Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Fuzzy logic for decision support in chronic care

Computerized clinical guidelines can provide significant benefits in terms of health outcomes and costs, however, their effective computer implementation presents significant problems. Vagueness and ambiguity inherent in natural language (textual) clinical guidelines makes them problematic for formulating automated alerts or advice. Fuzzy logic allows us to formalize the treatment of vagueness in a decision support architecture. In care plan on-line (CPOL), an intranet-based chronic disease care planning system for general practitioners (GPs) in use in South Australia, we formally treat fuzziness in interpretation of quantitative data, formulation of recommendations and unequal importance of clinical indicators. We use expert judgment on cases, as well as direct estimates by experts, to optimize aggregation operators and treat heterogeneous combinations of conjunction and disjunction that are present in the natural language decision rules formulated by specialist teams.

The influence of collectivism in society and its implications for research on information systems and national culture

This paper argues that the nature of IS research that deals with indigenous culture must be informed as much by context as it is by culture models, which has been the focus of such research in the past. This is considered important because it better reflects the meaning of the data collected for the researcher. To appreciate the importance of context this papers also argues that research subjects from designated individualist societies will inform the researcher in different ways from those subjects located in collectivist societies. To illustrate the practical implications of this argument the paper reports three separate case studies in IS research where the researchers reflect on the impact that a collectivist view has had on the research findings. The paper suggests that (1) similar ethnicity and appearance are significant in gaining the trust of subjects in a collectivist society; that is the researcher is part of the in-group as they belong to the same culture or ethnic group; that (2) who introduced the researcher to the subject is significant in that trust is best reflected when a member of the group/collective plays an important role in the research process itself; and that (3) an ability to (a) communicate in the natural language and (b) understand the implicit body language and (c) cultural codes is important in gaining significant and more meaningful research outcomes. This is enabled via the implicit meanings embedded in members of the collectivist society.

A virtual salesperson

This chapter describes the use of a graphical humane interface - a Virtual Salesperson. The face of the Virtual Salesperson is a generic Facial Animation Engine developed at the University of Genova in Italy and uses a 3-D computer graphics model based on the MPEG-4 standard supplemented by Cyberware scans for facial detail. The appearance of the head may be modified by Facial Definition Parameters to more accurately model the required visage allowing one model to represent many different Talking Heads. The “brain” of the Virtual Salesperson, developed at Curtin University, integrates natural language parsing, text to speech synthesis, and artificial intelligence systems to produce a “bot” capable of helping a user through a question/answer sales enquiry. The Virtual Salesperson is a specific example of a generic Human Computer Interface - a Talking Head.

Modelling trust structures for public key infrastructures

The development of Public Key Infrastructures (PKIs) is highly desirable to support secure digital transactions and communications throughout existing networks. It is important to adopt a particular trust structure or PKI model at an early stage as this forms a basis for the PKI’s development. Many PKI models have been proposed but use only natural language descriptions. We apply a simple formal approach to describe the essential factors of a PKI model. Rule sets for some PKI models are given and can be used to distinguish and classify the different PKI models. Advantages for this approach with conglomerate PKIs, those that are built from multiple distinct PKI models, are discussed.

Strategic knowledge for the identification and construction of goal states

There is widespread recognition that goal recognition strategies, in the context of structural analysis and cognitive (user) models, represent a major field of contemporary research into discourse understanding. This thesis reports a goal interpretation paradigm that embraces both a novel goal structure formalism and strategic knowledge. The goal interpretation processes involve the identification of goal primitives and the construction of goal states. The mechanisms developed for goal interpretation rely on explicit goal recognition (selection) and confirmation of feasibility. A goal state contains all the information required by the planner. By constructing a goal state, the chance of failure in planning is greatly reduced and the efficiency of the planning system is vastly improved. These mechanisms are not limited to inference. Other mechanisms are reported include goal structure processing, goal primitives identification and searching strategies, extended heuristic classification method and a new conceptual graph operation (i.e. SPLIT).

On the automated interpretation and indexing of American football

This work combines natural language understanding and image processing with incremental learning to develop a system that can automatically interpret and index American Football. We have developed a model for representing spatio-temporal characteristics of multiple objects in dynamic scenes in this domain. Our representation combines expert knowledge, domain knowledge, spatial knowledge and temporal knowledge. We also present an incremental learning algorithm to improve the knowledge base as well as to keep previously developed concepts consistent with new data. The advantages of the incremental learning algorithm are that is that it does not split concepts and it generates a compact conceptual hierarchy which does not store instances.

Combining NL processing and video data to query American football

We explore the use of natural language understanding and image processing to index and query American Football tapes. We present a model for representing spatio-temporal characteristics of multiple objects in dynamic scenes in this domain, and a recognition system which uses the model to recognise American Football plays.

Identifying emerging hotel preferences using emerging pattern mining technique

Hotel managers continue to find ways to understand traveler preferences, with the aim of improving their strategic planning, marketing, and product development. Traveler preference is unpredictable for example, hotel guests used to prefer having a telephone in the room, but now favor fast Internet connection. Changes in preference influence the performance of hotel businesses, thus creating the need to identify and address the demands of their guests. Most existing studies focus on current demand attributes and not on emerging ones. Thus, hotel managers may find it difficult to make appropriate decisions in response to changes in travelers' concerns. To address these challenges, this paper adopts Emerging Pattern Mining technique to identify emergent hotel features of interest to international travelers. Data are derived from 118,000 records of online reviews. The methods and findings can help hotel managers gain insights into travelers' interests, enabling the former to gain a better understanding of the rapid changes in tourist preferences.

Ontology-based automated support for goal–use case model analysis

Combining goal-oriented and use case modeling has been proven to be an effective method in requirements elicitation and elaboration. To ensure the quality of such modeled artifacts, a detailed model analysis needs to be performed. However, current requirements engineering approaches generally lack reliable support for automated analysis of consistency, correctness and completeness (3Cs problems) between and within goal models and use case models. In this paper, we present a goal–use case integration framework with tool support to automatically identify such 3Cs problems. Our new framework relies on the use of ontologies of domain knowledge and semantics and our goal–use case integration meta-model. Moreover, functional grammar is employed to enable the semiautomated transformation of natural language specifications into Manchester OWL Syntax for automated reasoning. The evaluation of our tool support shows that for representative example requirements, our approach achieves over 85 % soundness and completeness rates and detects more problems than the benchmark applications.