FUNCTIONAL DEPENDENCIES AND INCOMPLETE INFORMATION

Functional dependencies play an important role in relational database design. They are defined in the context of a single relation which at all times must contain tuples with non-null entries. In this paper we examine an extension of the functional dependency interpretation to handle null values, that is, entries in tuples that represent incomplete information in a relational database. A complete axiomatization of inference rules for extended functional dependencies is also presented. Only after having such results is it possible to talk about decompositions and normalization theory in a context of incomplete information. Finally, we show that there are several practical advantages in using nulls and a weaker notion of constraint satisfiability.Information Systems Working Papers Serie

Type-driven natural language analysis

The purpose of this thesis is in showing how recent developments in logic programming can be exploited to encode in a computational environment the features of certain linguistic theories. We are in this way able to make available for the purpose of natural language processing sophisticated capabilities of linguistic analysis directly justified by well developed grammatical frameworks. More specifically, we exploit hypothetical reasoning, recently proposed as one of the possible directions to widen logic programming, to account for the syntax of filler-gap dependencies along the lines of linguistic theories such as Generalized Phrase Structure Grammar and Categorial Grammar. Moreover, we make use, for the purpose of semantic analysis of the same kind of phenomena, of another recently proposed extension, interestingly related to the previous one, namely the idea of replacing first-order terms with the more expressive λ-terms of λ-Calculus

An Inheritance-Based Theory of the Lexicon in Combinatory Categorial Grammar

Institute for Communicating and Collaborative SystemsThis thesis proposes an extended version of the Combinatory Categorial Grammar (CCG) formalism, with the following features: 1. grammars incorporate inheritance hierarchies of lexical types, defined over a simple, feature-based constraint language 2. CCG lexicons are, or at least can be, functions from forms to these lexical types This formalism, which I refer to as ‘inheritance-driven’ CCG (I-CCG), is conceptualised as a partially model-theoretic system, involving a distinction between category descriptions and their underlying category models, with these two notions being related by logical satisfaction. I argue that the I-CCG formalism retains all the advantages of both the core CCG framework and proposed generalisations involving such things as multiset categories, unary modalities or typed feature structures. In addition, I-CCG: 1. provides non-redundant lexicons for human languages 2. captures a range of well-known implicational word order universals in terms of an acquisition-based preference for shorter grammars This thesis proceeds as follows: Chapter 2 introduces the ‘baseline’ CCG formalism, which incorporates just the essential elements of category notation, without any of the proposed extensions. Chapter 3 reviews parts of the CCG literature dealing with linguistic competence in its most general sense, showing how the formalism predicts a number of language universals in terms of either its restricted generative capacity or the prioritisation of simpler lexicons. Chapter 4 analyses the first motivation for generalising the baseline category notation, demonstrating how certain fairly simple implicational word order universals are not formally predicted by baseline CCG, although they intuitively do involve considerations of grammatical economy. Chapter 5 examines the second motivation underlying many of the customised CCG category notations — to reduce lexical redundancy, thus allowing for the construction of lexicons which assign (each sense of) open class words and morphemes to no more than one lexical category, itself denoted by a non-composite lexical type. Chapter 6 defines the I-CCG formalism, incorporating into the notion of a CCG grammar both a type hierarchy of saturated category symbols and an inheritance hierarchy of constrained lexical types. The constraint language is a simple, feature-based, highly underspecified notation, interpreted against an underlying notion of category models — this latter point is crucial, since it allows us to abstract away from any particular inference procedure and focus on the category notation itself. I argue that the partially model-theoretic I-CCG formalism solves the lexical redundancy problem fairly definitively, thereby subsuming all the other proposed variant category notations. Chapter 7 demonstrates that the I-CCG formalism also provides the beginnings of a theory of the CCG lexicon in a stronger sense — with just a small number of substantive assumptions about types, it can be shown to formally predict many implicational word order universals in terms of an acquisition-based preference for simpler lexical inheritance hierarchies, i.e. those with fewer types and fewer constraints. Chapter 8 concludes the thesis

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms

Dependencies in language: On the causal ontology of linguistic systems

Dependency is a fundamental concept in the analysis of linguistic systems. The many if-then statements offered in typology and grammar-writing imply a causally real notion of dependency that is central to the claim being made—usually with reference to widely varying timescales and types of processes. But despite the importance of the concept of dependency in our work, its nature is seldom defined or made explicit. This book brings together experts on language, representing descriptive linguistics, language typology, functional/cognitive linguistics, cognitive science, research on gesture and other semiotic systems, developmental psychology, psycholinguistics, and linguistic anthropology to address the following question: What kinds of dependencies exist among language-related systems, and how do we define and explain them in natural, causal terms