Abstract: A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory of (ROQ(R^2), conv, ≤) , where ROQ(R^2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ≤ is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.
The first part of the thesis concerns the existence of model companions of certain unstable theories with automorphisms. Let T be a first-order theory with the strict order property. According to Kikyo and Shelah's theorem, the theory of models of T with a generic automorphism does not have a model...
This study seeks to determine how the Internal Revenue Service influences religion in the United States. Using the theoretical frameworks of organizational ecology and new institutionalism this study examines the assumption that America has an unregulated religious economy. In particular, I look at...