The goal of data mining is to help market managers find relationships among items from large datasets to increase profits. Among the mining techniques, the Apriori algorithm is the most basic and important for association rule mining. Although a lot of mining approaches have been proposed based on the Apriori algorithm, most of them focus on positive association rules, such as R1: ¡§If milk is bought, then bread is bought¡¨. However, rule R1 may confuses users and makes wrong decision if the negative relation rules are not considered. For example, the rule such as R2: ¡§If milk is not bought, then bread is bought¡¨ may also be found. Then, the rule R2 conflicts with the positive rule R1. So, if two rules such as ¡§If milk is bought, then bread is bought¡¨ and ¡§If milk is not bought, then bread is not bought¡¨ are found at the same time, the rules which is called coherent rule may be more valuable.In this thesis, we thus propose two algorithms for solving this problem. The first proposed algorithm is named Highly Coherent Rule Mining algorithm (HCRM), which takes the properties of propositional logic into consideration and is based on Apriori approach for finding coherent rules. The lower and upper bounds of itemsets are also tightened to remove unnecessary check. Besides, in order to improve the efficiency of the mining process, the second algorithm, namely Projection-based Coherent Mining Algorithm (PCA), based on data projection is proposed for speeding up the execution time. Experiments are conducted on real and simulation datasets to demonstrate the performance of the proposed approaches and the results show that both HCRM and PCA can find more reliable rules and PCA is more efficient.

[pt] Neste trabalho investigou-se o emprego dos recentes algoritmos de minimização de funções não diferenciáveis para a resolução do problema da síntese de filtros digitais FIR de fase não linear. O problema desta síntese correspondente a um problema de Aproximações de Funções quando o domínio e o contradomínio da função são corpos diferentes, i.e. real e complexo respectivamente. Serão revistos definições e propriedades dos filtros FIR, as técnicas de síntese para o caso de resposta de fase linear e não linear, para a seguir, apresentar a teoria e implementação da Otimização de Funções não Diferenciáveis. Exemplos e extensões desta teoria também serão apresentados. / [en] This work will describes the use of the recent techniques of non smooth optimization to the synthesis of non-linear phase FIR filters. The problem of such synthesis corresponds to a problem of Approximation of Functions when the domain and the image sets of the function are different fields, i.e. real and complex respectively. A revision of the theory of FIR filters with a survey of the linear and non linear phase usual synthesis non-smooth optimization theory and implementation. Together with design examples will follow. An extension of these theories will be suggested.

Apresentamos alguns aspectos da teoria de funções modais, que é o correlato modal da teoria de funções de verdade. Enquanto as fórmulas da lógica proposicional clássica expressam funções de verdade, as fórmulas da lógica proposicional modal (S5) expressam funções modais. Generalizamos alguns dos teoremas da teoria de funções de verdade para o caso modal; em particular, exibimos provas da completude funcional de alguns conjuntos de funções modais e definimos uma (nova) noção de reduto vero-funcional de funções modais, bem como a composição de funções modais em termos destes redutos. / We present some aspects of the theory of modal functions, which is the modal correlate of the theory of truth-functions. While the formulas of classical propositional logic express truth-functions, the formulas of modal propositional logic (S5) express modal functions. We generalize some theorems of the theory of truth-functions to the modal case; in particular, we show the functional completeness of some sets of modal functions and define a (new) notion of truth-functional reduct of modal functions, as well as the composition of modal functions in terms of such reducts.

In this dissertation we investigate theoretical aspects of some practical approaches used in solving and understanding search problems. We concentrate on the Satisfiability problem, which is a strong representative from search problem domains. The work develops general theoretical foundations to investigate some practical aspects of satisfiability search. This results in a better understanding of the fundamental mechanics for search algorithm construction and behaviour. A theory of choice or branching heuristics is presented, accompanied by results showing a correspondence of both parameterisations and performance when the method is compared to previous empirically motivated branching techniques. The logical foundations of the backtracking mechanism are explored alongside formulations for reasoning in relevant logics which results in the development of a malleable backtracking mechanism that subsumes other intelligent backtracking proof construction techniques and allows the incorporation of proof rearrangement strategies. Moreover, empirical tests show that relevant backtracking outperforms all other forms of intelligent backtracking search tree construction methods. An investigation into modelling and generating world problem instances justifies a modularised problem model proposal which is used experimentally to highlight the practicability of search algorithms for the proposed model and related domains.

Atomic flows are a geometric invariant of classical propositional proofs in deep inference. In this thesis we use atomic flows to describe new normal forms of proofs, of which the traditional normal forms are special cases, we also give several normalisation procedures for obtaining the normal forms. We define, and use to present our results, a new deep-inference formalism called the functorial calculus, which is more flexible than the traditional calculus of structures. To our surprise we are able to 1) normalise proofs without looking at their logical connectives or logical rules; and 2) normalise proofs in less than exponential time.

Heuristic algorithms for logical reasoning are increasingly successful on computationally difficult problems such as satisfiability, and these solvers enable applications from circuit verification to software synthesis. Whether a problem instance can be solved, however, often depends in practice on whether the correct solver was selected and its parameters appropriately set. Algorithm portfolios leverage past performance data to automatically select solvers likely to perform well on a given instance. Existing portfolio methods typically select only a single solver for each instance. This dissertation develops and evaluates a more general portfolio method, one that computes complete solver execution schedules, including repeated runs of nondeterministic algorithms, by explicitly incorporating probabilistic reasoning into its operation. This modular architecture for probabilistic portfolios (MAPP) includes novel solutions to three issues central to portfolio operation: first, it estimates solver performance distributions from limited data by constructing a generative model; second, it integrates domain-specific information by predicting instances on which solvers exhibit similar performance; and, third, it computes execution schedules using an efficient and effective dynamic programming approximation. In a series of empirical comparisons designed to replicate past solver competitions, MAPP outperforms the most prominent alternative portfolio methods. Its success validates a principled approach to portfolio operation, offers a tool for tackling difficult problems, and opens a path forward in algorithm portfolio design. / text

Many problems that arise in the real world are difficult to solve partly because they present computational challenges. Many of these challenging problems are optimization problems. In the real world we are generally interested not just in solutions but in the cost or benefit of these solutions according to different metrics. Hence, finding optimal solutions is often highly desirable and sometimes even necessary. The most effective computational approach for solving such problems is to first model them in a mathematical or logical language, and then solve them by applying a suitable algorithm. This thesis is concerned with developing practical algorithms to solve optimization problems modeled in a particular logical language, MAXSAT. MAXSAT is a generalization of the famous Satisfiability (SAT) problem, that associates finite costs with falsifying various desired conditions where these conditions are expressed as propositional clauses. Optimization problems expressed in MAXSAT typically have two interacting components: the logical relationships between the variables expressed by the clauses, and the optimization component involving minimizing the falsified clauses. The interaction between these components greatly contributes to the difficulty of solving MAXSAT. The main contribution of the thesis is a new hybrid approach, MaxHS, for solving MAXSAT. Our hybrid approach attempts to decouple these two components so that each can be solved with a different technology. In particular, we develop a hybrid solver that exploits two sophisticated technologies with divergent strengths: SAT for solving the logical component, and Integer Programming (IP) solvers for solving the optimization component. MaxHS automatically and incrementally splits the MAXSAT problem into two parts that are given to the SAT and IP solvers, which work together in a complementary way to find a MAXSAT solution. The thesis investigates several improvements to the MaxHS approach and provides empirical analysis of its behaviour in practise. The result is a new solver, MaxHS, that is shown to be the most robust existing solver for MAXSAT.

Many problems that arise in the real world are difficult to solve partly because they present computational challenges. Many of these challenging problems are optimization problems. In the real world we are generally interested not just in solutions but in the cost or benefit of these solutions according to different metrics. Hence, finding optimal solutions is often highly desirable and sometimes even necessary. The most effective computational approach for solving such problems is to first model them in a mathematical or logical language, and then solve them by applying a suitable algorithm. This thesis is concerned with developing practical algorithms to solve optimization problems modeled in a particular logical language, MAXSAT. MAXSAT is a generalization of the famous Satisfiability (SAT) problem, that associates finite costs with falsifying various desired conditions where these conditions are expressed as propositional clauses. Optimization problems expressed in MAXSAT typically have two interacting components: the logical relationships between the variables expressed by the clauses, and the optimization component involving minimizing the falsified clauses. The interaction between these components greatly contributes to the difficulty of solving MAXSAT. The main contribution of the thesis is a new hybrid approach, MaxHS, for solving MAXSAT. Our hybrid approach attempts to decouple these two components so that each can be solved with a different technology. In particular, we develop a hybrid solver that exploits two sophisticated technologies with divergent strengths: SAT for solving the logical component, and Integer Programming (IP) solvers for solving the optimization component. MaxHS automatically and incrementally splits the MAXSAT problem into two parts that are given to the SAT and IP solvers, which work together in a complementary way to find a MAXSAT solution. The thesis investigates several improvements to the MaxHS approach and provides empirical analysis of its behaviour in practise. The result is a new solver, MaxHS, that is shown to be the most robust existing solver for MAXSAT.

Apresentamos alguns aspectos da teoria de funções modais, que é o correlato modal da teoria de funções de verdade. Enquanto as fórmulas da lógica proposicional clássica expressam funções de verdade, as fórmulas da lógica proposicional modal (S5) expressam funções modais. Generalizamos alguns dos teoremas da teoria de funções de verdade para o caso modal; em particular, exibimos provas da completude funcional de alguns conjuntos de funções modais e definimos uma (nova) noção de reduto vero-funcional de funções modais, bem como a composição de funções modais em termos destes redutos. / We present some aspects of the theory of modal functions, which is the modal correlate of the theory of truth-functions. While the formulas of classical propositional logic express truth-functions, the formulas of modal propositional logic (S5) express modal functions. We generalize some theorems of the theory of truth-functions to the modal case; in particular, we show the functional completeness of some sets of modal functions and define a (new) notion of truth-functional reduct of modal functions, as well as the composition of modal functions in terms of such reducts.

La représentation des connaissances et les problèmes d’inférence associés restent à l’heure actuelle une problématique riche et centrale en informatique et plus précisément en intelligence artificielle. Dans ce cadre, la logique propositionnelle permet d’allier puissance d’expression et efficacité. Il reste que, tant que P est différent de NP, la déduction en logique propositionnelle ne peut admettre de solutions à la fois générales et efficaces. Dans cette thèse, nous adressons le problème de satisfiabilité et proposons de nouvelles classes d’instances pouvant être résolues de manière polynomiale.La découverte de nouvelles classes polynomiales pour SAT est à la fois importante d’un point de vue théorique et pratique. En effet, on peut espérer les exploiter efficacement au sein de solveurs SAT. Dans cette thèse, nous proposons d’étendre deux fragments polynomiaux de SAT à l’aide de la propagation unitaire tout en s’assurant que ces fragments demeurent reconnus et résolus de manière polynomiale. Le premier résultat de cette thèse concerne la classe Quad. Nous avons établi certaines propriétés de cette classe d’instances et avons étendu cette dernière de manière à s’abstraire de l’ordre imposé sur les littéraux. Le fragment obtenu en remplaçant cet ordre par différents ordres sur les clauses, conserve lamême complexité dans le pire cas. Nous avons également étudié l’impact de la résolution bornée et de la redondance par propagation unitaire sur cette classe. La seconde contribution concerne la classe polynomiale proposée par Tovey. La propagation unitaire est une nouvelle fois utilisée pour étendre cette classe. Nous comparons le nouveau fragment polynomial obtenu à deux autres classes basées également sur la propagation unitaire : Quad et UP-Horn. Nousapportons également une réponse à une question ouverte au sujet des connexions de ces classes. Nous montrons que UP-Horn et d’autres classes basées sur la propagation unitaire sont strictement incluses dans S Quad qui représente l’union de toutes les classes Quad obtenues par l’exploitation de tous les ordres sur les clauses possibles. / Knowledge representation and reasoning is a key issue in computer science and more particularly in artificial intelligence. In this respect, propositional logic is a representation formalism that is a good trade-off between the opposite computational efficiency and expressiveness criteria. However, unless P = NP, deduction in propositional logic is not polynomial in the worst case. So, in this thesis we propose new extensions of tractable classes of the propositional satisfiability problem. Tractable fragments of SAT play a role in the implementation of the most efficient current SAT solvers, many of thesetractable classes use the linear time unit propagation (UP) inference rule. We attempt to extend two of currently-known polynomial fragments of SAT thanks to UP in such a way that the fragments can still be recognized and solved in polynomial time. A first result focuses on Quad fragments: we establish some properties of Quad fragments and extend these fragments and exhibit promising variants. The extension is obtained by allowing Quad fixed total orderings of clauses to be accompanied with specific additional separate orderings of maximal sub-clauses. The resulting fragments extend Quad without degrading its worst-case complexity. Also, we investigate how bounded resolution and redundancy through unit propagation can play a role in this respect. The second contribution on tractable subclasses of SAT concerns extensions of one well-known Tovey’s polynomial fragment so that they also include instances that can be simplified using UP. Then, we compare two existing polynomial fragments based on UP: namely, Quad and UP-Horn. We also answer an open question about the connections between these two classes: we show that UP-Horn and some other UP-based variants are strict subclasses of S Quad, where S Quad is the union of all Quad classes obtained by investigating all possible orderings of clauses.