Using Automated Reasoning Techniques for Deductive Databasis

This report presents a proposal for a deduction component that supports the query mechanism of relational databases. The query-subquery (QSQ) paradigm is currently very popular in the database community since it focuses the deduction process on the relevant data. We show how to extend the QSQ paradigm from Horn clauses to arbitrary predicate logic formulae such that disjunctions in the consequent of an implication, negation in its logical meaning and arbitrary recursive predicates can be handled without restrictions. Various techniques to improve the search behaviour, such as lemma generation, query generalization etc. can be incorporated. Furthermore we show how to use clause graphs for compile time optimizations in the presence of recursive clauses and to support the run time processing

Flux de l'information en programmation logique

Cette thèse est développée dans le but d'aborder la question du flux de l'information en programmation logique. Les contributions de cette thèse peuvent être divisées en trois parties: 1. Flux de l'information en programmation logique: Nous proposons une base théorique de ce que pourrait être un flux de l'information en programmation logique. Plusieurs définitions de flux d'information (basées sur la réussite / échec, les substitutions réponses, bisimulation entre les arbres de résolution des buts logiques) sont évaluées et comparées. Des problèmes de décision sont donnés pour chaque définition et la complexité est étudiée pour certaines catégories de programmes logiques. 2. Bisimulation de buts logiques: Nous introduisons la notion de bisimulation entre les buts Datalog: deux buts Datalog sont bisimilaires par rapport à un programme Datalog donné lorsque leurs SLD-arbres, considérés comme des structures relationnelles, sont bisimilaires. Nous abordons le problème de décider si deux buts donnés sont bisimilaires à l'égard d'un programme donné. Lorsque les programmes sont hiérarchiques ou restricted, ce problème est décidable en 2EXPTIME. 3. Contrôle préventif de l'inférence dans les bases de données déductives: Nous proposons un mécanisme de sécurité sûr et précis pour les bases de données déductives basé sur la notion de flux de l'information dans la programmation logique.This thesis is developed in order to tackle the issue of information flow in logic programming. The contributions of this thesis can be split into three mains parts: 1. Information flow in logic programming: we propose a theoretical foundation of what could be an information flow in logic programming. Several information flow definitions (based on success/failure, substitution answers, bisimulation between resolution trees of goals) are stated and compared. Decision procedures are given for each definition and complexity is studied for specific classes of logic programs. 2. Bisimulation of logic goals: We introduce the concept of bisimulation between Datalog goals: two Datalog goals are bisimilar with respect to a given Datalog program when their SLD-trees, considered as relational structures, are bisimilar. We address the problem of deciding whether two given goals are bisimilar with respect to given programs. When the given programs are hierarchical or restricted, this problem is decidable in 2EXPTIME. 3. Preventive inference control for deductive databases: We propose a secure and a precise security mechanism for deductive databases based on the notion of information flow in logic programming

Trading inference effort versus size in CNF Knowledge Compilation

Knowledge Compilation (KC) studies compilation of boolean functions f into some formalism F, which allows to answer all queries of a certain kind in polynomial time. Due to its relevance for SAT solving, we concentrate on the query type "clausal entailment" (CE), i.e., whether a clause C follows from f or not, and we consider subclasses of CNF, i.e., clause-sets F with special properties. In this report we do not allow auxiliary variables (except of the Outlook), and thus F needs to be equivalent to f. We consider the hierarchies UC_k <= WC_k, which were introduced by the authors in 2012. Each level allows CE queries. The first two levels are well-known classes for KC. Namely UC_0 = WC_0 is the same as PI as studied in KC, that is, f is represented by the set of all prime implicates, while UC_1 = WC_1 is the same as UC, the class of unit-refutation complete clause-sets introduced by del Val 1994. We show that for each k there are (sequences of) boolean functions with polysize representations in UC_{k+1}, but with an exponential lower bound on representations in WC_k. Such a separation was previously only know for k=0. We also consider PC < UC, the class of propagation-complete clause-sets. We show that there are (sequences of) boolean functions with polysize representations in UC, while there is an exponential lower bound for representations in PC. These separations are steps towards a general conjecture determining the representation power of the hierarchies PC_k < UC_k <= WC_k. The strong form of this conjecture also allows auxiliary variables, as discussed in depth in the Outlook.Comment: 43 pages, second version with literature updates. Proceeds with the separation results from the discontinued arXiv:1302.442

Generalization of predicates with string arguments

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2002.Thesis (Master's) -- Bilkent University, 2002.Includes bibliographical references leaves 60-63.String/sequence generalization is used in many different areas such as machine learning, example-based machine translation and DNA sequence alignment. In this thesis, a method is proposed to find the generalizations of the predicates with string arguments from the given examples. Trying to learn from examples is a very hard problem in machine learning, since finding the global optimal point to stop generalization is a difficult and time consuming process. All the work done until now is about employing a heuristic to find the best solution. This work is one of them. In this study, some restrictions applied by the SLGG (Specific Least General Generalization) algorithm, which is developed to be used in an example-based machine translation system, are relaxed to find the all possible alignments of two strings. Moreover, a Euclidian distance like scoring mechanism is used to find the most specific generalizations. Some of the generated templates are eliminated by four different selection/filtering approaches to get a good solution set. Finally, the result set is presented as a decision list, which provides the handling of exceptional cases.Canıtezer, GökerM.S

Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014

Preface For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas. As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems