Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

Report of a select committee to whom were referred the petition of Samuel Thompson and John Dailey: January 14, 1817, read, and ordered to lie upon the table (1817)

Concerning the request of the petitioners, former residents of Newark (present-day Niagara-on-the-Lake) in Upper Canada, for relief for the loss of their property when they were compelled to flee Canada after having aided the United States Army in the War of 1812.

Children's Lie-Telling and Self-Awareness as an Honesty Promoting Technique

The present study investigated how social-cognitive development relates to children’s lie-telling and the effectiveness of a novel honesty promoting technique (i.e., self-awareness). Sixty-four children were asked not to peek at a toy in the experimenter’s absence and were later asked about whether they had peeked as a measure of their honesty. Half of the children were questioned in the self-awareness condition and half in the control condition. Additionally, children completed a battery of cognitive and social-cognitive tests to assess executive functioning and theory-of-mind understanding. While first-order theory-of-mind understanding, inhibitory control, and visuospatial working memory did not significantly relate to children’s lie-telling, measures of inhibitory control in conjunction with working memory and complex working memory were significantly related to children’s lie-telling. Finally, the novel honesty promoting technique was effective: children in the self-aware condition lied significantly less often than children in the control condition.