Regarding Relationships

My theory relies heavily on the comparable properties of phenomena. But relationships are not properties of a single phenomenon. That makes them stand out, that's why they are different.

The way I see them, they are the mortar for combining primitive properties into complex ones. They are the building blocks of complexity, its glue.

Do not miss this post. Without it, everything in my theory falls apart. I mean the transition from primitive properties to complex ones is important to understand better than just intuitively.

Before continuing, consider reading the post about Intelligence and Language, if you haven’t already.

Formation

Nicola Guarino and Giancarlo Guizzardi in their paper "Relationships and Events: Towards a General Theory of Reification and Truthmaking" consider two terms - a relationship that must exist in order for a relation to hold ("a relation holds in virtue of a relationship's existence"). I propose to replace relationship with formation. I want to consider a slightly different phenomenon and for that the proposed term fits better.

Guarino and Guizzardi try to separate relationships in a class of their own things, hence reification. Adding truth conditions I consider unjustified. Meaning is not about truth. Besides, truth and relationship have little to do with each other.

I propose to start this analysis with two simple facts - 1) for a relationship more than one object is required, 2) relationship does not belong and is not determined by any one of them, all of them are required. What it implies is that the sum of two components is more than those two components. Something else emerges from their combination. I propose to call their system "formation."

Within a formation, we may analyze each component separately or we can analyze their relationships. We can analyze each one's function and the function of the whole formation.

Formations can be quite different - two trees growing next to each other, a parasite growing in the host's organism, cogwheels in a wrist watch, etc. Components may participate in a formation spatially, temporally, interacting with each other or not, etc.

Formation as Context

I view context as a set of objects with their relations and interactions. It makes any formation suitable for the role of context. What it allows us to do linguistically, is to form references based on relations - "the last to leave the room," "the car nearest to the entrance," "turn to your left," etc.

Formation as Concept

One tree is different from a forest, one sheet of paper is different from a book, one letter is different from a word, which in turn different from a sentence.

As I have already mentioned, formation is more than its components. Guarino and Guizzardi express the same idea saying that "such understanding of a relationship deviates from the mainstream, since Chen defines a relationship type as a mathematical relation (i.e. a set of tuples), and a relationship as one of such tuples. So, under the mainstream approach relations (relationship types) and relationships are extensional notions." It makes it possible to form different formations with the same components. This is important. In different points in time the same two people may be strangers, a couple, or a married couple. Can we say that such formations are different based on one relationship? In general, no. It is more approapriate to talk about a set of relationships.

It makes relationships perfect candidates for differentiating features of formations.

Abstract Nature of Relationships

Having something "to the right" adds nothing to an object. But it makes a difference in a system. Some systems break when their components are missing. Some systems may continue functioning. Whether a component is mission-critical is another relationship, this time between the component and the formation.

In my theory, we may differentiate abstract concepts just as well as tangible ones. The concepts "right" and "left" are different. Funny, but "right" may be different even from another "right." With relationships, it is even more evident that everything is recognized in comparison.

Categories Require Relationships

This makes them at least partially abstract even if categories are for tangible phenomena. A face has such components as eyes, nose, mouth, etc. But given a face, we expect those components in certain areas relative to the face's center. If they are outside of those areas we do not treat that face as a regular one. Some harmful action is called a crime if performed with malicious intent or accident otherwise. What if the intent was formed long after the action? Irrelevant to the past action.

Should we treat abstract features like spatial or temporal relations differently? If our categorization is based on differentiation, we should not. The same semantic binary search treats abstract and tangible properties similarly.

Representation of Relationships

We know how to store information about phenomena - by storing a respective object ID and a category. If necessary, we may be accurate about the ranges. When we retrieve that information from different modalities, the ID allows us to stitch those multimodal categories into one object.

How do we know how to perform that stitching? Relationships should help. How do we store those? Not with a component, obviously. At this moment, I can only speculate and I propose to consider a category as a reference point (in space, time, etc.). Then we relate respective components to that point. Where do we expect components on a face? What component should go into each area? Is it critical or optional?

For spatial categories, we may use something like polar coordinates - an angle and a distance from the reference point plus the category of an expected component. Note that our brain pays attention to the current head orientation and to the location of other objects in the field of sight. Those may be related to the proposed idea.

The reference point depends on the considered relationship. It has the "location" category for space, the "time" category for temporal relationships, etc. Gathering all those reference points together may hint at what a "self" is or it may not. But I like the idea that it may.

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Please consider this post as food for thought. More analysis is required.