Symbols and Relationships

Symbols always belong to some set, namely their domain of definition in which they exist. The relationships represented by symbols are the relationships between the elements in this area of existence. Manipulation of abstract symbols ignoring their areas of existence is meaningless. Conversely, only dealing with relationships makes sense.

• The shortest definition: Intelligence is an operator of meanings.
A subject operating with meanings, forming, creating meanings, i.e. determining (for oneself, since meanings are subjective) the existence of relations between elements of various sets, environmental objects or virtual entities

• Definition: Meaning is a representation of any kind (for example, awareness or description, including formula, algorithm, program code) of a single act of relationships. A relationship is the most general term indicating the presence of some connection between two (minimally) entities. Every meaning always comes down to the formulation of such a connection. Every. Always.

• Definition: Knowledge is a certain set of meanings as a representation of any kind (for example, awareness or description, including formula, algorithm, program code) of a relationship as a whole or any subset thereof.

• Definition: Data are elements of perception stored in any form

• Data is a source of knowledge. Intelligence is a processor generating knowledge from the data.

• Intelligence does not operate with symbols. Intelligence operates with relationships (well, relationships between symbols also)

• A word is an ordered sequence of symbols, so a word also represents a relationship between symbols. The word has different meanings depending on the context, so the context also represents the relationship between words

• Basic symbolic manipulations play the same role for intelligence as bit operations for a computer processor or the interaction of neurons for the brain. This is the lowest level of interaction that is not directly related to the intelligent activity of the mind. Matter consists of molecules, but when we build a house we don’t think about it. Smart texts consist of symbols, but when intelligence processes such texts, it works with a higher level of aggregation than symbols, namely with contexts that represent relationships…

• Symbols only represent relationships. Any symbols only represent (or even hide) some meaning, but are not meaning as such.

• Obviously, any relationship between objects of any complexity can be represented by a single symbol. Actually, the symbols are intended for such aggregation. Any formula demonstrates this fact. Accordingly, any symbol can be part of a relationship represented by another symbol in the hierarchy of relationships. Thus, symbols act as data for other symbols.

• A relationship is not a concept. But a concept is always a relationship. A relationship becomes a concept when it gets a name/symbol/designation. A symbol always denotes some concept.

• Concepts are hierarchical. There are covering complex concepts (someone may call them “contexts”, but they are still concepts if such contexts are given a name) that may well overlap. The name (symbol, sign) of a complex concept is necessary in order to collect under it the entire collection of its sub-concepts and refer to it as a whole object in other contexts and concepts

• Any symbol was once invented as a sign to indicate some relationship. Therefore, any symbol is initially iconic, i.e. visually describes the relationships between real or virtual objects denoted by this symbol.

• A symbol is just a reference to a meaning or a designation of meaning. And the essence of any meaning and knowledge is in relation between some objects.

• The minimal representation is
S = {name: value},
where S is the symbol, and the object represented by it is a relation, i.e. meaning or knowledge.
Or A = B + C, where A, B, C are symbols and + is a relation between B and C.

• And even the lack of meaning is also a meaning of an approximate representation
π = {isExist: “I have no idea”} or initially π = {}
for those who do not know what the number π is.
This is about how an AGI instance can form unknown concepts that it encounters in the text being processed. Further, this object containing a collection of relationships for a concept can be supplemented with other relationships when new meanings appear.

• Relationships are primary, symbols (entities) are secondary. Symbols without relations (meanings) they represent are meaningless by definition.

• It is meaningless to manipulate symbols/concepts that are not in a relationship, having different areas of existence. Thus, attempts to operate only with secondary symbols (but not primary relations) in AI are meaningless. And we may observe this meaninglessness.

• An ordered sequence of symbols forms the text. A text is meaningful if it represents a sufficiently complete hierarchy of relationships. I.e., symbols form known words or represent known relationships between other symbols, and words form contexts to which some relations between certain concepts / symbols can be associated.

• The process of understanding the text consists in determining the relations represented by this text. Here we have such options:

• If all the relationships are known, then the text is understandable and trivial.
• If new relationships are formed during the processing/comprehension of the text, then the text is understandable, non-trivial and knowledge-creating. New knowledge is a previously unknown relationship proposed in the text as a combination of known.
• If the text does not correspond to/does not create an internal sufficiently complete hierarchy of relations, then the text is incomprehensible and does not make sense to the reader.

• The internal representation of relationships containing a hierarchy of symbols (signs, concepts, contexts) forms a collection of “patterns of meaning” that the intelligence operates with and, in fact, represents the intelligence as a whole. Patterns of meaning are used by the intelligence in the process of understanding the text.

• The successful process of understanding the text has 3 options:

• Either patterns of meaning similar to contexts in the analyzed text already exist inside the perceiving intelligence (trivial).
• or the perceiving intelligence has the ability to receive such patterns of meaning from external sources during the process of understanding (to read dictionaries or to search the Internet etc.), (non-trivial, knowledge-creating)
• or the analyzed text directly helps to create such relationships by offering previously unknown new relationships, namely knowledge as a combination of previously known signs, concepts, contexts (2x2=4, where 2 is known, 4 as the result of an arithmetic operation is possibly previously unknown), (non-trivial, creating knowledge).

In the process of understanding the text, new concepts appear and existing concepts are replenished/changed as hierarchical collections of sub-concepts / patterns of meaning. In this way the knowledge base of the intelligence is formed in real time.