The paper focuses on the central aspect of any “intelligentlike” system: formal models of reasoning (plausible reasoning and plausible inference) and methods of mechanized implementation of these models in computer systems. A classification of inference types is presented and the historical development of the relevant theories is briefly reviewed. The so-called JSM method (for John Stuart Mill) of mechanized hypothesis generation is described in detail. This method is used in the “plausible inference + reliable inference” solver in logical information-computing systems.