This paper presents a comparison of controllers, specifically between conventional PID controllers with different structures and a Fuzzy Logic Controller. The performance has been evaluated by conducting experiments with the Ball and plate system, which is a system that is used to balance a ball on a plate. Furthermore, a large part of this work has been to assess how intuitive and straightforward the controllers are to design and implement. The results show that a PD controller with a proportional-on-error structure performs well for the Ball and plate system. Still, proportional-on-measurement is a viable alternative if a conservative controller is required. At the same time, the Fuzzy Logic Controller is a good alternative if you want more control over the system. Furthermore, the Fuzzy Logic Controller provides a design process that is easier to understand and closer to how we naturally think. However, it is more time-consuming than designing a conventional PID controller. Future work in the field should focus on optimizing this process to reduce the time required. / Denna studie består av en jämförelse mellan ett antal regulatorer. Dessa är olika strukturer av PID-regulatorer och en Suddig logik regulator. Prestandan har utvärderats genom att utföra experiment med Boll och platta systemet vilket är ett system som används för att balansera en boll på en platta. Vidare har en stor del av detta arbete handlat om hur intuitivt och enkelt det är att designa och implementera respektive regulator. Resultatet visar att en PD regulator med en proportionell-på-felet struktur presterar bra för Boll och platta systemet. Även proportionell-på-mätvärdet fungerar bra som ett mer konservativt alternativ. Dessutom är Suddig logik regulatorn ett bra alternativ om man vill ha mer kontroll över systemet. Designprocessen av denna är lättare att förstå och efterliknar hur man naturligt tänker i högre grad än de andra regulatorerna. Dock är denna mer tidskrävande att designa i jämförelse med de traditionella PID-regulatorerna. Framtida arbete bör fokusera på att optimera designprocessen så att den blir mindre tidskrävande.

We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach.

Most of the research on temporalized Description Logics (DLs) has concentrated on the case where temporal operators can occur within DL concept descriptions. In this setting, reasoning usually becomes quite hard if rigid roles, i.e., roles whose interpretation does not change over time, are available. In this paper, we consider the case where temporal operators are allowed to occur only in front of DL axioms (i.e., ABox assertions and general concept inclusion axioms), but not inside of concepts descriptions. As the temporal component, we use linear temporal logic (LTL) and in the DL component we consider the basic DL ALC. We show that reasoning in the presence of rigid roles becomes considerably simpler in this setting.

Aus dem Abstract: Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs by investigating whether the updated ABox can be expressed in these DLs and, if so, whether it is computable and what is its size.

Often the addition of metric operators to qualitative temporal logics leads to an increase of the complexity of satisfiability by at least one exponential. In this paper, we exhibit a number of metric extensions of qualitative temporal logics of the real line that do not lead to an increase in computational complexity. The main result states that the language obtained by extending since/until logic of the real line with the operators 'sometime within n time units', n coded in binary, is PSpace-complete even without the finite variability assumption. Without qualitative temporal operators the complexity of this language turns out to depend on whether binary or unary coding of parameters is assumed: it is still PSpace-hard under binary coding but in NP under unary coding.

We show how to combine the standard tableau system for the basic description logic ALC and Wolper´s tableau calculus for propositional temporal logic PTL (with the temporal operators ‘next-time’ and ‘until’) in order to design a terminating sound and complete tableau-based satisfiability-checking algorithm for the temporal description logic PTL ALC of [19] interpreted in models with constant domains. We use the method of quasimodels [17, 15] to represent models with infinite domains, and the technique of minimal types [11] to maintain these domains constant. The combination is flexible and can be extended to more expressive description logics or even do decidable fragments of first-order temporal logics.

Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results.

We study partially ordered sets of prime ideals as found in commutative Noetherian rings. These structures, commonly known as prime spectra, have long been a popular topic in the field of commutative algebra. As a consequence, there are many related questions that remain unanswered. Among them is the question of what partially ordered sets appear as Spec(A) of some Noetherian ring A, asked by Kaplansky during the 1950's. As a partial case of Kaplansky's question, we consider finite posets that are ring spectra of commutative Noetherian rings. Specifically, we show that finite spectra of such rings are always order-isomorphic to a bipartite graph. However, the most significant undertaking of this study is that of devising a constructive methodology for finding a ring with prime spectrum that is order-isomorphic to an arbitrary bipartite graph. As a result, we prove that any complete bipartite graph is order-isomorphic to the prime spectrum of some ring of essentially finite type over the field of rational numbers. Moreover, a series of potential generalizations and extensions are proposed to further enhance the constructive methodology. Ultimately, the results of this study constitute an original contribution and perspective on questions related to commutative ring spectra.

Die Tradierung von Studien über Hegel hat in den letzten Jahrzehnten sehr an Bedeutung gewonnen, und zwar sowohl was die zahlenmäβige Zunahme der Hegel gewidmeten Werke angeht, als auch im Hinblick auf den modus operandi der Theamtisierung und Präzisierung der Probleme und Reflexionen, die sich aus seinem Werk ergeben. In diesem Kontext der Renaissance der hegelschen Philosophie erscheint das Problem der Anerkennung als eines der wichtigsten der Hegelforschung. Freilich sind im Rahmen dieses neuen Interesses an der Anerkennung die Arbeiten selten, die darauf abzielen, das Thema Anerkennung von seiner logischen Wurzel her aufzugreifen. Die vorliegende Forschungsarbeit hat es sich zur Aufgabe gesetzt, die Rekonstruktion der logischen Struktur der Anerkennung herauszuarbeiten, wobei sie ihre Stufen anhand der Wissenschaft der Logik ausdrücken wird. Die vorliegende These von hermeneutisch-bibliografischem Charakter ist darauf angelegt, dieses Ziel zu erreichen, was sie in einer in 05 (funf) Kapitel aufgeteilten Struktur unternimmt. Die Aufgabe des ersten Kapitels ist es, den Forschungsstand über die Anerkennung in der zeitgenössischen Philosophie herauszuarbeiten. Das zweite Kapitel konstituiert die erste Schicht der Anerkennung und zeigt, wie die Logik als transitiver Nenner arbeitet. Das dritte Kapitel etabliert die zweite Schicht der logischen Struktur der Anerkennung und rekonstruiert die Konditionen der subjektiven Interaktion, die Andersheit als würde sie durch zwei ihr eigene Modi ausgedrückt: durch Beziehung und durch Verhältnis. Das vierte Kapitel stellt die dritte logische Schicht der Anerkennung vor durch die Präzisierung der Subjektivität und die Arten der Relation der Subjektivität, ausgehend von ihren semantisch-pragmatischen meta-Niveaus des Universellen, Partikulären und Singulären. In einer zweiten Argumentation stellt das viertel Kapitel dar, wie die Subjektivität in ihrer theoretischen Dimension als Wissen und in ihrer praktischen Dimension als Wollen zu verstehen ist. Das fünfte Kapitel schlieβlich stellt dar, wie die drei logischen Metaebenen der Erkenntnis, die sich aus dem Kennen und Anerkennen ergeben, im historischen Prozess erkennbar werden durch das Mittel der Phänomenologie des Geistes in seinem 4. Kapitel. Das fünfte Kapitel will auch zeigen, daβ es möglich ist, eine logische Struktur zu rekonstruieren, ohne die Fakten der Theorie zu unterwerfen. Wir erwarten deshalb als Schlussfolgerung, daβ angesichts der logischen Erklärung und Rekonstruktion der Schichten der Transitivität, des relationalen Andersseins und der Subjektivität in Bezug auf die Einheit des Subjekts zwischen dem theoretischen und praktischen Ich, die die Anerkennung betreffende logische Struktur sich zeigen wird. / A tradição de estudos hegelianos assumiu nos últimos decênios uma grande importância, tanto em referência a ampliação numérica dos trabalhos dedicados ao hegelianismo como em relação ao modus operandi de tematização e explicitação dos problemas e reflexões que lhe são oriundos. Dentro deste contexto de Renaissance da filosofia hegeliana, o problema do reconhecimento emerge como de importância capital na Hegel-Forschung. Todavia, a par deste novo interesse sobre o reconhecimento são raros os trabalhos que se propõem a enfrentar o tema reconhecimento desde a sua matiz lógica. O presente trabalho de pesquisa se propõe estabelecer a reconstrução da estrutura lógica do reconhecimento, exprimindo os seus níveis a partir da Wissenschaft der Logik. A presente tese de caráter hermenêutico bibliográfico se configura para a consecução de tal objetivo, dividindo internamente o trabalho em comento em 05 (cinco) capítulos. O primeiro capítulo se destina a situar o estado da arte nas pesquisas sobre o reconhecimento na filosofia contemporânea. O segundo capítulo constitui o primeiro nível do reconhecimento e apresenta a lógica operando como um denominador transitivo. O terceiro capítulo estabelece o segundo nível da estrutura lógica do reconhecimento e reconstitui as condições de interação subjetiva, a alteridade (Andersheit) como se explicitando por dois modos próprios: por referência (Beziehung) e por relação (Verhältnis). O quarto capítulo apresenta o terceiro estágio lógico do reconhecimento pela explicitação da subjetividade e os modos de relação da subjetividade a partir de seus metaníveis semântico-pragmáticos do: universal, particular e singular. Num segundo momento, o quarto capítulo expõe como a subjetividade se compreende enquanto dimensão teórica: como conhecer, e em sua dimensão prática como querer. Por fim, o quinto capítulo, expõe como os três metaníveis lógicos do reconhecimento, os quais seguem do conhecer (Kennen) ao reconhecer (Anerkennen), se fazem explicitar no processo histórico pelo recurso a Fenomenologia do Espírito em seu capítulo IV. O quinto capítulo objetiva ainda demonstrar que é possível reconstruir uma estrutura lógica sem subordinar os fatos à teoria. Espera-se por tanto, a título de conclusão, que mediante a explicitação e reconstrução lógica dos níveis da transitividade, da alteridade relacional, e da subjetividade enquanto unidade no sujeito entre o eu teórico e prático, se faça exprimir a estrutura lógica subjacente ao reconhecimento. / During the last decades, the tradition of studies of Hegel has assumed great importance, as much referring to the amount of work dedicated to his philosophy as to the mode of operation of focusing and explaining the problems and reflections raised by him. In this context of the revival of Hegel’s philosophy, the problem of recognition emerges as of capital importance in the research about Hegel. However, in the context of this new interest about recognition, studies that go about pursuing the theme of recognition until its logical matrix are rare. The present study aims at establishing a reconstruction of the logical structure of recognition, expressing its levels starting from the Wissenschaft der Logik. The present theses of hermeneutic-bibliographic character is conceived to reach this aim, internally dividing the work in 05 (five) chapters. The first chapter aims at showing the state of research in the studies of recognition in contemporary philosophy. The second constitutes the first level of recognition and presents logic working as transitive denominator. The third chapter establishes the second level of the logical structure of recognition and reconstitutes the conditions of subjective interaction, the otherness (Andersheit) as being made explicit by two proper modes: by reference (Beziehung) and relationship (Verhältnis). The fourth chapter presents the third logical stage of recognition by making explicit the subjectivity and the mode of relationship of subjectivity starting from its semantic-pragmatic metalevels: the universal, the particular and the singular. In a second moment, the fourth chapter exposes how subjectivity is to be understood in its theoretic dimension as knowledge, and in its practical dimension as wish. Lastly, the fifth chapter shows how the three logical metalevels of recognition, which proceed from knowledge (Kennen) to recognition (Anerkennen), are made explicit in the historical process by the tool of the Phenomenology of Spirit in its fourth chapter. The fifth chapter also aims at showing that it is possible to reconstruct a logical structure without subordinating fact to theory. It is hoped, however, in terms of a conclusion, that in the face of a logical attempt at making explicit and reconstructing the levels of transitivity, of relational otherness and the subjectivity in terms of unity of subject between the theoretical and the practical I, the logical structure subjacent to recognition can be made to express itself.