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17 Cards in this Set
- Front
- Back
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A derivation (or proof) is |
a finite string ofwffs, each ofwhich is either (1) an assumption or (2) a wffthat follows from at least one ofthe wffs in the string by one of our derivation rules. |
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A derivation rule is |
a rule that serves to justify the assertion ofa given wffin a derivation. |
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Consider any finite set ofwffs, and consider any wff, ‘’, that follows from the set by a given deriva- tion rule. The derivation rule is truth-preserving iff |
there is no interpretation that makes each wffin the set true and that makes ‘’ false. |
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An argument is |
a string of sentences; one of the sentences is the conclusion and the others are the premises. |
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The conclusion of an argument is |
the sentence whose truth is to be established. |
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A premise of an argument is |
a sentence that is said, or that is thought, or that appears, to play a role in establishing the truth ofthe conclusion. |
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A sequent is |
a string ofwffs. |
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A derivation is |
a string ofwffs, each ofwhich is either an assumption or a theorem or a wffthat follows, via our derivation rules, from one or more wffs in the string. |
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A wff ‘tri’ is a syntactic consequence ofa set ofwffs iff |
there is a derivation of ‘tri’ from the set. |
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A wff ‘tri’ is a semantic consequence ofa set ofwffs iff |
there is no interpretation that makes every wffin the set true and that makes ‘tri’ false. |
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^E |
A^B = A,B |
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^I |
must have A,B |
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vI |
A, then AvB |
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->E |
premise |
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A<->B |
(A->B)^(B->A) |
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‘If either Ardbeg or Bobo surrenders, then either Coco or Dagbar will be humiliated and the evil Egvalt’s star will rise. Ardbeg will surrender and the traitor Fortescue will sneak away. If Ardbeg surrenders and the evil Egvalt’s star rises then miserable Monty’s victory will be secure. So the traitor Fortescue will sneak away and miserable Monty’s victory will be secure.’ |
(A∨B)→[(C∨D)∧E],A∧F,(A∧E)→M├F∧M |
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‘Ardbeg doesn’t fail to surrender and Bobo doesn’t fail to surrender. If Ardbeg surrenders then Coco will be humiliated. Dagbar will be humiliated if and only ifBobo surrenders and Coco is humiliated. Therefore Dagbar will be humiliated.’ |
──A∧──B,A→C,D↔(B∧C)├D |
