Minsky’s cube

In work “A Framework for Representing Knowledge” by Marvin Minsky considered a simple example of frame [1] (for example, view on http://web.media.mit.edu/~minsky/papers/Frames/frames.html). This is frame of cube; see section “1.4 Tracking the image of a cube”. We shall consider this model in UML2 SP notation.

Example by M.Minsky

The A, B, C, and D symbols represent decorations on four facets of the cube. Can be moved view point into right or revolve of cube into left.

Figure 1. The perspective appearances of a cube (picture from web.media.mit.edu)

If make excursion around the cube then the “A” facet is disappears and “C” facet is appears. A human remember the “A” facet. This sequence of elements of memory is an image of cube. A knowledge about cube is frames and a transition betwin frames, i.e. frame-system to represent of knowledge.
We will few change situation. Let observer fix one visible facet of cube but not two facets. Let’s call this facet as the face of the cube.

Formal description of ‘Cube’ notion

In UML2 SP a definition diagram is intended to accurate define of concepts. A definition diagram is a three-layer diagram and include M0 (objects layer), M1 (classes layer), and M2 (metamodel layer). This diagram is depicted in Fig.2.

Figure 2. Formal describtion of the cube

For definition of a concept used (a) relations between concepts and (b) slots.
Relations are “is a” (instance), “has” (composition) and inheritance. All other relations are “dependencies”. The same element can be both instance and class. The list object is instance of List class and the List class is instance of “Ontology System” UML-element.
A slot is determine whenever definition its a type (also named facet). A type is a set of values for the slot. A type definition is an enumeration, a class (as mathematical set) or constraint. A class of type also can be a frame to other notion.

We will show accurate definition of the Minsky cube concept.

The “List” frame define “Minsky’s cube” concept. The frame is instance “Ontology System” UML-element (daughter “SPFrame” element, i.e. frame). The frame has example. It is list object or the cube in Fig.1 Three state (currentItem=item1,item2,item3) of object are three structure to bottom in Fig.1.
The frame has “currentItem” slot. It is slot define “face” concept. Face of cube is a visible facet of cube. The slot has a type and the ItemOfList class defines its the type; next() and previous() operations define change rule of the slot value. The operations call from Run operation.
A type is a set of values and authorized operations. The ItemOfList class is a set of objects. These objects depicted in Fig.2 in M0 layer. The ItemOfList class is a frame, it is instance “Ontology Atom” UML-element as depicted in Fig.2 in M2 layer. The frame define “Facet” concept. The “Facet” notion includes “Decoration” and “Binding” concepts. The “value”, “left”, and “right” slots define these concepts. The ItemOfList class has double definition both slot and frame and this definitions do not contradict each other.

A definition diagram use when concept best defined through relation of concepts. Ordinarily, if need to display an instances of class.

The simulation model in C++ code:

ClassesOfMinskyProject.h, ClassesOfMinskyProject.cpp

References

Minsky, Marvin. A framework for representing knowledge. MIT AI Laboratory Memo 306, June, 1974.