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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]
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] |