## 2 Related Work
A relationship between the grounding problem and cognitive semantics has not been deeply analyzed in the literature yet, as the research on the grounding problem (and on a related symbol anchoring problem [42]) mainly focused on simple languages consisting of names and labels and their applications, e.g., in robotics [3; 43; 44; 3; 5; 6]. An interesting outcome of the mentioned research is a finding that underlines a function of social learning in the collective shaping of symbols' meaning in semantic communication. As a consequence, a strategy for learning categories with a prototype proposed later in this paper ensures that cognitive semantics for languages of names and labels is a result of a socially-realized process of semiosis. Fourthly, this research needs to fulfill requirements formulated within models of conceptual spaces [45; 46; 47] which not only assume an existence, at the mental level, of a universe of internal representations of objects but further equip this universe with cognitive tools allowing the agent to meaningfully experience (and evaluate) a level of difference between said objects. These tools usually assume the practical form of a cognitive distance or a cognitive similarity function. A notion of cognitive distance has been directly applied to the mechanisms used for defining cognitive semantics which are presented further in this paper. Fifthly, as suggested by a focus in the presented research on the case of cognitive semantics for beliefs encoded in semantic communication using symbolic structures of a form \(\Sigma(x\in c)\) (assuming their commonsense interpretation), there is an important correlation between the methods and computational models presented in this paper and a wide range of research projects dedicated to the modeling and analysis of so-called modal operators of belief and knowledge. Among a variety of heterogeneous proposals, there is a group of results, mostly of theoretical nature: the original proposal of [PERSON] presented in 1962 in his influential work [48]; implementation-wise ideas about autoepistemic logic (with autoepistemic logic understood as in [49; 50; 51]); more practice-oriented approaches given as theories, architectures, and programming languages following the so-called BDI (Belief-Desire-Intention) approach to agency, founded mainly on the possible worlds semantics [52]. A range and characteristic of BDI-related approaches have been extensively reported, among others, in [53; 54; 55; 56; 57; 58]. Without further deliberation, we only want to state that the methods and models of belief representation proposed in this article, as well as in our previous works, e.g., [18; 19; 20; 26], differ from a typical BDI approach mostly for two main reasons:  
* We abstain from the goal of building a belief calculus (which typically serves as a deductive mechanism for building theorems expressed in a modal language for representing beliefs), and instead focus on the very fundamental level, that is, on a semantic mechanism for the construction of language representations which directly relies on existing mental structures of the agent (treated as a subject of knowledge), while maintaining a requirement of commonsense consistency of the final communicative behavior of the agent. * We follow a tendency of multiple natural languages and maintain three distinct levels (states) of confidence regarding an agent's beliefs. It extends other approaches which typically assume the following two states of belief confidence: a state of full confidence in regard to the consistency of beliefs with reality and a state of non-exclusive beliefs--allowing complementary beliefs to be present within the agent's mind.