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Single Idea 15426

[filed under theme 5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi ]

Full Idea

Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries.

Gist of Idea

We can build one expanding sequence, instead of a chain of deductions

Source

John P. Burgess (Philosophical Logic [2009], 5.3)

Book Ref

Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.105

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The 5 ideas with the same theme [proof were every step is a proof and not just a formula]:

13759

Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock]

13760

A sequent calculus is good for comparing proof systems [Bostock]

15426

We can build one expanding sequence, instead of a chain of deductions [Burgess]

15425

The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]

13686

We can build proofs just from conclusions, rather than from plain formulae [Sider]