Ratiocination defines Sherlock’s principal approach to a problem — that is deduction based on the evidence available — however Sherlock also uses variants of detection and logical thought that often place him several steps ahead of the regular, plodding police investigators.
Inductive reasoning, for example, is a technique used in mathematics and chemistry whereby a theoretical inference might be reached based purely upon the particular circumstances of an experiment or situation that itself stands outside “received” knowledge. While Sherlock takes this approach, it is also often coloured by the perception of the protagonists involved. Sherlock then finally reduces the mystery to an inevitable conclusion through a process of weighing up possible solutions alongside his perception of the protagonists characters.
However more often Sherlock uses abductive reasoning — quite literally the removal of a person or, in Sherlock’s case (memory palace), an idea, from the potential scenario of the crime, there by leaving the theoretical question “what if…?”
This sums up the concept of ratiocination in Sherlock’s absolute reduction of logic to an essential conclusion.