Editing Paraconsistent logic (section)

==Comparison with classical logic==
The entailment relations of paraconsistent logics are [[propositional calculus|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 every entailment 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 [[metalanguage]]s due to [[Alfred Tarski]] and others. 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."<ref>{{cite journal|author=Feferman, Solomon|year=1984|title=Toward Useful Type-Free Theories, I|doi=10.2307/2274093|pages=75–111|volume=49|issue=1|journal=The Journal of Symbolic Logic|jstor=2274093|s2cid=10575304 }}</ref> This expressive limitation can be overcome in paraconsistent logic.