 Deductive arguments are the objects of study of familiar logical systems such as (classical) propositional and predicate logic, as well as of subclassical systems such as intuitionistic and relevant logics (although in relevant logic the property of monotonicity does not hold, as it may lead to violations of criteria of relevance between premises and conclusion—see entry on  relevance logic).  In each of these systems, the relation of logical consequence in question satisfies the property of necessary truth-preservation (see entry on  logical consequence).  This is not surprising, as these systems were originally designed to capture arguments of a very specific kind, namely mathematical arguments (proofs), in the pioneering work of Frege, Russell, Hilbert, Gentzen, and others. Following a paradigm established in ancient Greek mathematics and famously captured in Euclid’s Elements, argumentative steps in mathematical proofs (in this tradition at least) must have the property of necessary truth preservation (Netz 1999). This paradigm remained influential for millennia, and still codifies what can be described as the “classical” conception of mathematical proof (Dutilh Novaes 2020a), even if practices of proof are ultimately also quite diverse. (In fact, there is much more to argumentation in mathematics than just deductive argumentation [Aberdein &amp; Dove 2013].)