This paper investigates the use of functions other than t-norms to model the Modus Ponens rule in a fuzzy inference process. For that purpose, new definitions for fuzzy inference related concepts are suggested, that take into account the possibility of using a larger class of functions. In particular, the concept of "Modus Ponens generating function" is revisited, allowing to find out when and where (in which subset of the defined universe) an operator is able to generate the Modus Ponens scheme. In addition, given such an operator, the conditional relations that may be used along with it to model an inference process are found. These results are applied to some common operators, finding their Modus Ponens generation capacity as well as their corresponding residuated fuzzy conditionals. Finally, the relation between an operator's ability to describe the Modus Ponens rule and its conjunctive/disjunctive behaviour is also studied, by means of a series of sufficient and/or necessary conditions relating both concepts.