Construction the description logic based on the lattice of truth values and the logical inference procedure

The logical representation formalism is proposed, based on the description logic with the truth evaluation on the compact finite De Morgan lattice, where qualitative uncertainty statements evaluation are expressed as intervals of the lattice carrier set and can express the uncertainties of different nature. The procedure of the concept subsumption checking in terminology by the plausible automaton is constructed, where the running should not lead to an emptying. It is shown that the plausible automaton algorithm is the inference procedure, and its launch leads to the limited models construction in the form of plausible tree structures.