Base-constructive analogy

     There are times when an analogy-like process is needed, but no base exists with which to draw the analogy. Consider the following story:

 

There was once a large area of the City which was a desolate wasteland of condemned buildings, known simply as the Neighborhood. The New Boys, a street gang, currently control the Neighborhood and have their headquarters in the exact center of the wasteland. Lately, a new gang calling itself the Elected Ones has shown an interest in acquiring control of the Neighborhood. Fearing the loss of control, the New Boys decide that they need to bring in an outside gang to aid their cause. The New Boys learn that the blood enemies of the Elected Ones are a group of men known simply as the Pros. The Elected Ones and Pros so fear each other that as long as one Pro is in the New Boys' territory for each Elected One there will be no violence. So, the New Boys bring in the exact number of Pros as there are Elected Ones. Frustrated in their takeover attempts, the Elected Ones are forced to stay outside the Neighborhood and only circle it. After a while, all three gangs decide to change their names to include ``-tron'' in their names. So, the Elected Ones become the Elec-trons, the Pros become the Pro-tons, and the New Boys become the New-trons. The Elec-trons continually circle a vast area of open space. At the center is a group of Pro-tons and New-trons. Notice that there is always the same number of Pro-tons as there are Elec-trons. ([#!creat:wkrp!#])

It is quite possible to describe atomic structure by appealing to ideas from the domain of gang warfare. And, yet, this is not the exact technique as when the solar system analogue was used. The solar system model is a pre-existing concept which acts immediately as a base, once retrieved; there is no pre-existing model of the Pros, New Boys, and Elected Ones which can act as an atomic base. Instead, the reasoner constructs the necessary base dynamically, driven by the constraints of the problem and by existing domain knowledge         (e.g., [#!creat:clement1!#,#!creat:moorman1!#,#!creat:nersessian1!#]).

  

Figure 26: Base-constructive analogy algorithm

An overview of the base-constructive analogy algorithm can be seen in Figure 26. Notice that the actual creation of the new base is handled by something I am calling FMS. This is short for   function-driven morphological synthesis. The basic outline of this mechanism can be seen in Figure 27.

 

  

Figure 27: Function-driven Morphological Synthesis

  It is assumed that the reasoner has encountered a concept that needs to be understood. The reasoner applies a set of manipulator functions to the concept, altering its attributes and producing new concepts. These manipulator functions include altering the value for a particular attribute, changing the restrictions which exist for the allowable values of an attribute, eliminating an attribute, adding a new attribute, and changing     primary attributes to secondary ones (and vice versa). The concepts which possess the original functionality and are novel to the reasoner are considered as creative ones.   The FMS technique was inspired by Allen's morphological synthesis (cited in [#!creat:finke!#]), in which a reasoner manipulates combinations of primary attributes to produce potentially creative results. Since only primary attributes were modified, Allen's technique was somewhat limited in what sorts of concepts could be constructed. By removing this restriction, a wider range of possible concepts are permitted. As Section 6.3 will discuss, however, this means that additional control must be in place to limit potentially   bizarre results.

    FMS can exist in two forms. Strong-FMS performs the needed manipulations by examining other concepts with the same functionality. In this form, several concepts are considered and ``mixed-and-matched'' until a proper concept is form. It might happen, though, that a single concept is all that exists when the need to create a new one arises. If this situation occurs, then weak-FMS is utilized. This mechanism uses general background knowledge to perform the needed manipulations.

  Consider the Lycanthrope story once more. If the reader already possesses the concepts of car and lycanthropy, then the novel concept of were-car can be understood through base-constructive analogy, by   utilizing strong-FMS. One possible sequence of tasks is the following:

1.

The concept which needs to be understood is were-car.

2.

Consider known concepts which fulfill the same functional role as the novel concept seems to be filling in the story. This set includes concepts such as were-wolf, were-tiger, and were-hyena.

3.

None of these succeed in an analogical mapping attempt; there is a functional restriction that what form is assumed is an animal form; this information is part of the original lycanthrope concept which is possessed by the reasoner. car fails to meet this functional requirement.

4.

The reasoner may elect to modify the concept of were-creature or the concept of car.

(a)

Modifying were-creature requires relaxing the functional constraint.

(b)

Modifying car requires transitioning the concept from the physical-object category into the physical-agent one.

5.

Of these two possibilities, the first is preferred as it makes less changes to the existing knowledge system (this will be described in more depth in Section 6.3).

6.

The reasoner therefore creates a new concept of were-creature which subsumes the previous one.

7.

This allows the reasoner to understand the novel concept of were-car.

    Another story, Experiment ([#!story:experiment!#]),   demonstrates the need for weak-FMS. In this story, a professor has invented a time machine. Without the time travel concept, a reader must dynamically create the concepts needed in order to comprehend the story. Unlike the Lycanthrope example, however, there is not a set of concepts which can be merged to develop the necessary concept. Rather, a reasoner must start with a particular single concept, that of physical-travel, and the knowledge which they possess about the temporal column of the   ontology grid. Properly manipulating the information will result in the concept of temporal-travel being created. One possible reasoning path is:

• Start with the concept being understood, temporal-travel.
• Find concepts which are related functionally to this one; in this case, physical-travel is a good candidate.
• Analogical mapping fails since there is no way to relate the physical locations to temporal-travel.
• The understanding process now begins to modify the concept of physical-travel, attempting to bring it to a point where it can be used to understand the time traveling in the story.
  • The purpose of physical-travel is to allow a physical agent to transport a physical object from one physical location to another one, which is different from the starting location. The purpose of the time travel depicted in the story is for a physical agent to transport a physical object from one temporal location to another.
  • To alter physical-travel, then, requires that the restrictions on starting and ending locations be modified from physical locations to temporal locations.
  • A new problem is now introduced if the reasoner does not possess the concept of temporal-location. If this is the case, then creative understanding is used to develop an understanding of temporal-location before continuing.
• With the modifications in place, the reasoner has transitioned the original concept from the physical action category into the temporal action category. However, while this is a relatively ``large'' modification, it still represents the minimal one, with respect to movement through the ontological grid, which can be made in order to understand the time-travel story.

These two examples demonstrate the power of base-constructive analogy. It could be argued that a more ``powerful'' implementation of the analogical mapping task could handle much of the same functionality of this task. This, however, is another case of blurring the distinction between the theory and the implementation. In my theory of creative understanding, I maintain that a task is necessary which takes two concepts and shows how they are functionally related. If attributes in the concepts are not   functionally equivalent, then the mapping task fails. This leads to the need for a task which can take multiple existing concepts and create ``on-the-fly'' a new concept which will fulfill the functional role that is required. My implementation models these two theoretical tasks as two separate computer tasks; another implementation of analogy may perform both of these tasks within the analogy process. It is important, though, to realize that the functionality of both is needed for creative understanding to succeed.