We investigate principles of rationality based on symmetry in Polyadic Pure Inductive Logic. The aim of Pure Inductive Logic (PIL) is to determine how to assign probabilities to sentences of a language being true in some structure on the basis of rational considerations. This thesis centres on principles arising from instances of symmetry for sentences of first-order polyadic languages. We begin with the recently introduced Permutation Invariance Principle (PIP), and find that it is determined by a finite number of permutations on a finite set of formulae. We test the consistency of PIP with established principles of the subject and show, in particular, that it is consistent with Super Regularity. We then investigate the relationship between PIP and the two main polyadic principles thus far, Spectrum Exchangeability and Language Invariance, and discover there are close connections. In addition, we define the key notion of polyadic atoms as the building blocks of polyadic languages. We explore polyadic generalisations of the unary principle of Atom Exchangeability and prove that PIP is a natural extension of Atom Exchangeability to polyadic languages. In the second half of the thesis we investigate polyadic approaches to the unary version of Constant Exchangeability as invariance under signatures. We first provide a theory built on polyadic atoms (for binary and then general languages). We introduce the notion of a signature for non-unary languages, and principles of invariance under signatures, independence, and instantial relevance for this context, as well as a binary representation theorem. We then develop a second approach to these concepts using elements as alternative building blocks for polyadic languages. Finally, we introduce the concepts of homomorphisms and degenerate probability functions in Pure Inductive Logic. We examine which of the established principles of PIL are preserved by these notions, and present a method for reducing probability functions on general polyadic languages to functions on binary languages.

This thesis investigates ways of incorporating reasoning by analogy into Pure (Unary) Inductive Logic. We start with an analysis of similarity as distance, noting that this is the conception that has received most attention in the literature so far. Chapter 4 looks in some detail at the consequences of adopting Hamming Distance as our measure of similarity, which proves to be a strong requirement. Chapter 5 then examines various adaptations of Hamming Distance and proposes a subtle modification, further-away-ness, that generates a much larger class of solutions.

We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.

La programmation par contraintes permet de modéliser des problèmes et offre des méthodes de résolution efficaces. Cependant, sa complexité augmentant ces dernières années, son utilisation, notamment pour modéliser des problèmes, est devenue limitée à des utilisateurs possédant une bonne expérience dans le domaine. Cette thèse s’inscrit dans un cadre visant à automatiser la modélisation. Les techniques existantes ont montré des résultats encourageants mais certaines exigences rendent leur utilisation encore problématique. Dans une première partie, nous proposons de dépasser une limite existante qui réside dans la nécessité pour l’utilisateur de fournir des solutions du problème qu’il veut modéliser. En remplacement, il nous fournit des solutions de problèmes proches, c’est-à-dire de problèmes dont la sémantique de fond est la même mais dont les variables et leur domaine peuvent changer. Pour exploiter de telles données, nous proposons d’acquérir, grâce à des techniques de programmation logique inductive, un modèle plus abstrait que le réseau de contraintes. Une fois appris, ce modèle est ensuite transformé pour correspondre au problème initial que souhaitait résoudre l’utilisateur. Nous montrons également que la phase d’apprentissage se heurte à des limites pathologiques et qui nous ont contraints à développer un nouvel algorithme pour synthétiser ces modèles abstraits. Dans une seconde partie, nous nous intéressons à la possibilité pour l’utilisateur de ne pas donner d’exemples du tout. En partant d’un CSP sans aucune contrainte, notre méthode consiste à résoudre le problème de l’utilisateur de manière classique. Grâce à un arbre de recherche, nous affectons progressivement des valeurs aux variables. Quand notre outil ne peut décider si l’affectation partielle courante est correcte ou non, nous demandons à l’utilisateur de guider la recherche sous forme de requêtes. Ces requêtes permettent de trouver des contraintes à ajouter aux modèles du CSP et ainsi améliorer la recherche. / Constraint programming allows to model many kind of problems with efficient solving methods. However, its complexity has increased these last years and its use, notably to model problems, has become limited to people with a fair expertise in the domain. This thesis deals with automating the modeling task in constraint programming. Methods already exist, with encouraging results, but many requirements are debatable. In a first part, we propose to avoid the limitation consisting, for the user, in providing solutions of the problem she aims to solve. As a replacement of these solutions, the user has to provide solutions of closed problem, i.e problem with same semantic but where variables and domains can be different. To handle this kind of data, we acquire, thanks to inductive logic programming, a more abstract model than the constraint network. When this model is learned, it is translated in the very constraint network the user aims to model. We show the limitations of learning method to build such a model due to pathological problems and explain the new algorithm we have developed to build these abstract models. In a second part, we are interesting in the possibility to the user to not provide any examples. Starting with a CSP without constraints, our method consists in solving the problem the user wants in a standard way. Thanks to a search tree, we affect to each variable a value. When our tool cannot decide if the current partial affectation is correct or not, we ask to the user, with yes/no queries, to guide the search. These queries allow to find constraints to add to the model and then to improve the quality of the search.

Σε αυτήν την εργασία μελετάται ο Επαγωγικός Λογικός Προγραμματισμός μέσα απο το πρίσμα της μάθησης της Γραμματικής της αγγλικής γλώσσας. Ο λόγος που επιλέχθηκε αυτό το πρόβλημα είναι ότι εξομοιώνει, μέχρι ενός σγημείου, τον τρόπο που τα παιδιά μαθαίνουν να μιλούν κάποια γλώσσα, υπό την έννοια ότι μαθαίνουν να μιλάνε χωρίς να έρθουν σε επαφή με τους κανόνες – τη γραμματική – της γλώσσας, αλλά από την επαφή τους με τα με τα ερεθίσματα – τα παραδείγματα – που έχουν από τον περίγυρό τους. / This paper is about Inductive Logic Programming through the prism of a problem. In our case Grammar Learning.

We propose and investigate several new principles of rational reasoning within the framework of Pure Inductive Logic, PIL, where probability functions defined on the sentences of a first-order language are used to model an agent's beliefs. The Elephant Principle is concerned with how learning, modelled by conditioning, may be uniquely `remembered'. The Perspective Principle requires that, from a given prior, conditioning on statistically similar experiences should result in similar assignments, and is found to be a necessary condition for Reichenbach's Axiom to hold. The Abductive Inference Principle and some variations are proposed as possible formulations of a restriction of C.S. Peirce's notion of hypothesis in the context of PIL, though characterization results obtained for these principles suggest that they may be too strong. The Finite Values Property holds when a probability function takes only finitely many values when restricted to sentences containing only constant symbols from some fixed finite set. This is shown to entail a certain systematic method of assigning probabilities in terms of possible worlds, and it is considered in this light as a possible principle of inductive reasoning. Classification results are given, stating which members of certain established families of probability functions satisfy each of these new principles. Additionally, we define the theory of a principle P of PIL to be the set of those sentences which are assigned probability 1 by every probability function which satisfies P. We investigate the theory of the established principle of Spectrum Exchangeability by finding separately the theories of heterogeneous and homogeneous functions. The theory of Spectrum Exchangeability is found to be equal to the theory of finite structures. The theory of Johnson's Sufficientness Postulate is also found. Consequently, we find that Spectrum Exchangeability, Johnson's Sufficientness Postulate and the Finite Values Property are all inconsistent with the principle of Super-Regularity: that any consistent sentence should be assigned non-zero probability.

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Some upstream open reading frames (uORFs) regulate gene expression (i.e. they are functional) and can play key roles in keeping organisms healthy. However, how uORFs are involved in gene regulation is not het fully understood. In order to get a complete view of how uORFs are involved in gene regulation, it is expected that a large number of functional uORFs are needed. Unfortunately , lab experiments to verify that uORFs are functional are expensive. In this thesis, for the first time, the use of inductive logic programming (ILP) is explored for the task of learning which uORFs regulate gene expression in the yeast Saccharomyces cerevisiae. This work is directed to help select sets of candidate functional uORFs for experimental studies. With limited background knowledge, ILP can generate hypotheses which make the search for novel functional uORFs 17 times more efficient than random sampling. Adding mRNA secondary structure to the background knowledge results in hypotheses with significantly increased performance. This work is the first machine learning work to study both uORFs and mRNA secondary structures in the context of gene regulation. Using a novel combination of knowledge about biological conservation, gene ontology annotations and genes' response to different conditions results in hypotheses that are simple, informative, have an estimated sensitivity of 81% and provide provisional insights into biological characteristics of functional uORFs. The hypotheses predict 299 further genes to have 450 novel functional uORFs. A comparison with a related study suggests that 8 of these predicted functional uORFs (from 8 genes) are strong candidates for experimental studies.

Inductive logic programming is a discipline investigating invention of clausal theories from observed examples such that for given evidence and background knowledge we are finding a hypothesis covering all positive examples and excluding all negative ones. In this thesis we extend an existing work on template consistency to general consistency. We present a three-phase algorithm DeMeR decomposing the original problem into smaller subtasks, merging all subsolutions together yielding a complete solution and finally refining the result in order to get a compact final hypothesis. Furthermore, we focus on a method how each individual subtask is solved and we introduce a generate-and-test method based on the probabilistic history-driven approach for this purpose. We analyze each stage of the proposed algorithms and demonstrate its impact on a runtime and a hypothesis structure. In particular, we show that the first phase of the algorithm concentrates on solving the problem quickly at the cost of longer solutions whereas the other phases refine these solutions into an admissible form. Finally, we prove that our technique outperforms other algorithms by comparing its results for identifying common structures in random graphs to existing systems.

O Aprendizado de Máquina trata da questão de como desenvolver programas de computador capazes de aprender um conceito ou hipótese a partir de um conjunto de exemplos ou casos observados. Baseado no conjunto de treinamento o algoritmo de aprendizado induz a classificação de uma hipótese capaz de determinar corretamente a classe de novos exemplos ainda não rotulados. Linguagens de descrição são necessárias para escrever exemplos, conhecimento do domínio bem como as hipóteses aprendidas a partir dos exemplos. Em geral, essas linguagens podem ser divididas em dois tipos: linguagem baseada em atributo-valor ou proposicional e linguagem relacional. Algoritmos de aprendizado são classificados como proposicional ou relacional dependendo da liguagem de descrição que eles utilizam. Além disso, no aprendizado simbólico o objetivo é gerar a classificação de hipóteses que possam ser facilmente interpretadas pelos humanos. Algoritmos de aprendizado proposicional utilizam a representação atributo-valor, a qual é inadequada para representar objetos estruturados e relações entre esses objetos. Por outro lado, a Programação lógica Indutiva (PLI) é realizada com o desenvolvimento de técnicas e ferramentas para o aprendizado relacional. Sistemas de PLI são capazes de aprender levando em consideração conhecimento do domínio na forma de um programa lógico e também usar a linguagem de programas lógicos para descrever o conhecimento induzido. Neste trabalho foi implementado um módulo chamado Kaeru para converter dados no formato atributo-valor para o formato relacional utilizado pelo sistema de PLI Aleph. Uma série de experimentos foram realizados com quatro conjuntos de dados naturais e um conjunto de dados real no formato atributo valor. Utilizando o módulo conversor Kaeru esses dados foram convertidos para o formato relacional utilizado pelo Aleph e hipóteses de classificação foram induzidas utilizando aprendizado proposicional bem como aprendizado relacional. É mostrado também, que o aprendizado proposicional pode ser utilizado para incrementar o conhecimento do domínio utilizado pelos sistemas de aprendizado relacional para melhorar a qualidade das hipóteses induzidas. / Machine Learning addresses the question of how to build computer programs that learn a concept or hypotheses from a set of examples, objects or cases. Descriptive languages are necessary in machine learning to describe the set of examples, domain knowledge as well as the hypothesis learned from these examples. In general, these languages can be divided into two types: languages based on attribute values, or em propositional languages, and relational languages. Learning algorithms are often classified as propositional or relational taking into consideration the descriptive language they use. Typical propositional learning algorithms employ the attribute value representation, which is inadequate for problem-domains that require reasoning about the structure of objects in the domain and relations among such objects. On the other hand, Inductive Logig Programming (ILP) is concerned with the development of techniques and tools for relational learning. ILP systems are able to take into account domain knowledge in the form of a logic program and also use the language of logic programs for describing the induced knowledge or hypothesis. In this work we propose and implement a module, named kaeru, to convert data in the attribute-value format to the relational format used by the ILP system Aleph. We describe a series of experiments performed on four natural data sets and one real data set in the attribute value format. Using the kaeru module these data sets were converted to the relational format used by Aleph and classifying hipoteses were induced using propositional as well as relational learning. We also show that propositional knowledge can be used to increment the background knowledge used by relational learners in order to improve the induded hypotheses quality.