An Ontology-Based Approach to Metaphor Cognitive Computation

Language understanding is one of the most important characteristics for human beings. As a pervasive phenomenon in natural language, metaphor is not only an essential thinking approach, but also an ingredient in human conceptual system. Many of our ways of thinking and experiences are virtually represented metaphorically. With the development of the cognitive research on metaphor, it is urgent to formulate a computational model for metaphor understanding based on the cognitive mechanism, especially with the view to promoting natural language understanding. Many works have been done in pragmatics and cognitive linguistics, especially the discussions on metaphor understanding process in pragmatics and metaphor mapping representation in cognitive linguistics. In this paper, a theoretical framework for metaphor understanding based on the embodied mechanism of concept inquiry is proposed. Based on this framework, ontology is introduced as the knowledge representation method in metaphor understanding, and metaphor mapping is formulated as ontology mapping. In line with the conceptual blending theory, a revised conceptual blending framework is presented by adding a lexical ontology and context as the fifth mental space, and a metaphor mapping algorithm is proposed.     

因素空间的结构与对偶回旋定理

基于概念的内涵与外延的对合性与反变关系，以及概念形成过程中概括与解析的辩证统一性，深入讨论了因素空间的数学结构问题。系统梳理了由认知本体论原理构造出的因素空间的基本概念与核心命题，为基于因素空间的知识发现理论与技术的研究提供了一种新的思想框架。首次提出了格上的交错自同构变换与回旋格的概念，证明了因素空间上的对偶回旋定理，揭示出因素空间数学结构的几何表象是一个麦乌比斯环，为阐释人类思维与概念形成过程的动力学机制提供了一个新的数学模型。     

PANEL DISCUSSION

When anthropologists talk about their discipline as a holistic study of human societies, particularly non-Western societies, mathematics and mathematical modeling do not immediately come to mind, either to persons outside of anthropology or even to most anthropologists. What does mathematics have to do with the study of religious beliefs, ideologies, rituals, kinship, and the like? Or, more generally, what does mathematical modeling have to do with culture? The application of statistical methods usually makes sense to the questioner when it is explained that these methods relate to the study of human societies through examining patterns in empirical data on how people behave. What is less evident, though, is how mathematical thinking can be part of the way anthropologists reason about human societies and attempt to make sense of not just behavioral patterns but the underlying cultural framework within which these behaviors are embedded. What is not widely recognized is the way theory in cultural anthropology and mathematical theory have been brought together, thereby constructing a dynamic interplay that helps elucidate what is meant by culture, its relationship to behavior, and how the notion of culture relates to concepts and theories developed not only in anthropology but in related disciplines. The interplay is complex and its justification stems from the kind of logical inquiry that is the basis of mathematical reasoning. Linking of mathematical theory with cultural theory, we argue, is not only appropriate but may very well be necessary for more effective development of theory aimed at providing a holistic understanding of human behavior.     

概念建模研究综述

概念建模是指创建概念模型的行为,这些模型用来描述问题,与具体用于解决问题的技术和策略独立无关。在过去数十年中,大量概念建模方法和工具纷纷涌现,许多理论如本体论、语言学和认知学的引入,增强了概念建模的理论基础。基于本体的概念建模研究得到了充分的重视。本文对概念建模的发展、概念建模语言、基于本体的概念建模以及概念模型的质量评估进行系统的阐述。     

An Overview of a Formal Framework for Managing Mathematics

Mathematics is a process of creating, exploring, and connecting mathematical models. This paper presents an overview of a formal framework for managing the mathematics process as well as the mathematical knowledge produced by the process. The central idea of the framework is the notion of a biform theory which is simultaneously an axiomatic theory and an algorithmic theory. Representing a collection of mathematical models, a biform theory provides a formal context for both deduction and computation. The framework includes facilities for deriving theorems via a mixture of deduction and computation, constructing sound deduction and computation rules, and developing networks of biform theories linked by interpretations. The framework is not tied to a specific underlying logic; indeed, it is intended to be used with several background logics simultaneously. Many of the ideas and mechanisms used in the framework are inspired by the IMPS Interactive Mathematical Proof System and the Axiom computer algebra system.     

A case study in mapping conceptual designs to object‐relational schemas

The recent emergence of object‐relational technology into the commercial database market has caused new challenges for the implementation of conceptual database designs. This paper presents our experience with using the Oracle 8 object‐relational data model in the implementation of an engineering application described using the EXPRESS conceptual modeling language. EXPRESS is part of the engineering community's Standard for the Exchange of Product Data and can be characterized as a structurally object‐oriented modeling language, supporting the notion of entities, entity hierarchies, complex constraints on entity hierarchies, relationships and inverse relationships between entities, and user‐defined types. As a result, EXPRESS provides an excellent framework for studying the mapping of conceptual modeling concepts into an object‐relational model. In this paper, we describe the way in which the features of EXPRESS can be mapped into object‐relational features such as object tables, object references, and nested tables. We also describe the manner in which features such as member functions on object types, triggers, and stored procedures can be used to support the implementation of constraints associated with a conceptual schema. Although the mappings presented are specific to EXPRESS and Oracle 8, the mappings are generalizable to conceptual modeling languages and object‐relational models with similar features. Our work defines how traditional mapping concepts must be revised in order to make adequate use of the features now found in object‐relational models. As part of this paper, we also compare our mapping approach using Oracle 8 to mapping issues for the PostgreSQL object‐relational model and the Objectivity/DB object‐oriented data model. Copyright © 2000 John Wiley & Sons, Ltd.     

Developing a unified framework of the business model concept

Recent rapid advances in Information and Communication Technologies (ICTs) have highlighted the rising importance of the Business Model (BM) concept in the field of Information Systems (IS). Despite agreement on its importance to an organization's success, the concept is still fuzzy and vague, and there is little consensus regarding its compositional facets. Identifying the fundamental concepts, modeling principles, practical functions, and reach of the BM relevant to IS and other business concepts is by no means complete. This paper, following a comprehensive review of the literature, principally employs the content analysis method and utilizes a deductive reasoning approach to provide a hierarchical taxonomy of the BM concepts from which to develop a more comprehensive framework. This framework comprises four fundamental aspects. First, it identifies four primary BM dimensions along with their constituent elements forming a complete ontological structure of the concept. Second, it cohesively organizes the BM modeling principles, that is, guidelines and features. Third, it explains the reach of the concept showing its interactions and intersections with strategy, business processes, and IS so as to place the BM within the world of digital business. Finally, the framework explores three major functions of BMs within digital organizations to shed light on the practical significance of the concept. Hence, this paper links the BM facets in a novel manner offering an intact definition. In doing so, this paper provides a unified conceptual framework for the BM concept that we argue is comprehensive and appropriate to the complex nature of businesses today. This leads to fruitful implications for theory and practice and also enables us to suggest a research agenda using our conceptual framework.     

IMPS: An interactive mathematical proof system

IMPS is an interactive mathematical proof system intended as a general-purpose tool for formulating and applying mathematics in a familiar fashion. The logic of IMPS is based on a version of simple type theory with partial functions and subtypes. Mathematical specification and inference are performed relative to axiomatic theories, which can be related to one another via inclusion and theory interpretation. IMPS provides relatively large primitive inference steps to facilitate human control of the deductive process and human comprehension of the resulting proofs. An initial theory library containing over a thousand repeatable proofs covers significant portions of logic, algebra, and analysis and provides some support for modeling applications in computer science.Supported by the MITRE-Sponsored Research program.     

Analogical proportions

Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language acquisition, and story telling. This paper introduces from first principles an abstract algebraic framework of analogical proportions of the form ‘a is to b what c is to d’ in the general setting of universal algebra. This enables us to compare mathematical objects possibly across different domains in a uniform way which is crucial for AI-systems. It turns out that our notion of analogical proportions has appealing mathematical properties. As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings. This provides conceptual evidence for its applicability. In a broader sense, this paper is a first step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like common sense reasoning and computational learning and creativity.

     

Cognitive engineering of a new telephone operator workstation using COGNET

Many cognitive engineering methodologies for user-centered design involve modeling procedural knowledge; others deal with domain semantics or conceptual models. COGnitive NEwork of Tasks (COGNET) is a framework for modeling human cognition and decision-making which provides an integrated representation of the knowledge, behavioral actions, strategies and problem solving skills used in a domain or task situation, yielding a powerful cognitive engineering tool. A case study of the design of the user interface for a new telephone operator workstation is presented to illustrate the derivation of the design from the components of the COGNET model. The model does not directly convey any specific feature of the interface design, but rather a formal representation of what the user must do with the resulting interface. This information is then evolved through a set of transformations which systematically move toward design features, in a fully traceable manner.

Relevance to industry

With the increasing prevalence of technical systems in complex work domains, cognitive engineering is necessary in designing the user interface for those systems to promote efficient integration of person and machine. The cognitive engineering methodology presented here addresses that need.     

Applications of a categorical framework for conceptual data modeling

For successful information systems development, conceptual data modeling is essential. Nowadays a plethora of techniques for conceptual data modeling exist. Many of these techniques lack a formal foundation and a lot of theory, e.g. concerning updates or schema transformations, is highly data model specific. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper, focus is on the applications of such a framework defined in category theory. Well-known conceptual data modeling concepts, such as relationship types, generalization, specialization, and collection types are defined from a categorical point of view in this framework and an essential advantage is its “configurable semantics”. Features such as null values, uncertainty, and temporal behavior can be added by selecting appropriate instance categories. The addition of these features usually requires a complete redesign of the formalization in traditional set-based approaches to semantics. Applications of the framework in the context of schema transformations and improved automated modeling support are discussed. Received: 10 September 1996 / 19 February 1997     

Can interactive visualization tools engage and support pre-university students in exploring non-trivial mathematical concepts?

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational contexts. This seems to be the case with educational visualization tools. Much evidence about the effectiveness of these tools appears to be more suggestive than based on empirical evaluations. In this paper, we attempt to fill this gap and provide empirical evidence for the use of visualization tools in supporting exploratory and other learning-related activities. In particular, we aim to investigate whether visualization tools can be used to engage pre-university students in exploring non-trivial mathematical concepts. We focus particularly on this age group and content domain because of the difficulty these students may encounter when trying to investigate more challenging mathematical concepts. Also, it is during their formative years before university that students’ predisposition and likeness towards mathematical ideas are formed. We report in this paper a study assessing whether a visualization tool, whose design was informed explicitly by research from information visualization and human–computer interaction, could engage pre-university students in their exploration and learning of more advanced mathematical concepts. Students who participated in this study came from multiple grade levels and have diverse cognitive and language skills as well as preferences towards mathematics. The results of this study indicate that visualization tools can effectively engage these students and support their exploration of non-trivial mathematical concepts, only if the tool is designed such that it can cater the diverse needs of these students.     

Statics and dynamics of cognitive and qualitative matchmaking in task fulfillment

Two main ingredients related to successful task performance are cognition and quality. Supply and demand of these concepts for knowledge intensive tasks are studied in this paper to fuel successful task fulfillment. Cognitive characteristics are supplied by actors performing tasks. Organizational developments such as growing complexity and increasing customer orientation may increase cognitive load. Stakeholders of tasks have quality requirements. These requirements may be affected if actors experience an increase in cognitive load. It is observed that knowledge intensive tasks demand cognitive characteristics and supply quality factors. Actors supply cognition and stakeholders demand quality. The gap between supply and demand can be bridged by introducing several models. These models consist of a matchmaking framework, conceptual models, and dynamic models. The matchmaking framework shows how supply and demand of cognitive characteristics or quality factors can be matched. Relations and roles of the concepts involved in task fulfillment are mapped out by the conceptual models. The dynamic models show causes that have effects on the supply of cognitive characteristics and the level of quality. These insights in the relations and dependencies between cognition and quality increase our understanding of the key concepts for successful task fulfillment.     

Mixed group ranks: preference and confidence in classifier combination

Classifier combination holds the potential of improving performance by combining the results of multiple classifiers. For domains with very large numbers of classes, such as biometrics, we present an axiomatic framework of desirable mathematical properties for combination functions of rank-based classifiers. This framework represents a continuum of combination rules, including the Borda Count, Logistic Regression, and Highest Rank combination methods as extreme cases. Intuitively, this framework captures how the two complementary concepts of general preference for specific classifiers and the confidence it has in any specific result (as indicated by ranks) can be balanced while maintaining consistent rank interpretation. Mixed Group Ranks (MGR) is a new combination function that balances preference and confidence by generalizing these other functions. We demonstrate that MGR is an effective combination approach by performing multiple experiments on data sets with large numbers of classes and classifiers from the FERET face recognition study.     

非功能需求的结构化定义以及概念性追踪管理框架

针对需求工程中非功能需求概念非常模糊甚至相互矛盾、非功能需求与其他非功能需求及功能需求之间的关系繁复而难以分析和建模、非功能需求与设计阶段制品之间的追踪关系模糊而不易记录和维护等问题,分析了与非功能需求相关的概念在需求分析阶段和体系结构设计阶段的表现形式,给出了一个结构化的非功能需求定义;规范了不同类型需求之间的各种复杂关系,建立了一个跨越分析和设计阶段的概念性非功能需求追踪管理框架,规范了需求分析和体系结构设计阶段与非功能需求相关的概念和制品之间的关系。提出的结构化定义以及概念性追踪管理框架明确地刻画了非功能需求概念的外延,为简化需求模型以及进一步研制系统化、实用化的非功能需求建模及追踪管理技术奠定了理论基础。     

Decision and stress: cognition and e-accessibility in the information workplace

Cognitive abilities and disabilities are increasingly important in today’s information-based workplace, particularly in relation to the accessibility of advanced information society technologies. As this paper discusses, new technologies can create problems for human decision making, stress levels, general cognition and e-accessibility. Yet it is not easy to identify possible new e-accessibility solutions to these problems. This is where theories of cognitive aspects of e-accessibility could be useful to generate solutions to these problems of HCI in general and of accessibility in particular. The purpose of this paper is to report a new generative theory (called Simplex 2), provide validating evidence for it from two meta-analyses and demonstrate a proof of concept through the application of Simplex to the solution of HCI problems. Two qualitative meta-analyses are reported for two different samples (N ₁ = 90 and N ₂ = 100) of relevant and contemporary conference papers. Whilst a few more concepts were identified, only nine cognitive concepts emerged from both analyses, validating the predictions of Simplex, which is also used for cognitive user modeling. Given the sample sizes and the successful replication, it is clear that these nine factors feature prominently in current research and practice in universal access and inclusive design. Further support for the value of this theory is found in a consideration of the requirements of older adult users and from studies of cognitive overload and augmentation. Uses of Simplex include the evaluation of existing systems, assessment of user requirements, system development in combination with models of task, context of use and technology platform and through the concepts of cognitive augmentation and overload to identify future opportunities for new, accessible, cognitive solutions. A proof of concept of Simplex is demonstrated by the treatment of HCI accessibility problems and as a generative theory for the development of new solutions.     

Spice: a cognitive agent framework for computational crowd simulations in complex environments

Pedestrian behavior is an omnipresent topic, but the underlying cognitive processes and the various influences on movement behavior are still not fully understood. Nonetheless, computational simulations that predict crowd behavior are essential for safety, economics, and transport. Contemporary approaches of pedestrian behavior modeling focus strongly on the movement aspects and seldom address the rich body of research from cognitive science. Similarly, general purpose cognitive architectures are not suitable for agents that can move in spatial domains because they do not consider the profound findings of pedestrian dynamics research. Thus, multi-agent simulations of crowd behavior that strongly incorporate both research domains have not yet been fully realized. Here, we propose the cognitive agent framework Spice. The framework provides an approach to structure pedestrian agent models by integrating concepts of pedestrian dynamics and cognition. Further, we provide a model that implements the framework. The model solves spatial sequential choice problems in sufficient detail, including movement and cognition aspects. We apply the model in a computer simulation and validate the Spice approach by means of data from an uncontrolled field study. The Spice framework is an important starting point for further research, as we believe that fostering interdisciplinary modeling approaches will be highly beneficial to the field of pedestrian dynamics.     

Toward a well-founded theory for multi-level conceptual modeling

Multi-level conceptual modeling addresses the representation of subject domains dealing explicitly with multiple classification levels. Despite the recent advances in multi-level modeling techniques, we believe that the literature in multi-level conceptual modeling would benefit from a theory that: (1) formally characterizes the nature of classification levels and (2) precisely defines the structural relations that may occur between elements of different classification levels. This work aims to fill this gap by proposing an axiomatic theory that can be considered a reference top-level ontology for types in multi-level conceptual modeling. The theory provides the modeler with basic concepts and patterns to articulate domains that require multiple levels of classification as well as to inform the development of well-founded languages for multi-level conceptual modeling. The whole theory is founded on a basic instantiation relation and characterizes the concepts of individuals and types, with types organized in levels related by instantiation. Further, it includes intra-level structural relations that are used to define expressive multi-level models and cross-level relations that allow us to account for and incorporate the different notions of power type in the literature.     

Representation of Non-Metric Concepts of Space in Architectural Design Theories

The concept of space is one of the most important parts of architectural theory. There are many theories of space in architecture which can be examined from different point of views including mathematics and philosophy. In a mathematical sense, most of the architectural space theories deal with the three-dimensional Euclidean geometry. However, the development of the contemporary architecture has been marked with some other geometric concepts as well. New concepts of space, different from the three-dimensional Euclidean space, have had an impact on architecture since the beginning of the twentieth century. Moreover, in the past two decades growing interest toward a non-metric conception of spaces, where a notion of distance is not relevant, emerged in the theory and design of some contemporary architects. In this paper the relationship between non-metric conception of spaces and architectural design theories are analyzed and evaluated in order to show and the extent to which they are related.