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.

Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determining and can be used for radically different logics. For example, a paradigmatic case is the sequent calculus, which can be used to express the consequence relations of both intuitionistic logic and relevance logic. Thus, loosely speaking, a proof calculus is a template or design pattern, 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.

Read more about Proof Calculus: Examples of Proof Calculi

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### Famous quotes containing the words calculus and/or proof:

“I try to make a rough music, a dance of the mind, a *calculus* of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”

—Judith Johnson Sherwin (b. 1936)

“The thing with Catholicism, the same as all religions, is that it teaches what should be, which seems rather incorrect. This is “what should be.” Now, if you’re taught to live up to a “what should be” that never existed—only an occult superstition, no *proof* of this “should be”Mthen you can sit on a jury and indict easily, you can cast the first stone, you can burn Adolf Eichmann, like that!”

—Lenny Bruce (1925–1966)