these two criteria are mentioned in patrick suppes book- intro to logic.
then to account for criterion 1 , some rules of restrictions on quantifiers are given.
But about criterion 2, how do we know these rules are enough ?
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Arjun
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The 2nd Criterion is satisfied with the Completeness Theorem. – Mauro ALLEGRANZA May 26 '15 at 08:04
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See Suppes, page 23 : "Criterion I says that the rules of inference must be sound". – Mauro ALLEGRANZA May 26 '15 at 19:29
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See Suppes, page 24 : "Criterion II says that the rules of inference must be complete". – Mauro ALLEGRANZA May 26 '15 at 19:30
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i have not yet read about Completeness Theorem, but will this prove all conclusions can be derived? – Arjun May 27 '15 at 03:34
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2Yes; for proof systems that are complete, i.e. for which a Completeness Th does hold, this means that all conclusions that follow logically from the premises are derivable (with the rules of the proof system) from the premises. – Mauro ALLEGRANZA May 27 '15 at 08:32