On a mathematical model for indicative conditionals

This address deals with the concept of μ-T-conditional in indicative mode, which is inscribed in what perhaps can be called theoretical fuzzy logic, summarizes a part of the previous work the author did alone or with some colleagues and concerns something controversial from the very beginning in the history of logic, namely the concept of conditional relation. Firstly, the concepts of implication and conditional in Boolean classical logic are briefly reconsidered. Secondly, the evolution from implication functions to T-conditional generating functions is reviewed, μ-T-conditionals are characterized and particularized to the crisp case and both logical T-states and the obtention of fuzzy consequences from fuzzy premises are considered. Thirdly, after a definition, we particularize to the crisp case and when possible characterize two types of monotonic fuzzy relations, it is shown that the obtained results allow us to write as many non-monotonic fuzzy or crisp conditional relations as we like