What are proof calculus?

Proof Calculus

In mathematical logic, a proof calculus corresponds to a family of formal systems that use a common style of formal inference for its inference rules. The specific inference rules of a member of such a family characterize the theory of a logic.

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Some articles on proof calculus:

Proof Calculus - Examples of Proof Calculi
... The most widely known proof calculi are those classical calculi that are still in widespread use The class of Hilbert systems, of which the most famous example is the 1928 Hilbert-Ackermann system of ... Many other proof calculi were, or might have been, seminal, but are not widely used today ... Aristotle's syllogistic calculus, presented in the Organon, readily admits formalisation ...

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