Tijn Borghuis

The DenK-architecture : a fundamental approach to user-interfaces

In this paper we present the basic principles underlying the DenK-system, a generic cooperative interface combining linguistic and visual interaction. The system integrates results from fundamental research in knowledge representation, communication, natural language semantics and pragmatics, and object-oriented animation. Our design incorporates a cooperative and knowledgeable electronic assistant that communicates with a user in natural language, and an application domain, which is presented visually. The assistant, that we call thecooperator, has an information state that is represented in a rich form of Type Theory, a formalism that enables us to model the inherent cognitive dynamics of a dialogue participant. Pragmatic issues in man-machine interaction, concerning the use of natural language and knowledge in cooperative communication, are central to our approach.

Multimodal Cooperation with the DENK System

In this chapter we present the DenK project, a long-term effort where the aim is to build a generic cooperative human-computer interface combining multiple input and output modalities. We discuss the view on human-computer interaction that underlies the project and the emerging DenK system. The project integrates results from fundamental research in knowledge representation, communication, natural language semantics and pragmatics, and object-oriented animation. Central stage in the project is occupied by the design of a cooperative and knowledge-able electronic assistant that communicates in natural language and that has internal access to an application domain which is presented visually to the user. The assistant, that we call the Cooperative Assistant, has an information state that is represented in a rich form of type theory, a formalism that enables us to model the inherent cognitive dynamics of a dialogue participant. This formalism is used both for modeling domain knowledge, for representing the current dialogue context, and for implementing a context-change theory of communication.

Interpreting Modal Natural Deduction in Type Theory

The purpose of this paper is to propose an interpretation (i.e. a translation which preserves valid inferences) of modal logic in typed λ-calculus. There are several ways one could go about this, depending on the kind of interpretation used as a startingpoint. We shall be working in the frame of the “propositions-astypes”-interpretation, which is well-established for propositional and predicate logics1. Under this interpretation of typed λ-terms there is a direct correspondence between natural deduction in logic and deduction in typed λ-calculus. One way to exploit this correspondence for our purposes would be to interpret modal logic via its translation in predicate logic, but we shall take a more straightforward approach by widening the correspondence in such a manner that it encompasses modal natural deduction.

Modal Pure Type Systems

We present a framework for intensional reasoning in typed λ-calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a “propositions-as-types”-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.

Quality Criteria for Mathematical Models in Relation to Models’ Purposes: Their Usefulness in Engineering Education

A taxonomy of eight quality criteria for mathematical models was developed for the common basic modelling course in the innovated BSc curriculum of Eindhoven University of Technology. First year engineering students of all disciplines reflected on their group modelling projects, indicating how their models could be improved, using the criteria. The students were also asked to indicate the purpose(s) of their models from a list of 16 purposes. This study explores the usefulness of the purposes and criteria, defined as relevance combined with understandability. Optimisation proved to be the most relevant purpose, followed by analysis, prediction (what), and verification.Specialisation, genericity, scalability, distinctiveness, and convincingness criteria proved useful; but audience, impact, and surprise did not.

Communication Modelling and Context-Dependent Interpretation: An Integrated Approach

In this paper we present a simple model of communication. We assume that communication takes place between two agents. Each agent has a private and subjective knowledge state. The knowledge of both agents is partial, finite, and represented in a computational way. We investigate how ideas can be transferred from one agent to the other one, in spite of the subjective nature of the knowledge of both participants. Posing the problem in this way, it can be seen that mechanisms for context-dependent interpretation are a prerequisite for succesfull communication.

Mathematical modelling in Dutch textbooks : is it genuine mathematical modelling?

In this chapter, we analyse the two most frequently used Dutch mathematics textbooks for upper secondary schools in order to determine to what extent the tasks in these textbooks meet the criteria we have set for genuine mathematical modelling: does a modelling task have a modelling purpose, and do the students have to perform characteristic modelling activities? The criterion of having a modelling purpose stems from a modelling course in tertiary education by the last two authors. For the characteristic modelling activities, we used the research of the first two authors. Only a very small percentage of the analysed tasks meets the criteria. So, there is hardly any genuine mathematical modelling in the two textbooks, although it is explicitly mentioned in the formal curriculum.

Competencies in Higher Education: Experience with the Academic Competences and Quality Assurance (ACQA) Framework

The ACQA framework has been developed at the Eindhoven University of Technology (TU/e) as an alternative to the European Dublin Descriptors. Its goals were a characterisation of academic education, a detailed description of competencies, adding design competencies, and a sensibility for differences between disciplines.