115:, characterized by a certain style of formal inference, that may be specialized to produce specific formal systems, namely by specifying the actual inference rules for such a system. There is no consensus among logicians on how best to define the term.
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Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics. For example, a paradigmatic case is the
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in a proof system is a set of axioms and rules of inference of proof system that infers that the well-formed formula is a theorem of proof system.
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Several systems have been proposed that replace the usual textual syntax with some graphical syntax.
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The most widely known proof calculi are those classical calculi that are still in widespread use:
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Many other proof calculi were, or might have been, seminal, but are not widely used today.
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Modern research in logic teems with rival proof calculi:
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282:Proof nets
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164:Gentzen's
47:: The set
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271:See also
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36:Overview
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