A logical Reconstruction of Leonard Bloomfield's Linguistic Theory

In this work we present a logical reconstruction of Leonard Bloom- field’s theory of structural linguistics. First, the central notions of this theory are analyzed and discussed. In the following section, a recon- struction with the so-called structuralist approach in the philosophy of science is presented. After defining the general framework of Bloom- field’s theory, questions of lawlikeness and theoretical terms will be discussed. In a further step, this work aims to contribute to the dis- cussion of theory change and scientific realism, applied to linguistic theory. After the reconstruction of further theories of linguistics, it can be studied whether certain inter theoretical relations hold. It aims to be a contribution to the discussion on the foundations of linguistics

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

A logical Reconstruction of Leonard Bloomfield's Linguistic Theory

In this work we present a logical reconstruction of Leonard Bloom- field’s theory of structural linguistics. First, the central notions of this theory are analyzed and discussed. In the following section, a recon- struction with the so-called structuralist approach in the philosophy of science is presented. After defining the general framework of Bloom- field’s theory, questions of lawlikeness and theoretical terms will be discussed. In a further step, this work aims to contribute to the dis- cussion of theory change and scientific realism, applied to linguistic theory. After the reconstruction of further theories of linguistics, it can be studied whether certain inter theoretical relations hold. It aims to be a contribution to the discussion on the foundations of linguistics

Distance functional dependencies in the presence of complex values

Distance functional dependencies (dFDs) have been introduced in the context of the relational data model as a generalisation of error-robust functional dependencies (erFDs). An erFD is a dependency that still holds, if errors are introduced into a relation, which cause the violation of an original functional dependency. A dFD with a distance d=2e+1 corresponds to an erFD with at most e errors in each tuple. Recently, an axiomatisation of dFDs has been obtained. Database theory, however, does no longer deal only with flat relations. Modern data models such as the higher-order Entity-Relationship model (HERM), object oriented datamodels (OODM), or the eXtensible Meakup Language (XML) provide constructors for complex values such as finite sets, multisets and lists. In this article, dFDs with complex values are investigated. Based on a generalisation of the HAmming distance for tuples to complex values, which exploits a lattice structure on subattributes, the major achievement is a finite axiomatisation of the new class of dependencies

Research in Architectural Education: Theory and Practice of Visual Training

Today, the significance of vision is often considered from multiple points of view including perceptual, cognitive, imaginative, historical, technical, ethical, cultural, and critical perspectives.  Visual Studies, Visual Communication and Visual Design are popular courses of study found in many programs of higher education. This paper centers on a course called Visual Training within the domain of architectural education. To illustrate the pedagogical significance of the 78-year old practice, a methodology of Visual Training as it has been conducted at Illinois Institute of Technology is presented.  The paper describes the program of exercises used, and through an interpretation of the course outcomes, it reveals the course structure and pedagogical theory. The discussion shows how Visual Training establishes grounds for architectural critique based on visual perception and aesthetic judgment. In looking at this case of Visual Training, the paper revisits some of the fundamental premises of architectural pedagogy – from methods to ideals – and challenges assumptions about the role of vision in education by calling attention to existing biases shaping many of today's programs

Representing Model Theory in a Type-Theoretical Logical Framework

AbstractWe give a comprehensive formal representation of first-order logic using the recently developed module system for the Twelf implementation of the Edinburgh Logical Framework LF. The module system places strong emphasis on signature morphisms as the main primitive concept, which makes it particularly useful to reason about structural translations, which occur frequently in proof and model theory.Syntax and proof theory are encoded in the usual way using LF's higher order abstract syntax and judgments-as-types paradigm, but using the module system to treat all connectives and quantifiers independently. The difficulty is to reason about the model theory, for which the mathematical foundation in which the models are expressed must be encoded itself. We choose a variant of Martin-Löf's type theory as this foundation and use it to axiomatize first-order model theoretic semantics. Then we can encode the soundness proof as a signature morphism from the proof theory to the model theory. We extend our results to models given in terms of set theory using an encoding of Zermelo-Fraenkel set theory in LF and giving a signature morphism from Martin-Löf type theory into it. These encodings can be checked mechanically by Twelf.Our results demonstrate the feasibility of comprehensively formalizing large scale representation theorems and thus promise significant future applications