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Intro to Logic notes18

# Intro to Logic notes18 - 18 Wednesday 10:21 AM Derivation...

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Unformatted text preview: 18 Wednesday, August 08, 2007 10:21 AM Derivation rules for PL These follow the same rules as for SL. 1 2 3 1 2 3 SHOW: Fa Ga CD Fa As SHOW: Ga SHOW:~ x Fx&Gx ID x Fx&Gx As SHOW:X We need to introduce rules for dealing with quantifiers. 1 2 3 1 2 3 UD O ~ O I O ~ O O vF v x Rax Sx any and all This says that we can replace any free term with any constant we like. Example 1: 1 2 3 4 5 x Fx Hx Pr Fc Pr SHOW:Hc DD Fc Hc 1, O Hc 2,4, O Example 2: 1 2 3 4 5 6 7 x Sx Px Pr x Sx&Px Dx Pr Sm Pr SHOW:Dm DD Sm Pm 1, O Pm 3,5, O Sm&Pm Dm 2, O Intro to Logic Page 1 8 9 Sm&Pm 3,6,&I Dm 7,8, O I Example 1: 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 x Fx Hx Pr Fa Pr SHOW: xHx DD Fa Ha 1, O Ha 2,4, O xHx 5, 1 x Gx Hx Pr Gb Pr SHOW: x Gx&Hx DD Gb Hb 1, O Hb 2,4, O Gb&Hb 2,5,&I x Gx&Hx 6, I x~Rxa ~ xRax Pr ~Raa Pr SHOW: ~Rab ID Rab As SHOW:X DD x~Rxa 2, I ~ xRax 1,6, O xRax 4, I X 1 2 3 4 5 6 7 x yRxy yRxy Pr Raa Pr SHOW:Rab DD yRay yRay 1, O yRay 2, I yRay 4,5, O Rab 6, O Intro to Logic Page 2 ...
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