Deductive reasoning and the argument is “valid”, it is possible for the conclusion to be false (determined to be false with a counterexample or other means). Aristotle started documenting deductive reasoning in the 4th century BC. Deductive reasoning Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily
Connexive logic the consequent, such as might be the result of real class inclusion relations. For example, the class relations, "All men are mortal," would provide a real connection that would warrant the conditional, "If Socrates is a man, then Socrates is mortal." However, more remote connections, for example "If she apologized to him, then he lied to me," (suggested by Bennett) still defy connexivist analysis. Connexive logic Connexive logic names one class of alternative, or non-classical, logics designed to exclude the so-called paradoxes of material implication. (Other logical theories with the same agenda include relevance logic, also known as relevant logic.)