Stanislaw Jaskowski published a non-adjunctive paraconsistent logic, which does not have the inference rule $\vdash A \ \& \ \vdash B\Rightarrow \ \vdash A\wedge B$. The paper first appeared in Polish: Rachunek zdań dla systemow dedukcyjnych sprzecznych, Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 5, 1948, 57-77. The last English translation is A Propositional Calculus for Inconsistent Deductive Systems, in Logic and Logical Philosophy, Vol. 7, 35-56, 1999.
Let logic T be sparked just if it for some sentence $A$ has $\vdash_T A$ as well as $\vdash_T \lnot A$.
Let CL be classical logic.
Let logic T be moderate just if $\vdash_T B \Rightarrow \ \not\vdash_{CL}\lnot B$.
Let J+ be a minimal sparking of Jaskowski's system J.
Is J+ moderate?
