A deductive system developed by the logician Stanisław Jaśkowski (1906–1965) as a formal analysis of what may be inferred by the sum of assertions made by agents in discourse with one another. On the discursive (sometimes called discussive) picture, a set of premisses $\Gamma$ does not represent a collection of assumptions made by a single agent. Instead, the introduction of a formula $\phi$ as a premise corresponds to its being asserted by any participant in a particular discourse; inference then corresponds to the construction ‘Given that each formula in $\Gamma$ has been asserted by some participant in the discourse, $\phi$ must be endorsed by some participant as well’. Jaśkowski’s system is an early example of a paraconsistent logic in that its consequence relation does not in general accept the inference $\phi ,\neg \phi ⊢\psi$; the fact that two participants have vocally disagreed about the truth of $\phi$ does not entail that every formula $\psi$ has been asserted or endorsed by some participant in the discourse. Likewise, the logic is non-adjunctive in that $\phi ,\psi ⊬\phi \wedge \psi$; that one participant has accepted $\phi$ as true and another has accepted $\neg \phi$ as true should not entail that some participant has endorsed $\phi \wedge \neg \phi$. Discursive logic can be represented by a translation into the modal logic $\text{S}5$ (or some other modal propositional logic) in which, e.g., atomic formulae $p$ in Jaśkowski’s system are translated as $♢p$ in the modal logic, i.e., an atomic assertion in discursive logic is analogous to the assertion that this proposition is possible in $\text{S}5$.