The paper is devoted to the application of model-theoretical methods for extraction of knowledge from medical texts and documents and its formal representation. The aim of the work is to automate the filling of knowledge bases of the IACPaaS platform using knowledge from texts of disease descriptions. IACPaaS is a cloud platform for the development, management and remote use of intelligent cloud services. The peculiarities of disease description texts are the presence of medical word terms (such as 'blood pressure') and the abundance of sentences with clauses and homogeneous sentence members. To solve the problem of knowledge extraction, methods of transforming natural language sentences into quantifier-free formulas of the first-order predicate logic are used. Knowledge extracted from texts is formalized in the form of sets of atomic sentences that form fragments of atomic diagrams of algebraic systems. Further, a knowledge tree is built from the fragments of atomic diagrams, which serves as an intermediate representation of knowledge for subsequent translation into the format of IACPaaS information resources. The software system allows medical workers to fill knowledge bases with descriptions of diseases in shorter time, and gives the opportunity to check the consistency of the obtained formal specifications automatically.