Efficient Computation of Descriptive Patterns

A pattern $\alpha$ is a word consisting of constants and variables and the pattern language $L(\alpha)$ (over an alphabet $\Sigma$) is the set of all words that can be obtained from $\alpha$ by uniformly replacing the variables with words over $\Sigma$. We investigate the problem of computing a pattern $\alpha$ that is descriptive of a given finite set $S \subseteq \Sigma^*$ of words, i.\,e., $S \subseteq L(\alpha)$ and there is no other pattern $\beta$ with $S \subseteq L(\beta) \subset L(\alpha)$. A pattern $\alpha$ that is descriptive of a set $S$ represents the structural commonalities of the words in $S$ and, thus, can serve as a classifier with respect to this structure. Furthermore, (polynomial time) computability of descriptive patterns is sufficient for (polynomial time) inductive inference of pattern languages. We investigate the complexity of computing descriptive patterns and, for subclasses of patterns, we present efficient algorithms for computing them

Tractable Reasoning in Knowledge Representation Systems

This document addresses some problems raised by the well-known intractability of deductive reasoning in even moderately expressive knowledge representation systems. Starting from boolean constraint propagation (BCP), a previously known linear-time incomplete reasoner for clausal propositional theories, we develop fact propagation (FP) to deal with non-clausal theories, after motivating the need for such an extension. FP is specified using a confluent rewriting systems, for which we present an algorithm that has quadratic-time complexity in general, but is still linear-time for clausal theories. FP is the only known tractable extension of BCP to non-clausal theories; we prove that it performs strictly more inferences than CNF-BCP, a previously-proposed extension of BCP to non-clausal theories. We generalize a refutation reasoner based on FP to a family of sound and tractable reasoners that are "increasingly complete" for propositional theories. These can be used for anytime reasoning, i.e. they provide partial answers even if they are stopped prematurely, and the "completeness" of the answer improves with the time used in computing it. A fixpoint construction based on FP gives an alternate characterization of the reasoners in this family, and is used to define a transformation of arbitrary theories into logically-equivalent "vivid" theories -- ones for which our FP algorithm is complete. Our final contribution is to the description of tractable classes of reasoning problems. Based on FP, we develop a new property, called bounded intricacy, which is shared by a variety of tractable classes that were previously presented, for example, in the areas of propositional satisfiability, constraint satisfaction, and OR-databases. Although proving bounded intricacy for these classes requires domain-specific techniques (which are based on the original tractability proofs), bounded intricacy is one more tool available for showing that a family of problems arising in some application is tractable. As we demonstrate in the case of constraint satisfaction and disjunctive logic programs, bounded intricacy can also be used to uncover new tractable classes

Learning and consistency

In designing learning algorithms it seems quite reasonable to construct them in such a way that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail. It may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. Therefore we study several types of consistent learning in recursion-theoretic inductive inference. We show that these types are not of universal power. We give “lower bounds ” on this power. We characterize these types by some versions of decidability of consistency with respect to suitable “non-standard ” spaces of hypotheses. Then we investigate the problem of learning consistently in polynomial time. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to work inconsistently. 1

Learning categorial grammars

In 1967 E. M. Gold published a paper in which the language classes from the Chomsky-hierarchy were analyzed in terms of learnability, in the technical sense of identification in the limit. His results were mostly negative, and perhaps because of this his work had little impact on linguistics. In the early eighties there was renewed interest in the paradigm, mainly because of work by Angluin and Wright. Around the same time, Arikawa and his co-workers refined the paradigm by applying it to so-called Elementary Formal Systems. By making use of this approach Takeshi Shinohara was able to come up with an impressive result; any class of context-sensitive grammars with a bound on its number of rules is learnable. Some linguistically motivated work on learnability also appeared from this point on, most notably Wexler & Culicover 1980 and Kanazawa 1994. The latter investigates the learnability of various classes of categorial grammar, inspired by work by Buszkowski and Penn, and raises some interesting questions. We follow up on this work by exploring complexity issues relevant to learning these classes, answering an open question from Kanazawa 1994, and applying the same kind of approach to obtain (non)learnable classes of Combinatory Categorial Grammars, Tree Adjoining Grammars, Minimalist grammars, Generalized Quantifiers, and some variants of Lambek Grammars. We also discuss work on learning tree languages and its application to learning Dependency Grammars. Our main conclusions are: - formal learning theory is relevant to linguistics, - identification in the limit is feasible for non-trivial classes, - the `Shinohara approach' -i.e., placing a numerical bound on the complexity of a grammar- can lead to a learnable class, but this completely depends on the specific nature of the formalism and the notion of complexity. We give examples of natural classes of commonly used linguistic formalisms that resist this kind of approach, - learning is hard work. Our results indicate that learning even `simple' classes of languages requires a lot of computational effort, - dealing with structure (derivation-, dependency-) languages instead of string languages offers a useful and promising approach to learnabilty in a linguistic contex

Derivation methods for hybrid knowledge bases with rules and ontologies

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaFirst of all, I would like to thank my advisor, José Júlio Alferes, for his incredible support. Right from the start, during the first semester of this work, when we were 2700 km apart and meeting regularly via Skype, until the end of this dissertation, he was always committed and available for discussions, even when he had lots of other urgent things to do. A really special thanks to Terrance Swift, whom acted as an advisor, helping me a lot in the second implementation, and correcting all XSB’s and CDF’s bugs. This implementation wouldn’t surely have reached such a fruitful end without his support. I would also like to thank all my colleagues and friends at FCT for the great work environment and for not letting me take myself too serious. A special thanks to my colleagues from Dresden for encouraging me to work even when there were so many other interesting things to do as an Erasmus student. I’m indebted to Luís Leal, Bárbara Soares, Jorge Soares and Cecília Calado, who kindly accepted to read a preliminary version of this report and gave me their valuable comments. For giving me working conditions and a partial financial support, I acknowledge the Departamento de Informática of the Faculdade de Ciências e Tecnologias of Universidade Nova de Lisboa. Last, but definitely not least, I would like to thank my parents and all my family for their continuous encouragement and motivation. A special thanks to Bruno for his love, support and patience