• Generic Matrix Manipulator System

      Killingbeck, Dylan; Department of Computer Science
      In this thesis we describe in detail a generic matrix manipulator system that performs operations on matrices in a flexible way, using a graphical user interface. A user defines allowable data entries called a coefficient set, as well as closed n-ary operations based on the coefficient set, called coefficient operators. Together the coefficient set and the coefficient operators form a basis. The defined coefficient operators can then further define operations on matrices. A basis and n-ary matrix operations can be entered into the system by various ways including predefined, Java data types, JavaScript, and various XML formats defining certain mathematical structures. This described system functions similar to the RelView system, while offering additional features. These features are designed to increase convenience and usability for a user by providing support for arbitrary coefficient set types, cross platform capability, and automatic type checking for user defined expressions.
    • Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

      Ghosh, Manas; Department of Computer Science (Brock University, 2013-11-05)
      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.