Mara Alagic

Order-sorted model theory for temporal executable specifications

Abstract An order-sorted, temporal programming paradigm is presented. It consists of a typed, modular, declarative language, its associated order-sorted temporal Horn clause logic basis, and a model theory generalizing order-sorted algebras with predicates to temporal order-sorted structures. The essence of this generalization is in time-dependent interpretation of predicates, so that a temporal order-sorted model amounts to a sequence of order-sorted equational models with predicates, one per each state. The main advantage of the presented paradigm in comparison with paradigms based on Horn-clause logic with equality is that it is more expressive, particularly so in representing properly state transitions, and other event-oriented, temporal behavioral properties of objects. At the same time, the generalized paradigm is proved to have the initial model semantics. The rules for temporal order-sorted deduction are established as an appropriate generalization of the rules for order-sorted Horn-clause logic with equality. The initial model is a quotient temporal order-sorted structure constructed from the initial temporal order-sorted structure and a congruence relation derived from a given set of temporal constraints. Temporal order-sorted model theoretic properties are also naturally established for temporal queries. The temporal constraint language has an execution model, and it is intended to be a basis for a prototyping tool for complex, typed, modular software systems.

Collaborative Mathematics Learning in Online Environments

In formal education, learning mathematics is typically done by receiving direct instruction within the confines of a classroom. From first grade through graduate school, students are expected to learn mathematics primarily by being taught by instructors with previous knowledge of the subject. Research mathematicians, on the other hand, must rely on other methods; the mathematics they are trying to understand may not, as yet, be known to anyone else. Hence, they learn primarily through experimentation, self-directed study, and collaboration with peers. In recent years, these methods have been expanded to use modern tools and ideas. Research mathematicians initiated several successful large-scale online collaboration projects, such as the Polymath project and the MathOverflow website. In this chapter, we discuss these two projects, along with various other examples of online collaborative learning of mathematics. Our primary motivation is captured in the following question: why aren’t we all learning math this way? While a complete answer is beyond the scope of this work, we hope to at least stimulate a debate among a wide audience. The major part of our discussion is thus informal; we defer the contextualization of these examples within modern education research until the end of the chapter.

Third Place Learning Environments: Perspective Sharing and Perspective Taking

In this paper we deliberate on intercultural and global communication strategies of perspective sharing and perspective taking, and potential perspective transformation. Consideration to these strategies is given within the two instances of third place learning environments: (a) Role-play simulation environment in which learners develop experiment with strategies for resolving intercultural misconceptions, and (b) a professional virtual learning network that may provide just-in-time support for its members encountering disorienting dilemma. The central purpose of the second environment is actually development of knowledge basis for understanding of Third Place Learning.

Innovations in mathematics education via the arts BIRS Workshop 07w5062 22–26 January 2007 Banff, Alberta, Canada

‘There are no excuses.’ Jim Oliver, Banff Centre Service Director

Corporate Social Responsibility: ThirdPlaceLearning for Absorbing Diverse Perspectives

In this chapter, we consider the stakeholder approach to proactive corporate social responsibility (CSR), which hinges on company executives and managers absorbing diverse stakeholder perspectives and vice versa, so that communication and decision-making can be meaningful. The ThirdPlaceLearning (TPL) framework, with associated relational criteria, facilitates systematically learning and absorbing the diversity of stakeholder perspectives. Application of TPL in this way represents a paradigm shift toward absorbing stakeholder and contextual complexity. This paradigm shift underpins complexification of business structures and processes, skillful management of diversity, and improvement of financial performance, as well as ensuring social and environmental sustainability. Together, these attributes can help businesses nurture proactive CSR, which in turn can help successfully avoid or respond to crises.

Cage Painting within the fifth discipline of learning organisations

Learning organisations face new challenges in the 21st century. Increased flow of trade in commodities, manufactured goods and information as well as mobility of people have led to increased global interdependence, interconnectedness and cultural diversity. People and teams within learning organisations have become globally distributed with the aid of improved communication technologies. As a result, more sophisticated approaches to developing a global mindset, understanding multiple perspectives and improving intercultural communication are needed for successful collaboration between teams and team members. A tool that has proved beneficial in educational learning environments – the Cage Painting Simulator (CPS) – can be used to improve: intercultural communication, perspective taking and development of a global mindset. In this article, we integrate the CPS-framework for intercultural communication competence and global mindset development into the Senges theoretical framework for learning organisations, focusing on the context of globally distributed teams and team members.