## 1 Introduction
### The Main Research Target and Outline of This Article  
This article introduces elements of technical implementations of the cognitive semantics and corresponding computational methods. From a broader perspective, it should be seen as an applied research work aiming at an application of models and methods of cognitive linguistics designed for modeling the meaning of symbols for semantic languages. These models are now being applied in a context of technical systems with linguistic capabilities, e.g., interactive AI systems.  
In a more detailed and specific approach, the main research target of this article is to propose and at least partially verify an original version of a model of a software agent with a competence to process autoepistemic modal statements with the above-characterized cognitive semantics and pragmatics. This goal has led to the formulation of the following set of crucial functionalities required by the cognitive agent:  
* implementation of a mental space of objects with a corresponding ability to tell the objects apart using an effective evaluation of the designed function of cognitive similarity (or distance) of objects,
* a formal model of a category specifying a prototype of the category and an \"area\" of applicability of the category,
* an internal learning process--a mechanism for an autonomous acquisition of a category model with a prototype.  
The organization of the rest of this article is as follows. The next section presents a brief review of related research works which influenced the final shape of the described research project. Due to the nature of the project, it includes chosen papers from the authors' research group on other classes of autoepistemic modal statements, as well as papers setting a broader theoretical background for the original approach to modeling the meaning of the languages of semantic communication.  
The third section is devoted to a more detailed discussion of the syntax of the considered class of modal statements and the commonsense (intuitive) meaning attributed to these statements. In other words, the section is devoted to an enumerative review of the basic syntactic elements that comprise the modal statements considered in this article, and to a discussion of the relationship of these elements with their equivalents in natural languages.  
The fourth section contains a detailed discussion of the software agent model. The software agent ultimately acts as an entity that uses the original semantics of autoepistemic modal statements proposed in this article and manages the collection of categories with a prototype available to the agent. The agent model includes, in particular, the basic empirical database used in the process of acquiring and updating models of categories with a prototype.  
The fifth section is devoted to a detailed presentation of an original strategy for learning categories with a prototype. This section considers a version of the strategy based on a universe of objects that is paired with a measure of distance as a tool for the technical realization of the agent's mental ability to compare objects. An extended computational example using an assumed distance function is provided for convenience in this section.  
The sixth and seventh sections are devoted to the presentation of original cognitive semantics and to the discussion of its properties. Suitable illustrative computational examples are included.  
The last two sections contain the summary of this article and point at some of our further research goals.