Paraconsistent Logics Are Propositionally Weaker Than Classical Logic
Paraconsistent logics are propositionally weaker than classical logic; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate everything that classical logic does. In some sense, then, paraconsistent logic is more conservative or cautious than classical logic. It is due to such conservativeness that paraconsistent languages can be more expressive than their classical counterparts including the hierarchy of metalanguages due to Alfred Tarski et al. According to Solomon Feferman : "…natural language abounds with directly or indirectly self-referential yet apparently harmless expressions—all of which are excluded from the Tarskian framework." This expressive limitation can be overcome in paraconsistent logic.
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