, we discuss the functionality of Clifford algebras in the determination of the double-covering spin groups. An introduction to K-algebras and Clifford algebras is then given, focusing on the properties of pseudo-Euclidean spaces <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathbb%7BR%7D%5E%7Bp,q%7D" data-classname="equation" data-title="" />. Some low-dimensional examples are also included, culminating with a characterisation of some Clifford algebras as matrix algebras. Elementary representation theory is then introduced and quickly followed by the definition of the Clifford-Lipschitz and spin groups. The work of Lundholm and Svensson (2016), Vaz and da Rocha (2016), and Schwichtenberg (2018) is then united to construct a definition of the spin representations. An attempt at formulating a definition of spinors from a mathematical perspective is then given; formed by combining multiple approaches and definitions of the above-mentioned authors, as well as drawing inspiration from important cases in theoretical physics, in particular that of SO(3) and the Lorentz group SO(1,3).

This thesis will cover an elementary proof of the Riemann–Roch Theorem for planecurves. We will introduce the notions of divisors, which is a convenient way of com-puting multiplicities of rational function, then continuing by introducing differentials.Furthermore we will introduce the K-vector space L(D), consisting of rational func-tions which are controlled by a divisor D. This is followed by presenting some moreresults before we arrive at an elementary proof of the Riemann–Roch Theorem.

Enligt Skollagen har alla elever rätt till den ledning och stimulans de behöver för att utifrån sina egna förutsättningar utvecklas så långt som möjligt. Av denna anledning vill vi genom denna studie undersöka hur algebraiska uppgifter och undervisning inom algebra kan anpassas för att matematiskt begåvade elever ska ges den utmaning och stimulans de behöver för att utvecklas så långt som möjligt. Detta har undersökts genom att genomföra en lektionsserie, bestående av tre lektionstillfällen. Efter att lektionsserien avslutats genomfördes semistrukturerade intervjuer i fokusgrupper med de deltagande eleverna, för att undersöka vad som krävs för att algebraiska uppgifter och undervisning inom algebra ska upplevas som utmanande och stimulerande av matematiskt begåvade elever i årskurs 5. Den teori som använts för att analysera resultaten är positioneringsteorin. De viktigaste resultaten som framkommit är att dessa elever ska erbjudas att arbeta med utmanande uppgifter och att detta med fördel görs genom att låta dem arbeta med dessa i par/grupper, med andra elever på en liknande kunskapsnivå. / According to the School Act, all students have the right to the guidance and stimulation they need to develop to the best of their abilities based on their individual conditions. For this reason, we want to investigate through this study how algebraic tasks and teaching within algebra can be adapted to provide mathematically gifted students with the challenge and stimulation they need to develop to the fullest extent possible. This has been examined by conducting a series of lessons consisting of three class sessions. After the lesson series concluded, semi-structured interviews were conducted in focus groups with the participating pupils to explore what is required for algebraic tasks and algebraic teaching to be perceived as challenging and stimulating by fifth-grade students. The theory used to analyze the results is positioning theory. The most important findings that have emerged are that these pupils should be offered the opportunity to work with challenging tasks, preferably by allowing them to work with these tasks in pairs/groups with other students at a similar level of knowledge.