We present theoretical rudiments of Petri nets over ontological graphs as well as the designed and implemented Python toolkit for dealing with such nets. In Petri nets over ontological graphs, the domain knowledge is enclosed in a form of ontologies. In this way, some valuable knowledge (especially in terms of semantic relations) can be added to model reasoning and control processes by means of Petri nets. In the implemented approach, ontological graphs are obtained from ontologies built in accordance with the OWL 2 Web Ontology Language. The implemented tool enables the users to define the structure and dynamics of Petri nets over ontological graphs.

Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.

Imagination is the critical point in developing of realistic artificial intelligence (AI) systems. One way to approach imagination would be simulation of its properties a nd operations. We developed two models "Brain Network Hierarchy of Languages", "Semantical Holographic Calculus" and simulation system ScriptWriter that e mulate the process of imagination through an automatic ani mation of English texts.