Driving Mechanisms and Patterns

Introduction

The top structures of our knowledge network describe learned situations and experience. We can create new models of other structures spontaneously. To create or derive new situational models and scenarios, the old models and scenarios must be split into smaller models. Language provides this opportunity, breaking everything into a set of smaller structures – sentences. In a certain order, they create a larger complete network model that describes a new situation, or scenario.

A simple sentence carries an observation that is called “fact.” The observed facts have a very high degree of certainty because it is observed. There are also cause and effect links when events are coming together, and existing of one observation may lead to anticipation of the linked one. Such related observations also have a high degree of certainty because they are observed together as cause and effect.

Spatial knowledge is represented by specifying qualitative relationships of and between spatial entities. Different kinds of spatial relationships representing different aspects of space: size, distance, orientation, shape, etc.

Spatial relationships are universal, and they describe how observed distinct entities may locate in space about each other. For instance, there are eight spatial relations for regions on the planar surface that are the basis for the Region Connected Calculus (RCC-8), depicted in Figure 1. The Region Connection Calculus (RCC) by Randell, Cui, and Cohn (1992) is the best-known approach to qualitative spatial representation.

Qualitative spatial representation is intended to describe relationships between spatial entities such as regions or points of a particular space, for instance, of a two- or three-dimensional Euclidean space. Topology offers a theory of space by categorizing different kinds of spaces, so-called topological spaces, according to different properties. And topology fits well to the case which does not depend on a 2 or 3-dimensional space but can be applied to a more general notion of space, which is the case here.

The topology may include the concept of a topological space; different kinds of regions such as open/closed; different parts of regions such as the interior, the exterior and the boundary of a region, as well as neighborhoods, neighborhood systems, and different kinds of points. These concepts are very basic and can be found in this or a similar form in any book on general topology or point-set topology.

Figure 1.

Fundamental spatial relationships between planar regions that comprise RCC-8

Such relations represent not only spatial schema. But in a primary sense, they represent a particular logical schema. Regions may represent restricted areas that have certain information phenomena included, while outside of those areas such phenomena do not exist. This is pretty much the concept of Space, which was introduced earlier.

We should mention that this boundary is purely imaginary, and is not limited to a 2D or any n-dimensional spatiality. Space may include informational phenomena even in very remote areas. The spatial RCC-8 illustration is just a very vivid private case, which is very easy to understand and take as an analogy.

Such relations also serve as an illustration for some logical phenomena. For instance, the Overlay is frequently used for illustrating logics, such as for example Venn Diagrams. Logical AND and OR are usually perfectly illustrated with some Venn or Euler diagrams.

It is pretty easy to take two Symbolic or Model Spaces and to check them for the common elements or patterns. If such common elements or patterns do exist, they form AND. On the diagram, it is an intersection. The union of both Spaces makes logical OR.

However, such models are artificial. We can conclude that they can be handled on the level of their symbols. Assume that we have two spaces: A and B, both represented with their symbols a and b on the next level of the hierarchy. Assume that there is a standard part of them, which can be identified with patterns matching. It appears to be either a subset or a subsystem. Such a common element may have its own symbol C, which will stand for such a subset or a subsystem. This symbol also may denote A ∩ B.

Spaces A and B can be spatially remote but have same common part.