Differentiating assumptions from extra-logical axioms in natural deduction
In this work, we provide a presentation of classical and intuitionistic logics in a natural deduction style, making a clear distinction between extra-logical axioms and assumptions. Some important theorems about these presentations were proved — cut-elimination, consistency and completeness. Moreover, it was proved that the consequence relations defined for these logics have some interesting properties: reflexivity, monotonicity and transitivity.
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