Description Logics (DLs) are a family of logic-based knowledge representation (KR) formalisms designed to represent and reason about static conceptual knowledge in a semantically well-understood way. On the other hand, standard action formalisms are KR formalisms based on classical logic designed to model and reason about dynamic systems. The largest part of the present work is dedicated to integrating DLs with action formalisms, with the main goal of obtaining decidable action formalisms with an expressiveness significantly beyond propositional. To this end, we offer DL-tailored solutions to the frame and ramification problem. One of the main technical results is that standard reasoning problems about actions (executability and projection), as well as the plan existence problem are decidable if one restricts the logic for describing action pre- and post-conditions and the state of the world to decidable Description Logics. A smaller part of the work is related to decidable extensions of Description Logics with concrete datatypes, most importantly with those allowing to refer to the notions of space and time.

Let G = (V, E) be a graph and let S ⊆ V be a subset of vertices. The set S is a defensive alliance if for all x ∈ S, |N[x] ∩ S| ≥ |N[x] − S|. The concept of defensive alliances was introduced in [KHH04], primarily for the modeling of nations in times of war, where allied nations are in mutual agreement to join forces if any one of them is attacked. For a vertex x in a defensive alliance, the number of neighbors of x inside the alliance, plus the vertex x, is at least the number of neighbors of x outside the alliance. In a graph model, the vertices of a graph represent nations and the edges represent country boundaries. Thus, if the nation corresponding to a vertex x is attacked by its neighbors outside the alliance, the attack can be thwarted by x with the assistance of its neighbors in the alliance. In a different subject matter, [FLG00] applies graph theory to model the world wide web, where vertices represent websites and edges represent links between websites. A web community is a subset of vertices of the web graph, such that every vertex in the community has at least as many neighbors in the set as it has outside. So, a web community C satisfies ∀x ∈ C, |N[x] ∩ C| > |N[x] − C|. These sets are very similar to defensive alliances. They are known as strong defensive alliances in the literature of alliances in graphs. Other areas of application for alliances and related topics include classification, data clustering, ecology, business and social networks. iii Consider the application of modeling nations in times of war introduced in the first paragraph. In a defensive alliance, any attack on a single member of the alliance can be successfully defended. However, as will be demonstrated in Chapter 1, a defensive alliance may not be able to properly defend itself when multiple members are under attack at the same time. The concept of secure sets is introduced in [BDH07] for exactly this purpose. The non-empty set S is a secure set if every subset X ⊆ S, with the assistance of vertices in S, can successfully defend against simultaneous attacks coming from vertices outside of S. The exact definition of simultaneous attacks and how such attacks may be defended will be provided in Chapter 1. In [BDH07], the authors presented an interesting characterization for secure sets which resembles the definition of defensive alliances. A non-empty set S is a secure set if and only if ∀X ⊆ S, |N[X] ∩ S| ≥ |N[X] − S| ([BDH07], Theorem 11). The cardinality of a minimum secure set is the security number of G, denoted s(G). A secure set S is a global secure set if it further satisfies N[S] = V . The cardinality of a minimum global secure set of G is the global security number of G, denoted γs(G). In this work, we present results on secure sets and global secure sets. In particular, we treat the computational complexity of finding the security number of a graph, present algorithms and bounds for the global security numbers of trees, and present the exact values of the global security numbers of paths, cycles and their Cartesian products.

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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24030号 / 情博第786号 / 新制||情||133(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)准教授 宮崎 修一, 教授 岡部 寿男, 教授 阿久津 達也, 教授 湊 真一 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

No / This paper presents an investigation into the challenges in implementing a hard real-time optimal non-stationary system using general regression neural network (GRNN). This includes investigation into the dynamics of the problem domain, discretisation of the problem domain to reduce the computational complexity, parameters selection of the optimization algorithm, convergence guarantee for real-time solution and off-line optimization for real-time solution. In order to demonstrate these challenges, this investigation considers a real-time optimal missile guidance algorithm using GRNN to achieve an accurate interception of the maneuvering targets in three-dimension. Evolutionary Genetic Algorithms (GAs) are used to generate optimal guidance training data set for a large missile defense space to train the GRNN. The Navigation, Constant of the Proportional Navigation Guidance and the target position at launching are considered for optimization using GAs. This is achieved by minimizing the. miss distance and missile flight time. Finally, the merits of the proposed schemes for real-time accurate interception are presented and discussed through a set of experiments. (C) 2012 Elsevier Ltd. All rights reserved.

Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.

Description Logics form a family of powerful ontology languages widely used by academics and industry experts to capture and intelligently manage knowledge about the world. A key advantage of Description Logics is their amenability to automated reasoning that enables the deduction of knowledge that has not been explicitly stated. However, in order to ensure decidability of automated reasoning algorithms, suitable restrictions are usually enforced on the shape of structures that are expressible using Description Logics. As a consequence, Description Logics fall short of expressive power when it comes to representing cyclic structures, which abound in life sciences and other disciplines. The objective of this thesis is to explore ontology languages that are better suited for the representation of structured objects. It is suggested that an alternative approach which relies on nonmonotonic existential rules can provide a promising candidate for modelling such domains. To this end, we have built a comprehensive theoretical and practical framework for the representation of structured entities along with a surface syntax designed to allow the creation of ontological descriptions in an intuitive way. Our formalism is based on nonmonotonic existential rules and exhibits a favourable balance between expressive power and computational as well as empirical tractability. In order to ensure decidability of reasoning, we introduce a number of acyclicity criteria that strictly generalise many of the existing ones. We also present a novel stratification condition that properly extends `classical' stratification and allows for capturing both definitional and conditional aspects of complex structures. The applicability of our formalism is supported by a prototypical implementation, which is based on an off-the-shelf answer set solver and is tested over a realistic knowledge base. Our experimental results demonstrate improvement of up to three orders of magnitude in comparison with previous evaluation efforts and also expose numerous modelling errors of a manually curated biochemical knowledge base. Overall, we believe that our work lays the practical and theoretical foundations of an ontology language that is well-suited for the representation of structured objects. From a modelling point of view, our approach could stimulate the adoption of a different and expressive reasoning paradigm for which robustly engineered mature reasoners are available; it could thus pave the way for the representation of a broader spectrum of knowledge. At the same time, our theoretical contributions reveal useful insights into logic-based knowledge representation and reasoning. Therefore, our results should be of value to ontology engineers and knowledge representation researchers alike.

Query processing is a core task in probabilistic databases: Given a query and a database that encodes uncertainty in data by means of probability distributions, the problem is to compute possible query answers together with their respective probabilities of being correct. This thesis advances the state of the art in two aspects of query processing in probabilistic databases: complexity analysis and query evaluation techniques. A dichotomy is established for non-repeating, con- junctive relational algebra queries with negation that separates #P-hard queries from those with PTIME data complexity. A framework for computing proba- bilities of relational algebra queries is presented; the probability computation algorithm is based on decomposition methods and provides exact answers in the case of exhaustive decompositions, or anytime approximate answers with absolute or relative error guarantees in the case of partial decompositions. The framework is extended to queries with aggregation operators. An experimental evaluation of the proposed algorithms’ implementations within the SPROUT query engine complements the theoretical results. The SPROUT² system uses this query engine to compute answers to queries on uncertain, tabular Web data.

Le problème d'intersection d'automates consiste à vérifier si plusieurs automates finis déterministes acceptent un mot en commun. Celui-ci est connu PSPACE-complet (resp. NL-complet) lorsque le nombre d'automates n'est pas borné (resp. borné par une constante). Dans ce mémoire, nous étudions la complexité du problème d'intersection d'automates pour plusieurs types de langages et d'automates tels les langages unaires, les automates à groupe (abélien), les langages commutatifs et les langages finis. Nous considérons plus particulièrement le cas où chacun des automates possède au plus un ou deux états finaux. Ces restrictions permettent d'établir des liens avec certains problèmes algébriques et d'obtenir une classification intéressante de problèmes d'intersection d'automates à l'intérieur de la classe P. Nous terminons notre étude en considérant brièvement le cas où le nombre d'automates est fixé. / The automata non emptiness intersection problem is to determine whether several deterministic finite automata accept a word in common. It is known to be PSPACE-complete (resp. NL-complete) whenever the number of automata is not bounded (resp. bounded by a constant). In this work, we study the complexity of the automata intersection problem for several types of languages and automata such as unary languages, (abelian) group automata, commutative languages and finite languages. We raise the issue of limiting the number of final states to at most two in the automata involved. This way, we obtain relationships with some algebraic problems and an interesting classification of automata intersection problems inside the class P. Finally, we briefly consider the bounded version of the automata intersection problem.