Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semantic approach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraic viewpoint. A representation theorem is proved and various properties of the resulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heyting algebras.

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its fundamental intrinsic properties, is indispensable and provides the basis of an informed choice. One such intrinsic property of logic-based knowledge representation languages is the context-dependency of pieces of knowledge. In classical propositional logic, for example, there is no such context-dependence: whenever two sets of formulas are equivalent in the sense of having the same models (ordinary equivalence), then they are mutually replaceable in arbitrary contexts (strong equivalence). However, a large number of commonly used formalisms are not like classical logic which leads to a series of interesting developments. It turned out that sometimes, to characterize strong equivalence in formalism L, we can use ordinary equivalence in formalism L0: for example, strong equivalence in normal logic programs under stable models can be characterized by the standard semantics of the logic of here-and-there. Such results about the existence of characterizing logics has rightly been recognized as important for the study of concrete knowledge representation formalisms and raise a fundamental question: Does every formalism have one? In this thesis, we answer this question with a qualified “yes”. More precisely, we show that the important case of considering only finite knowledge bases guarantees the existence of a canonical characterizing formalism. Furthermore, we argue that those characterizing formalisms can be seen as classical, monotonic logics which are uniquely determined (up to isomorphism) regarding their model theory. The other main part of this thesis is devoted to argumentation semantics which play the flagship role in Dung’s abstract argumentation theory. Almost all of them are motivated by an easily understandable intuition of what should be acceptable in the light of conflicts. However, although these intuitions equip us with short and comprehensible formal definitions it turned out that their intrinsic properties such as existence and uniqueness, expressibility, replaceability and verifiability are not that easily accessible. We review the mentioned properties for almost all semantics available in the literature. In doing so we include two main axes: namely first, the distinction between extension-based and labelling-based versions and secondly, the distinction of different kind of argumentation frameworks such as finite or unrestricted ones.

Bolted connection with perpendicular to grain loading has been considered as a high priority research area by Smith and Foliente (2002), for the advancement of the load resistance factor design (LRFD) of connections. The results obtained from the experimental testing of this research will provide information regarding the behavior of connections at conditions of capacity and yield, and a comparison between single and two bolted connections for laminated veneer lumber (LVL) from different manufacturers. Comparison of the experimental results with the predicted results from three models: Technical Report -12 (AF&PA 1999), Van der Put and Leijten (2000) and Jensen et. al. (2003), for single and two bolt connections loaded perpendicular to grain will help in accurately predicting LVL connection behavior. Success in achieving the goals of this research will provide enhancement of knowledge and information for single and two bolted connections loaded in perpendicular to the grain connections for LVL and thereby help in calibrating LRFD parameters on pure reliability basis in future. The variables considered included LVL from two different manufacturers, single and two bolt connections with different bolt sizes and loaded edge distances. The connections were loaded to capacity for all the tests. Tests for the material property input values required for these models were also performed as a part of this research. Connection testing showed splitting failures combined with crushing of main member material and formation of a single plastic moment. Connection resistance increased with increased loaded edge distance and number of bolts. The allowable shear design value controlled the National Design Specification Allowable Stress Design (NDS ASD) lateral design value to the connection design except for one connection configuration with 7D loaded edge distance for two bolts of ½ inch, where connection design strength values controlled. The displacement limit decided for the dowel bearing strength test had a direct impact on the predicted TR-12 capacity values. The capacity resistance calculated by both fracture models increased with increase in loaded edge distances. The Mode-I fracture energy values directly affected the predicted fracture model values. The tension perpendicular to grain strength values directly affected the Jensen model values. Statistical comparison of 4D and 7D loaded edge distances and LVL-1 and LVL-2 material revealed that Van der Put model had no difference in the calculated to test (C/T) ratios with respect to different loaded edge distances and materials and the Jensen model predicted the C/T ratios at 4D to be significantly greater than at 7D and for LVL-1 to be significantly greater than LVL-2. Van der Put model over predicts at capacity and the C/T values are consistent with change in loaded edge distance. Jensen model C/T ratios over predicted for single bolt connection and predicts accurate for two bolt connection with respect to loaded edge distances. Comparing the two fracture models with a ductile model TR-12 with respect to different loaded edge distances, material, number and size of bolts, Jensen model best predicted the C/T ratios. The Van der Put model tended to over predict values, while the TR-12 model had no consistent trend in C/T ratios, but seemed to be affected inversely by changes in loaded edge distance. / Master of Science

The research summarized by this thesis was comprised of an experimental analysis of beams loaded perpendicular to grain at midspan by a bolted double-shear laterally-loaded connection. Connection specimens were loaded monotonically until capacity was reached. Variables of consideration included the loaded edge distance of the connection main member, the span:depth ratio of the main member, and the main member material. Southern pine machine-stress-rated (MSR) lumber, laminated veneer lumber (LVL), and parallel strand lumber (PSL) were the three material types included in the program. Experimental results were compared with theoretical predictions from three models: the yield theory-based general dowel equations, which are currently the standard for laterally-loaded connection design in the U.S., and two models based upon fracture mechanics. All material property inputs required by the three models, were measured in the experimental program of this research and used to produce theoretical predictions. Comparisons were also made with respect to design values in the form of calculated factors of safety, over-strengths, and design factors of safety. Test results and observed trends are provided for all connection and material property tests. Notable trends included failure by splitting for all connections at low loaded edge distances, and variable span:depth ratios generally having a negligible effect on both connection and model performance. In most cases, the general dowel equations were more accurate than the two fracture models, however it should be noted that all three models over-predicted connection capacity at low loaded edge distances. / Master of Science

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We show how the non-monotonic nature of common-sense reasoning can be formalised by circumscription. Various forms of circumscription are discussed. A new form of circumscription, namely naive circumscription, is introduced in order to facilitate the comparison of the various forms. Finally, some issues connected with the automation of circumscriptive reasoning are examined. / Computing / M. Sc. (Computer Science)

In the literature, Cognitive radio (CR) as well as full-duplex (FD) communication technologies are proposed to increase the spectrum efficiency. The main contribution of this thesis is to introduce prediction and estimation techniques with low control overhead, and use the predicted or estimated information in resource allocation in CR networks, both in the overlay networks and the underlay networks. Prediction and estimation are important in increasing the data rate and keeping the interference at a low level. In the overlay scheme, I modeled the primary user (PU) traffic characteristics of the channels using the Probabilistic Suffix Tree (PST) algorithm. Then using this PST algorithm, I introduced a frequency hopping based control channel and derived its theoretical properties. Then I proposed two methods for selecting a channel set for transmission, which took into account both the PU channel usage statistics and, secondary user (SU) channel usage statistics as perceived by an SU of interest. The first scheme selected channels having the highest probability of successful transmission, while the second calculated a net reward using a marked Markov chain. Then using simulations, I showed that our scheme caused acceptable interference to the PUs and has better throughput performance, compared to a scheme selecting channels randomly. Then I proposed two joint channel assignment and power allocation schemes for a bi-directional FD underlay CR network with network assistance. The first scheme used the information on the number of total SU pairs present in the network. In the second scheme, I used least squares based estimation and Kalman filtering to estimate the interference at the monitoring stations using the local interference. It reduced the control overhead of keeping track of active SUs. In both of these schemes each SU pair decided on the channels to be used in the half-duplex mode and the full-duplex mode using local information. This joint optimization was done running channel assignment and power allocation algorithms alternatively. In the power allocation problem, I used a technique called monotonic optimization. After simulating both of these schemes I showed that the scheme based on estimation performs satisfactorily given that it has less control overhead. / October 2016

Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants et des plus importants de l'analyse mathématique ; à savoir qu'une fonction à variation bornée est dérivable presque partout. Le but de ce travail est de fournir, à part la démonstration souvent proposée dans les cours de la théorie de la mesure, d'autres démonstrations élaborées avec des outils mathématiques plus simples. Ma contribution a consisté essentiellement à détailler et à compléter ces démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité. Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes, en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the most stricking and ultimate of mathematical analysis ; namely a function with bounded variation has a derivative almost everywhere. The aim of our research is to provide, apart from the proof usually offered in measure theory courses, other demontrations achieved with more simple mathematical tools. My contribution was primarily to simplify and to complete these demonstrations, to include the most of the drawings in order to visualize what is being said. For this theorem, which has other presentations, we will give now the history and three different demonstrations.

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

Monotonic optimization consists of minimizing or maximizing a monotonic objective function over a set of constraints defined by monotonic functions. Many optimization problems in economics and engineering often have monotonicity while lacking other useful properties, such as convexity. This thesis is concerned with the development and application of global optimization algorithms for monotonic optimization problems. First, we propose enhancements to an existing outer-approximation algorithm | called the Polyblock Algorithm | for monotonic optimization problems. The enhancements are shown to significantly improve the computational performance of the algorithm while retaining the convergence properties. Next, we develop a generic branch-and-bound algorithm for monotonic optimization problems. A computational study is carried out for comparing the performance of the Polyblock Algorithm and variants of the proposed branch-and-bound scheme on a family of separable polynomial programming problems. Finally, we study an important class of monotonic optimization problems | probabilistically constrained linear programs. We develop a branch-and-bound algorithm that searches for a global solution to the problem. The basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partitions and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires the solution of only linear programming subproblems. We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions are presented.