Deduction: Ifs and Ands
Weshallnowstarttoconstructaformalcalculusfortherigorousproofoflogically
validsequents.
o Beforecomingtodetails,however,wemustsaywhatingeneralistocountas
aproofinthesystem,andto
Proof 4
p (p q) p q
1 (1)
p
(p q)
2 (2) p
A
A
1,2 (3) p q
1, 2 E
1,2 (4) q
2, 3 E
1 (5) p q
4 [2] I
Thislittleproofisworthasecondlook.Whatthesequentsaysineffectisthatifpgetsyou
fromitselftoqthenp(allo
CountingassumptionsDeduction:IfsAndAnds
Theorems
AnapplicationofIallowsoneoftheassumptionstobedischarged.Nowwhathappensif
wecarryonapplyingtheruleanddischargingwhenthereisonlyoneassumptionleft?
Natura
Deduction Examples 1
Thefollowingproofsprovidemoreillustrationsoftheuseoftherules.Linearformatisused
forwritingthemout,forreasonsoftypography.
Proof 1
p (q r) (p q) r
1 (1)
p
(q r)
A
1 (2) p
1 E
1 (3)