Title: Reasoning in Description Logics Author: Mgr. Jaromír Malenko Department: Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Prof. RNDr. Petr Štěpánek, DrSc.; Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University in Prague Keywords: Description logic, Reasoner, Cartesian product, Non-monotonic reasoning Abstract: We deal with several aspects of reasoning in Description Logics. First, since description logic (DL) is a subset of First Order Logic (FOL), we use a FOL reasoner to reason in DL. We implemented dl2fol, a DL reasoner that takes an ontology (a DL theory with rules), translates it into a FOL theory, passes this set of formulae to an underling FOL reasoner, and interprets the result in terms of given ontology. This is an effective method for reasoning with newly introduced language constructors. However, we observed longer running times and that satisfiability of some DL concepts wasn't proved due to FOL undecidability. Second, we extend two DLs by introducing new language construct: cartesian product (CP) of concepts and roles. This allows for expressing relationships, that are not expressible by other means in weaker DLs. We...

The first chapter considers the asymptotic validity of bootstrap methods in a linear trend model with a change in slope at an unknown time. Perron and Zhu (2005) analyzed the consistency, rate of convergence, and limiting distributions of the parameter estimates in this model. I provide theoretical results for the asymptotic validity of bootstrap methods related to forming confidence intervals for the break date. I consider two bootstrap schemes, the residual (for white noise errors) and the sieve bootstrap (for correlated errors). Simulation experiments confirm that confidence intervals obtained using bootstrap methods perform well in terms of exact coverage rate. The second chapter extends Perron and Zhu's (2005) analysis to cover more general fractionally integrated errors with memory parameter d in the interval (-0.5,1.5). My theoretical results uncover some interesting features. For example, with a concurrent level shift allowed, the rate of convergence of the estimate of the break date is the same for all values of d in the interval (-0.5,0.5), a feature linked to the contamination induced by allowing a level shift. In all other cases, the rate of convergence is decreasing as d increases. I also provide results about the spurious break issue. The third chapter considers constructing confidence intervals for the break date in linear regressions. I compare the performance of various procedures in terms of the exact coverage rates and lengths: Bai's (1997) based on the asymptotic distribution with shrinking shifts, Elliott and Müller's (EM) (2007) based on inverting a test locally invariant to the magnitude of the change, Eo and Morley's (2013) based on inverting a likelihood ratio test, and various bootstrap procedures. In terms of coverage rates, EM's approach is the best but with a high cost in terms of length. With serially correlated errors and a change in intercept or in the coefficient of a regressor with a high signal-to-noise ratio, or when a lagged dependent variable is present, the length approaches the whole sample as the magnitude of the change increases. This drawback is not present for the other methods. Theoretical results are provided to explain the drawbacks of EM's method.

Dans ce mémoire, on s’inspire des sciences cognitives pour aborder la question de la modélisation logique du raisonnement et de l’apprentissage. Notre principale conviction est qu’il faudrait, pour traiter ce problème, prendre modèle sur la manière dont les agents naturels (c’est à dire les humains et les animaux) procèdent lorsqu’ils raisonnent ou apprennent. Considérant que le raisonnement fait appel à un grand nombre de facultés cognitives distinctes, et qu’il ne serait donc pas raisonnable d’espérer modéliser d’un seul coup l’ensemble du raisonnement humain, on se concentre ici sur un type d’inférences très simples dont on soutient qu’elles constituent le coeur du raisonnement chez tous les animaux à cerveau. On identifie un processus sous-jacent plausible pour ces inférences, d’abord au niveau mental de description, puis au niveau neuronal, et on développe une famille de modèles logiques permettant de le simuler. On s’attache ensuite à produire un ensemble de règles d’inférence caractérisant les relations d’inférence induites par ces modèles. Ces règles résultent du processus suggéré, et doivent donc être vues comme des règles qui, d’après le modèle, émergent fonctionnement des cerveaux. Enfin, on analyse les processus d’apprentissage attachés aux inférences considérées, et on montre comment le formalisme proposé permet de les modéliser. Pour conclure on évoque brièvement les possibles développements futurs du modèle, et notamment on donne quelques indications quant à la manière dont la modélisation d’un certain nombre de facultés additionnelles pourrait être envisagée. / In this dissertation, we take inspiration in cognitive sciences to address the issue of the logical modelling of reasoning and learning. Our main thrust is that to address these issues one should take inspiration in the way natural agents (i.e., humans and animals) actually proceed when they draw inferences and learn. Considering that reasoning incorporates a wide range of cognitive abilities, and that it would thus be unreasonable to hope to model the whole of human’s reasoning all at once, we focus here on a very basic kind of inferences that, we argue, can be considered as the primary core of reasoning in all brained animals. We identify a plausible underlying process for these inferences, first at the mental level of description and then at the neural level, and we develop a family of logical models that allow to simulate it. Then we tackle the issue of providing sets of rules to characterise the inference relations induced by these models. These rules are a by-product of the posited process, and should thus be seen as rules that, according to the model, result from the very functioning of brains. Finally we examine the learning processes attached to the considered inferences, and we show how to they can be modelled within our framework. To conclude we briefly discuss possible further developments of the framework, and in particular we give indications about how the modelling of some other cognitive abilities might be envisioned.

Em virtude da presença cada vez mais frequente de solicitações cíclicas nas estruturas de engenharia e do aprimoramento da análise de projetos, os ensaios em solos sob carregamentos cíclicos tiveram seu interesse renovado nos últimos anos. Os ensaios de laboratório são realizados de forma que simulem, da melhor maneira possível, as condições observadas em campo. Tais condições auxiliam na escolha dos ensaios a serem conduzidos para a determinação de parâmetros geotécnicos relevantes a cada situação observada em campo. Dentre os ensaios empregados na Engenharia Geotécnica, destaca-se o simple shear. Este ensaio é conhecido e utilizado para medir a resistência ao cisalhamento e a rigidez de solos. Este é o único ensaio de laboratório capaz de submeter uma amostra a condições de deformação plana sob volume constante e permitir a rotação das tensões principais. Tais condições são frequentemente representativas em diversas situações em campo como, por exemplo, o modo de cisalhamento adjacente ao fuste de uma estaca ou sob plataformas offshore com base gravitacional. Nesse contexto, um equipamento foi desenvolvido para a realização de ensaios do tipo simple shear. O aparato conta com uma câmara, na qual é aplicada pressão à amostra de solo. Diferenciando-se do equipamento comercial para tais ensaios, que emprega uma membrana com anéis metálicos, a amostra de solo neste equipamento é envolta por uma membrana de látex, o que possibilita a consolidação de forma isotrópica ou anisotrópica. Quanto ao carregamento, o equipamento desenvolvido permite que o carregamento seja realizado de forma monotônica ou clíclica. Quando do carregamento cíclico, este pode ainda ser realizado de forma a se manter a tensão controlada ou a deformação. Foram conduzidos ensaios de calibração e validação do equipamento empregando-se uma areia fina de granulometria uniforme cujas propriedades são amplamente conhecidas através de outros ensaios. Os resultados obtidos foram então comparados com estudos no mesmo material em equipamentos triaxiais, cisalhamento direto e outro simple shear. Os resultados mostraram-se satisfatórios, validando o equipamento desenvolvido. / In view of the ever more frequent presence of the cyclic solicitations on Engineering structures and the enhancement of design analysis, the soil testing under cyclic loading conditions had its interest renewed in the last years. The laboratory tests are conduced in a way that simulates, in the best way possible, the observed field conditions. Said conditions aid on the choice of the tests to be conducted in order to determinate the relevant geomechanics parameters.to each situation observed on the field. Among the employed tests in Geotechnical Engineering, it is highlighted the simple shear. This test is known and used to measure the shear strength and soil righty. This is the only laboratory test capable of submitting the sample to plane strain conditions under constant volume and allows the main stress rotations. Said conditions are frequently representative in many field situations, such as, the adjacent shear mechanism to the shaft of a pile or, under offshore platforms with gravitational base. In this context, a equipment was developed to perform simple shear tests. The apparatus has a chamber, in which it is applied confining pressure to the soil sample. Contrasting from the commercial equipment for said tests, that uses a membrane with metallic rings, in this equipment the soil sample is involved by a latex membrane, allowing the consolidation being carried out isotropically or anisotropically. The loading on this equipment can be conduced on monotonic or cyclic conditions. The cyclic loading can even be conduced by controlling the deformation or the stress. Calibration and validation testes where conduced on the equipment using a fine sand of uniform granulometry which properties are largely known through other tests. The obtained results where then compared to other tests carried out on the same material in triaxial tests, direct shear and other simple shear, The results obtained were considered satisfactory, validating the developed equipment.

Doctor of Philosophy / Civil Engineering / Asadollah Esmaeily / Accurate and realistic assessment of the performance of columns in general, and those in critical locations that may cause progressive failure of the entire structure, in particular, is significantly important. This performance is affected by the load history, pattern, and intensity. Current design code does not consider the effect of load pattern on the load and displacement capacity of columns. A primary research sponsored by Kansas Department of Transportation (KDOT) was conducted as the initial step of the present study (No. K-TRAN: KSU-11-5). The main goals of the KDOT project were: (1) investigation of new KDOT requirements in terms of the column design procedure and detailing and their consistency with AASHTO provisions; (2) verification of the KDOT assumptions for the plastic hinge regions for columns and bridge piers, (3) provide assessment of the load capacity of the existing columns and bridge piers in the light of the new specifications and using the new load demand as in the new provisions; and finally recommendations for columns and bridge piers that do not meet the new requirements. A conclusion was drawn that there is a need for conducting more studies on the realistic performance of Reinforced Concrete (RC) sections and columns. The studies should have included performance of RC members under various loading scenarios, assessment of columns capacity considering confinement effect provided by lateral reinforcement, and investigation on performance of various monotonic and cyclic material models applied to simulate the realistic performance. In the study reported here, monotonic material models, cyclic rules, and plastic hinge models have been utilized in a fiber-based analytical procedure, and validated against experimental data to simulate behavior of RC section under various loading scenarios. Comparison of the analytical predictions and experimental data, through moment–curvature and force–deflection analyses, confirmed the accuracy and validity of the analytical algorithm and models. The performance of RC columns under various axial and lateral loading patterns was assessed in terms of flexural strength and energy dissipation. FRP application to enhance ductility, flexural strength, and shear capacity of existing deficient concrete structures has increased during the last two decades. Therefore, various aspects of FRP-confined concrete members, specifically monotonic and cyclic behavior of concrete members confined and reinforced by FRP, have been studied in many research programs, suggesting various monotonic models for concrete confined by only FRP. Exploration of existing model performances for predicting the behavior of several tested specimens shows a need for improvement of existing algorithms. The model proposed in the current study is a step in this direction. FRP wrapping is typically used to confine existing concrete members containing conventional lateral steel reinforcement (tie/spiral). The confining effect of lateral steel reinforcement in analytical studies has been uniquely considered in various models. Most models consider confinement due to FRP and ignore the effect of conventional lateral steel reinforcement. Exploration of existing model performances for predicting the behavior of several tested specimens confined by both FRP and lateral steel shows a need for improvement of existing algorithms. A model was proposed in this study which is a step in this direction. Performance of the proposed model and four other representative models from literature was compared to experimental data from four independent databases. In order to fulfill the need for a simple, yet accurate analytical tool for performance assessment of RC columns, a computer program was developed that uses relatively simple analytical methods and material models to accurately predict the performance of RC structures under various loading conditions, including cyclic lateral displacement under a non-proportionally variable axial load (Esmaeily and Xiao 2005, Esmaeily and Peterman 2007). However, it was limited to circular, rectangular, and hollow circular/rectangular sections and uniaxial lateral curvature or displacement. In this regards, a computer program was developed which is the next generation of the aforesaid program with additional functionality and options. Triangulation of the section allows opportunity for cross-sectional geometry. Biaxial lateral curvature/displacement/force combined with any sequence of axial load provides opportunity to analyze the performance of a reinforced concrete column under any load and displacement path. Use of unconventional reinforcement, such as FRP, in lateral as well as longitudinal direction is another feature of this application.

Em virtude da presença cada vez mais frequente de solicitações cíclicas nas estruturas de engenharia e do aprimoramento da análise de projetos, os ensaios em solos sob carregamentos cíclicos tiveram seu interesse renovado nos últimos anos. Os ensaios de laboratório são realizados de forma que simulem, da melhor maneira possível, as condições observadas em campo. Tais condições auxiliam na escolha dos ensaios a serem conduzidos para a determinação de parâmetros geotécnicos relevantes a cada situação observada em campo. Dentre os ensaios empregados na Engenharia Geotécnica, destaca-se o simple shear. Este ensaio é conhecido e utilizado para medir a resistência ao cisalhamento e a rigidez de solos. Este é o único ensaio de laboratório capaz de submeter uma amostra a condições de deformação plana sob volume constante e permitir a rotação das tensões principais. Tais condições são frequentemente representativas em diversas situações em campo como, por exemplo, o modo de cisalhamento adjacente ao fuste de uma estaca ou sob plataformas offshore com base gravitacional. Nesse contexto, um equipamento foi desenvolvido para a realização de ensaios do tipo simple shear. O aparato conta com uma câmara, na qual é aplicada pressão à amostra de solo. Diferenciando-se do equipamento comercial para tais ensaios, que emprega uma membrana com anéis metálicos, a amostra de solo neste equipamento é envolta por uma membrana de látex, o que possibilita a consolidação de forma isotrópica ou anisotrópica. Quanto ao carregamento, o equipamento desenvolvido permite que o carregamento seja realizado de forma monotônica ou clíclica. Quando do carregamento cíclico, este pode ainda ser realizado de forma a se manter a tensão controlada ou a deformação. Foram conduzidos ensaios de calibração e validação do equipamento empregando-se uma areia fina de granulometria uniforme cujas propriedades são amplamente conhecidas através de outros ensaios. Os resultados obtidos foram então comparados com estudos no mesmo material em equipamentos triaxiais, cisalhamento direto e outro simple shear. Os resultados mostraram-se satisfatórios, validando o equipamento desenvolvido. / In view of the ever more frequent presence of the cyclic solicitations on Engineering structures and the enhancement of design analysis, the soil testing under cyclic loading conditions had its interest renewed in the last years. The laboratory tests are conduced in a way that simulates, in the best way possible, the observed field conditions. Said conditions aid on the choice of the tests to be conducted in order to determinate the relevant geomechanics parameters.to each situation observed on the field. Among the employed tests in Geotechnical Engineering, it is highlighted the simple shear. This test is known and used to measure the shear strength and soil righty. This is the only laboratory test capable of submitting the sample to plane strain conditions under constant volume and allows the main stress rotations. Said conditions are frequently representative in many field situations, such as, the adjacent shear mechanism to the shaft of a pile or, under offshore platforms with gravitational base. In this context, a equipment was developed to perform simple shear tests. The apparatus has a chamber, in which it is applied confining pressure to the soil sample. Contrasting from the commercial equipment for said tests, that uses a membrane with metallic rings, in this equipment the soil sample is involved by a latex membrane, allowing the consolidation being carried out isotropically or anisotropically. The loading on this equipment can be conduced on monotonic or cyclic conditions. The cyclic loading can even be conduced by controlling the deformation or the stress. Calibration and validation testes where conduced on the equipment using a fine sand of uniform granulometry which properties are largely known through other tests. The obtained results where then compared to other tests carried out on the same material in triaxial tests, direct shear and other simple shear, The results obtained were considered satisfactory, validating the developed equipment.

Neste trabalho tratamos da homotopia monotônica entre trajetórias de um sistema de controle ∑ sobre uma variedade M. Esta é uma variante apropriada da homotopia usual, na qual duas trajetórias são consideradas homotopicas se podem ser deformadas continuamente através de trajetórias. Inicialmente apresentamos alguns aspectos gerais e resultados fundamentais da teoria do controle. Em seguida, introduzimos a noção de regularidade para controles e a homotopia monotônica entre trajetórias de ∑ geradas por essa classe de controles. Em particular, apresentamos um exemplo de um sistema que admite trajetórias que são homotópicas mas não são monotonicamente homotópicas. O objetivo principal foi entender a construção (análoga), para homotopia monotônica, de espaço de recobrimento universal. Entre outros, o conjunto Γ(∑,x) de classes de homotopia monotônica das trajetórias do sistema ∑ a partir x ∈ M possui uma estrutura de variedade diferenciável de mesma dimensão que a variedade M(o espaço estado). Como consequência desse resultado temos um difeomorfismo local que nos permitirá levantar ∑ para a variedade Γ(∑,x), obtendo assim um novo sistema ∑^ em Γ(∑,x). A fim de compreendermos as propriedades universais de Γ(∑,x), tomamos um recobrimento π : N → ΑR(∑,x) no sentido de que N é uma variedade diferenciável munida com um sistema de controle ∑~ e π é um difeomorfismo local que leva e∑~ ao ∑. Comparando as trajetórias de sistemas ∑^ e ∑~ construímos uma aplicação de levantamento ƒ : Γ(∑,x) → N que relaciona ∑^ e ∑~. Finalizamos este trabalho levando em conta a classe particular de sistemas simétricos, para qual os espaços de recobrimento monotônico Γ(∑,x) e topológico M~ de M coincidem. / In this work, we deal with monotonic homotopy between trajectories of a control system ∑ on a manifold M. This is an apropriate variant of usual homotopy, where two trajectories are considered to be homotopic if they can be deformed to each other in a continuous way through trajectories. We introduce regularity for controls and consider monotonic homotopy between trajectories generated by regular controls. In particular, we present an example of a system having homotopic trajectories which are not monotonically homotopic. The main goal was to understand the construction for monotonic homotopy of the universal covering space and, in particular, the differentiable manifold structure on the set Γ(∑,x) of monotonic homotopy classes of trajectories starting at x ∈ M. As a consequence of that result, we obtain a local diffeomorphism which permits lifting of ∑ to another system ∑^ in Γ(∑,x). To consider universal properties of Γ(∑, x) we take a covering π : N → ΑR(∑,x) in the sense that N is a differentiable manifold provided with a control system ∑~ and π is a local diffeomorphism mapping ∑~ to ∑. Comparing the trajectories of ∑^ and ∑~ we construct a lifting mapping ƒ : Γ(∑,x) → N that relates ∑^ and ∑~. Finally, we take into account the particular class of symmetric systems, for which both coverings Γ(∑,x) and M~ coincide.

In recent years, the popularity of graph databases has grown rapidly. This paper focuses on single-graph as an effective model to represent information and its related graph mining techniques. In frequent pattern mining in a single-graph setting, there are two main problems: support measure and search scheme. In this paper, we propose a novel framework for constructing support measures that brings together existing minimum-image-based and overlap-graph-based support measures. Our framework is built on the concept of occurrence / instance hypergraphs. Based on that, we present two new support measures: minimum instance (MI) measure and minimum vertex cover (MVC) measure, that combine the advantages of existing measures. In particular, we show that the existing minimum-image-based support measure is an upper bound of the MI measure, which is also linear-time computable and results in counts that are close to number of instances of a pattern. Although the MVC measure is NP-hard, it can be approximated to a constant factor in polynomial time. We also provide polynomial-time relaxations for both measures and bounding theorems for all presented support measures in the hypergraph setting. We further show that the hypergraph-based framework can unify all support measures studied in this paper. This framework is also flexible in that more variants of support measures can be defined and profiled in it.

Abstract dialectical frameworks (ADFs) are a formalism for representing knowledge about abstract arguments and various logical relationships between them. This work studies ADFs in detail. Firstly, we use the framework of approximation fixpoint theory to define various semantics that are known from related knowledge representation formalisms also for ADFs. We then analyse the computational complexity of a variety of reasoning problems related to ADFs. Afterwards, we also analyse the formal expressiveness in terms of realisable sets of interpretations and show how ADFs fare in comparison to other formalisms. Finally, we show how ADFs can be put to use in instantiated argumentation, where researchers try to assign meaning to sets of defeasible and strict rules. The main outcomes of our work show that in particular the sublanguage of bipolar ADFs are a useful knowledge representation formalism with meaningful representational capabilities and acceptable computational properties.

Conflicting information in an agent's knowledge base may lead to a semantical defect, that is, a situation where it is impossible to draw any plausible conclusion. Finding out the reasons for the observed inconsistency and restoring consistency in a certain minimal way are frequently occurring issues in the research area of knowledge representation and reasoning. In a seminal paper Raymond Reiter proves a duality between maximal consistent subsets of a propositional knowledge base and minimal hitting sets of each minimal conflict -- the famous hitting set duality. We extend Reiter's result to arbitrary non-monotonic logics. To this end, we develop a refined notion of inconsistency, called strong inconsistency. We show that minimal strongly inconsistent subsets play a similar role as minimal inconsistent subsets in propositional logic. In particular, the duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the stronger notion of inconsistency is used. We cover various notions of repairs and characterize them using analogous hitting set dualities. Our analysis also includes an investigation of structural properties of knowledge bases with respect to our notions. Minimal inconsistent subsets of knowledge bases in monotonic logics play an important role when investigating the reasons for conflicts and trying to handle them, but also for inconsistency measurement. Our notion of strong inconsistency thus allows us to extend existing results to non-monotonic logics. While measuring inconsistency in propositional logic has been investigated for some time now, taking the non-monotony into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly inconsistent subsets of a knowledge base. We propose measures based on this notion and investigate their behavior in a non-monotonic setting by revisiting existing rationality postulates, and analyzing the compliance of the proposed measures with these postulates. We provide a series of first results in the context of inconsistency in abstract argumentation theory regarding the two most important reasoning modes, namely credulous as well as skeptical acceptance. Our analysis includes the following problems regarding minimal repairs: existence, verification, computation of one and characterization of all solutions. The latter will be tackled with our previously obtained duality results. Finally, we investigate the complexity of various related reasoning problems and compare our results to existing ones for monotonic logics.