A Note on Nonemptiness of Cognitive Semantics for Linguistic Representations of Modal Equivalence

In this paper we deal with an original model of technically oriented cognitive semantics of modal equivalences, stated in semi-controlled natural languages and used as surface linguistic representations of internal knowledge states of artificial autonomous systems. The cognitive semantics is defined to support generation of natural language statements extended with auto-epistemic operators of modality, representing subjectively experienced certainty, strong belief and week belief of the autonomous system that the relationship between occurrence of two chosen properties in a real object is the logical equivalence relation. An internal architecture of the autonomous system is briefly presented with particular emphasis on computational modules responsible for verification of compliance of current knowledge processing states with states described by the cognitive semantics as proper for application of a particular case of modal equivalence. The major issue discussed in the paper concerns an original theory of grounding of modal equivalences in empirical knowledge resources, encapsulated in the autonomous system. The whole theory consists of theorems describing basic and advanced properties of the cognitive semantics. In the paper, the attention is limited to presentation and proof of four theorems about nonemptiness of the proposed cognitive semantics. The research results cover the next stage of some research and development efforts, concerning the technical implementation of cognitive computing models, describing the artificial generation of semi-natural languages by the interactive autonomous system to describe their encapsulated knowledge resources.