Triviality
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Triviality is a property of formal systems in logic. A system is trivial if its set of axioms
entails every well-formed formula according to the inference rules of the system, i.e.,
![\forall \phi.\left[X\vdash \phi\right]](/w/images/math/a/7/7/a778cc8f9ca1427c797e0a7d9071de45.png)
An example of triviality is a classical propositional system containing contradictory sentences for axioms; in such a system the principle of explosion can be used to infer any possible proposition or sentence.
On the other hand, a system of paraconsistent logic can be non-trivial even if it contains contradictory axioms, since its inference rules do not include the principle of explosion.