**3.1 Semantics – the physical information's twin**

It is clear that physical information does not exhaust the whole visual information that we usually expect to reveal in an image. But on the other hand, it is perfectly clear that relying on our approach the only information that could be extracted from an image is the physical information, and nothing else. What immediately follows from this is that the other part of visual information, the high-level knowledge that makes grouping of disjoint image segments meaningful, is not an integral part of image information content (as it is traditionally assumed). It cannot be seen more as a natural property of an image. And it has to be seen as a property of a human observer that watches and scrutinizes an image.

This way I came to the conclusion that the notion of visual information must be disintegrated to two composite parts – physical information and semantic information.

The first is contained in an image while the other is contained in the observer's head. The first can be extracted from an image while the second – and that is an eternal problem – cannot be studied by opening the human's head in order to verify its existence or to explore its peculiarities. But, if we are right in our guess that semantics is information, then we have some general principals, some insights, which can be drawn from physical information studies and applied to our semantics investigations.

In such a case, all previously defined aspects of the notion of information must also hold in the case of semantic information. That is, we can say – Semantics is a language-based description of the structures that are observable in a given image. While physical

Fig. 2. Semantic Information hierarchical arrangement.

information describes structures formed by agglomeration of physical data elements (e.g., image pixels), semantic information describes structures formed by interrelations among data clusters (or segments) produced by preliminary pixel arrangements.

Bearing in mind this difference between semantic and physical information, we will proceed with what must be common to all information descriptions. That is, as all other information descriptions, semantics has to be a hierarchical structure which evolves in a top-down coarse-to-fine manner. Unlike physical information, which can be based on a variety of languages (be reminded – mathematics is also a sort of a language), semantic information is commonly based on the human natural language descriptions. This is the reason why historically semantics was always strongly tied with human language.

Let Us First Agree on what the Term "Semantics"

semantic word.

(semantic) convention establishment.

Means: An Unorthodox Approach to an Age-Old Debate 11

In this regard, I hope that a hypothetical semantic information hierarchical arrangement depicted in Fig. 2 can be seen as a trustworthy representation of the inner semantic information architecture. It must also be mentioned that this architecture resembles the structure of a written document, a piece of literary artwork, a tale, a paper, a narrative. As usual, it begins with a title, which is immediately followed by an abstract. From the abstract it descends to the paragraphs of the text body, and then it descends to phrases, which, in

At this stage, the standard linguistic semantic decomposition goes down to the syntactic components of a word. And this is not accidental – what traditional linguistics calls syntax in our case (information framework) should be called physical information (attributes), or more precisely – the underlying physical information contained in a single semantic word.

What must be specially emphasized is that these attributes (united, generalized by a higher level semantic word) could be: 1) multiple representations of different word's physical information components, which belong to the same modality; and 2) representations of different word's physical information components, which belong to different modalities. That is – the word's attributes could be represented as visual information (e.g., our case), acoustical information (as in the case of a spoken language), or any other type of physical information, including letters of a certain alphabet (as in a classical linguistic case, when a written language is used as an information bearer). It can also be a mixture of different modalities, where all physical information components are pointing (leading) to the same

Now we can switch to the most important part of our discussion: From where semantics hierarchy does initially emerge? How it comes into existence? Somewhere in above I have mentioned that physical information is a description of structures formed by grouping of nearby data elements (I prefer to call them primary data structures) and semantic information is a description of structures formed by grouping of these nearby primary structures (I prefer to call them secondary data structures). While primary data structures are formed by grouping of nearby data elements tied by similarity in some physical property (e.g., pixel's color or brightness in an image), secondary data structures are formed without any grouping rules compliance. That means that secondary structures production (and their further naming/description) is a subjective arbitrary process, guided by mutual agreements and conventions among a specific group of observers which are involved in this

This is a very important point, because what follows from it is that a new member of this specific company can not gain the established semantic conventions independently and autonomously. The conventions have to be given (transferred) to his disposal in a complete form from the outside (from the other community members) and then must be incorporated into his semantic information hierarchy. That is, fused and memorized in this hierarchy.

Publications dealing with some similar and related issues of internet documents understanding refer to this process as "a priory knowledge" acquisition and sharing. What is meant by "knowledge" is usually undefined and not considered. I think that my

turn, are further decomposed into single separate words that build up a phrase.

**3.2 Semantics – physical information's interpretation** 

That is shown in Fig. 2 as the lowest level of semantics hierarchy.

10 Semantics – Advances in Theories and Mathematical Models

Fig. 2. Semantic Information hierarchical arrangement.

information describes structures formed by agglomeration of physical data elements (e.g., image pixels), semantic information describes structures formed by interrelations among

Bearing in mind this difference between semantic and physical information, we will proceed with what must be common to all information descriptions. That is, as all other information descriptions, semantics has to be a hierarchical structure which evolves in a top-down coarse-to-fine manner. Unlike physical information, which can be based on a variety of languages (be reminded – mathematics is also a sort of a language), semantic information is commonly based on the human natural language descriptions. This is the reason why

data clusters (or segments) produced by preliminary pixel arrangements.

historically semantics was always strongly tied with human language.

In this regard, I hope that a hypothetical semantic information hierarchical arrangement depicted in Fig. 2 can be seen as a trustworthy representation of the inner semantic information architecture. It must also be mentioned that this architecture resembles the structure of a written document, a piece of literary artwork, a tale, a paper, a narrative. As usual, it begins with a title, which is immediately followed by an abstract. From the abstract it descends to the paragraphs of the text body, and then it descends to phrases, which, in turn, are further decomposed into single separate words that build up a phrase.
