## 4 Model of the Agent
### Repository of Episodes
The tuple is related by the agent to a particular time point \(t\) and its elements are interpreted as follows:_  
* \(X_{t}\) _denotes a finite set of individual representations of objects recognized in the state of environment,_
* \(A\) _denotes a set of attributes assigned to objects (according to the adopted definition of the basic mental space),_
* \(V=\bigcup_{a\in A}V_{a}\)_, where_ \(V_{a}\) _denotes a domain of a particular attribute_ \(a\)_,_
* \(L_{t}\) _denotes a finite set of adopted labels,_
* \(\mathit{percept}_{t}\) _denotes a total function_ \(X_{t}\times A\longrightarrow V\)_, such that for all_ \(x\in X_{t}\) _and_ \(a\in A\) _percept_\({}_{t}(x,a)\in V_{a}\) _and represents a value of attribute a observed by the agent for object_ \(x\)_,_
* \(\mathit{label}_{t}\) _denotes a (not-necessarily total) function_ \(X_{t}\longrightarrow\Pi(L)\)_, such that for all_ \(x\in X_{t}\) _label_\({}_{t}(x)\subseteq L\) _contains all the labels recognized by the agent as being assigned to object_ \(x\) _in the observed state of the external world._  
From the formal point of view, the concept of an episode just introduced can be treated as an extension of the classic definition of a single-valued and complete information system [61; 62]. The part of an episode which is equivalent to a complete information system is used by the agent to represent the result of a particular observation of a certain state of the external world. The extension is used as a collection of other agents' beliefs about the membership of objects cognitively distinguished in the observed state of the external world to specific conceptual categories. Recognition of other agents' beliefs is based on observed occurrences of the labels introduced above _is-c_ or _not-c_. It is important to note that individual episodes are constructed by the agent in working memory and then are used to update the main repository of episodes (see Figure 2). In order to distinguish individual states of the overall empirical knowledge base at particular time points (given by all collected episodes), the following symbol is additionally introduced:  
**Definition 6**. : _At each time point \(t\in T\), the state of empirical knowledge about the external world is defined by a temporal collection of episodes given as follows:_  
\[\mathit{Episodes}(t)=\{\mathit{Episode}(t_{n}):t_{n}\in T\quad\text{and} \quad t_{n}\leq^{TM}t\}. \tag{8}\]  
The following example illustrates the way in which the above concepts are used to represent basic knowledge about the external world, stored internally in the agent. It is based on a deliberately simplified knowledge base, defined under the influence of the work [12] where the main considered objects were _birds_ described by a mutual set of attributes (including attributes: _having peak or bill, having wings, dominant color_, further in the example denoted by \(a_{1}\), \(a_{2}\) and \(a_{3}\), respectively. **Example 1**. : _The Table 3 shows the internal knowledge base built by an agent up to the time point \(t_{2}\). It is represented by the collection \(\mathit{Episodes}(t_{2})=\{\mathit{Episode}(t_{1}),\mathit{Episode}(t_{2})\}\)._  
_In the first recognized state of the external world, the agent could recognize three objects, so therefore the following three-element set of objects \(X_{t_{1}}=\{x_{1,t},x_{1,2},x_{1,3}\}\) was created as a component of \(\mathit{Episode}(t_{1})\). Meanwhile, in the second state of the world, only the following two-element set \(X_{t_{2}}=\{x_{2,1},x_{2,2}\}\) was created as a component of \(\mathit{Episode}(t_{2})\)._The minimum basic mental space \(O\) that would allow for the agent to distinguish the objects listed above and described in Table 3 would have to be defined over the set of attributes given as follows: \(A=\{a_{1},a_{2},a_{3}\},V_{a_{1}}=\{yes,no\},V_{a_{2}}=\{yes,no\},V_{a_{3}}=\{ black,white\}\). As a consequence, the related cognitive competence of the agent in recognizing objects at all would be constrained to the eight-element set \(O=V_{a_{1}}\times V_{a_{2}}\times V_{a_{3}}\).