more from this thinker | more from this text
Full Idea
In a tableau system no sequent is established until the final step of the proof, when the last branch closes, and until then we are simply exploring a hypothesis.
Gist of Idea
In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored
Source
David Bostock (Intermediate Logic [1997], 7.3)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.283
A Reaction
This compares sharply with a sequence calculus, where every single step is a conclusive proof of something. So use tableaux for exploring proofs, and then sequence calculi for writing them up?
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] |