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Single Idea 13758
[filed under theme 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
]
Full Idea
When looking for a proof of a sequent, the best we can do in natural deduction is to work simultaneously in both directions, forward from the premisses, and back from the conclusion, and hope they will meet in the middle.
Gist of Idea
In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle
Source
David Bostock (Intermediate Logic [1997], 6.5)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.270
Related Idea
Idea 13757
Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock]
The
14 ideas
with the same theme
[proofs built from introduction and elimination rules]:
13832
|
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool)
[Gentzen, by Hacking]
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13753
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Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part
[Bostock]
|
13755
|
Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it
[Bostock]
|
13754
|
Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E)
[Bostock]
|
13758
|
In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle
[Bostock]
|
18120
|
The Deduction Theorem is what licenses a system of natural deduction
[Bostock]
|
13823
|
In natural deduction, inferences are atomic steps involving just one logical constant
[Prawitz]
|
10602
|
A 'natural deduction system' has no axioms but many rules
[Smith,P]
|
21612
|
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
[Williamson]
|
13685
|
Natural deduction helpfully allows reasoning with assumptions
[Sider]
|
19298
|
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems
[Hale]
|
18783
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Many-valued logics lack a natural deduction system
[Mares]
|
15001
|
'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted
[Sider]
|
18800
|
Introduction rules give deduction conditions, and Elimination says what can be deduced
[Rumfitt]
|