Grounding and extracting modal responses in cognitive agents: 'AND' query and states of incomplete knowledge

In this study an original way of modeling language grounding and generation for a simple set of language responses is presented. It is assumed that the language is used by a cognitive agent and consists of a few modal belief and possibility formulas that are used by this agent to communicate its opinions on the current state of an object. The cognitive agent is asked a simple AND query and the language is tailored to this situation. The agent's knowledge bases are characterized by certain incompleteness of information on the current state of objects. The language of the available responses is originally grounded in the agent's previous empirical experience. According to the assumptions of the cognitive linguistics and the phenomenology of knowledge, this experience is the basic source of meaning represented by the available formulas (responses). In the study the idea of an epistemic satisfaction relation is introduced that describes states of the agent's knowledge in which particular formulas are satisfied in the epistemic sense. Additionally, a formal description of the semantic power of formulas is presented. The concepts of the empirical satisfaction relation and the semantic power of formulas are used to define a model of particular language behavior that preserves the assumption of language grounding. Two examples of possible implementations are given. These implementations are basic ones and refer to statistical characteristics of the stored empirical experience of the cognitive agent.