1
Q
SD
A
A system for testing entailments in SL
2
Q
Natural deduction
A
breaks down premise into simple steps
3
Q
Derivable (P is derivable from \gamma, \gamma |- P)
A
If a derivation occurs where:
- All primary assumptions are members of \gamma
- P occurs within the scope of only the primary assumptions
4
Q
SD is sound
A
If \gamma |- P (derivable in SD), \gamma |= P (TF entails P)
5
Q
SD is complete
A
if \gamma |= P (TF entails), \gamma |- P (derivable in SD)
6
Q
Theorem
A
A sentence that can be constructed from the empty set
7
Q
Equivalence in SD
A
{P} |- Q and {Q} |- P (P === Q)
8
Q
Inconsistency in SD (\gamma is inconsistent)
A
\gamma |- P and \gamma |- ~P or…
\gamma entails every sentence
9
Q
principle of explosion
A
From a contradiction you can entail every sentence
Phil 220
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