  The four themata can be used repeatedly and in any combination in a reduction. Thus propositional arguments of indeterminate length and complexity can be reduced. Stoic syllogistic has been formalized, and it has been shown that the Stoic deductive system shows strong similarities with relevance logical systems like those by Storrs McCall. Like Aristotle, the Stoics aimed at proving non-evident formally valid arguments by reducing them by means of accepted inference rules to evidently valid arguments. Thus, although their logic is a propositional logic, they did not intend to provide a system that allows for the deduction of all propositional-logical truths, but rather a system of valid propositional-logical arguments with at least two premises and a conclusion. Nonetheless, we have evidence that the Stoics expressly recognized many simple logical truths. For example, they accepted the following logical principles: the principle of double negation, stating that a double negation (‘not: not: p’) is equivalent to the assertible that is doubly negated (i.e. p) (D. L. 7.69); the principle that any conditional formed by using the same assertible as antecedent and as consequent (‘if p, p’) is true (S. E. M 8.281, 466); the principle that any two-place disjunctions formed by using contradictory disjuncts (‘either p or not: p’) is true (S. E. M 8.282, 467); and the principle of contraposition, that if ‘if p, q’ then ‘if not: q, not: p’ (D. L. 7.194, Philodemus Sign., PHerc. 1065, XI.26–XII.14).