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Full Idea
An open branch in a completed tableau will always yield an interpretation that verifies every formula on the branch.
Gist of Idea
A completed open branch gives an interpretation which verifies those formulae
Source
David Bostock (Intermediate Logic [1997], 4.7)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.177
A Reaction
In other words the open branch shows a model which seems to work (on the available information). Similarly a closed branch gives a model which won't work - a counterexample.
Related Idea
Idea 7790 If an argument is invalid, a truth tree will indicate a counter-example [Girle]
| 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] |