Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Online Anonymity and the Kantian Publicity Principle: Can the Internet Solve the Paradox of Tyranny?

Immanuel Kant’s publicity maxim states that other-regarding actions are wrong if their maxim is not compatible with their being made public. This has the effect of forbidding dissent or rebellion against tyranny, since rebels cannot make their intentions and plans public. However, new internet technologies offer public speech from behind the “shield” of anonymity, allowing dissent to be public but preventing reprisals from tyrants. This thesis examines not only this possibility, but the value of internet-based discursive spaces for politics, their viability as a mode for political communication, and their implications for Classical and Enlightenment approaches to politics and intellectual virtue. Anonymous internet communications favour logos-based reasoning and discourse, which, in the liberal-democratic tradition, is preferable to phronesis and its attendant elitism and chauvinism. These technologies can open new vistas for liberal-democratic politics.

The Search for Scholarly Teaching in Elementary Education

Elementary teachers are expected to prepare students to work efficiently with others, solve complex problems and self-regulate their own learning. Considering the importance of a solid educational foundation in the early years, students would benefit if elementary teachers engaged in scholarly teaching. The purpose of this study was to investigate Boyer’s (1990) four dimensions of scholarship, application, integration, teaching and discovery, to better understand if there is scholarly teaching in elementary education. Four professional teaching documents were analyzed using a hermeneutic orientation. A deductive analysis suggests that we do have scholarly teaching in elementary education, with strong evidence that elementary teachers are scholars of application and integration. An inductive analysis of latent and manifest content suggests that underlying humanistic values run deeply through elementary education driving current curricular, instructional and pedagogical practices.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

A Mixed-Method Study of Educator Knowledge and Practice Related to Student Socio-moral Development

The purpose of this study was to explore elementary educators’ knowledge of moral development, how this knowledge relates to their beliefs and sense of efficacy pertaining to character education practices and the socio-moral reasoning of their students. It was hypothesized that educators’ beliefs and practices related to character education would reflect their pedagogy rather than knowledge of moral development theory. It was further hypothesized that there would be differences in student socio-moral reasoning specifically the beliefs and desires that guide actions would differ based on grade and gender. This mixed-method study employing self-report questionnaires, open response vignettes, and semi-structured educator interviews yielded quantitative and qualitative data. Findings indicated socio-moral reasoning of students differed according to grade (age) and gender. Knowledge of moral development theory was found to vary among participants however some practices employed by educators did align with a social cognitive approach to moral development. Significant variables identified consistently among educator and student participants included, autonomy, social competence, sense of school community, and supportiveness. These variables, in conjunction with a sense of fairness, have been identified elsewhere as foundational to moral development (Nucci, 2009), and intrinsic motivation (Ryan & Deci, 2000) and are relevant to educators working to develop student socio-moral reasoning as an aspect of character.