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Single Idea 13756

[filed under theme 5. Theory of Logic / H. Proof Systems / 5. Tableau Proof ]

Full Idea

When the only rule of inference is Modus Ponens, the branches of a tree proof soon spread too wide for comfort.

Gist of Idea

A tree proof becomes too broad if its only rule is Modus Ponens

Source

David Bostock (Intermediate Logic [1997], 6.4)

Book Ref

Bostock,David: 'Intermediate Logic' [OUP 1997], p.263

Related Idea

Idea 9394 MPP: Given A and A→B, we may derive B [Lemmon]

The 8 ideas with the same theme [proof by eliminating branches on inference trees]:

13611 Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock]
13612 Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock]
13613 A completed open branch gives an interpretation which verifies those formulae [Bostock]
13756 A tree proof becomes too broad if its only rule is Modus Ponens [Bostock]
13757 Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock]
13762 Tableau rules are all elimination rules, gradually shortening formulae [Bostock]
13761 In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock]
7790 If an argument is invalid, a truth tree will indicate a counter-example [Girle]