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INTRO LOGIC

INTRO LOGIC

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INTRO LOGIC

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  1. INTRO LOGIC Derivations in PL4 DAY 25

  2. Overview • Exam 1 Sentential Logic Translations (+) • Exam 2 Sentential Logic Derivations • Exam 3 Predicate Logic Translations • Exam 4 Predicate Logic Derivations • 6 derivations @ 15 points + 10 free points • Exam 5 very similar to Exam 3 • Exam 6 very similar to Exam 4

  3. Rules Introduced – Day 1 O I ––––– ––––– OLD name OLD name a name counts as OLDprecisely if it occurs somewhereunboxed and uncancelled

  4. Rules Introduced – Day 2 O UD ––––– : :  NEW name NEW name a name counts as NEW precisely if it occurs nowhere unboxed or uncancelled

  5. Rules Introduced – Day 3 O O  –––––  ––––– • is any formula  is any variable

  6. Strategies main operator show-strategy ,, &,  SL strategy  UD  DD or D

  7. Show- Strategy (UD) • :  • :  • ° • ° • ° UD ?? must be a NEW name

  8. Show- Strategy (D) • :  •  • :  • ° • ° •  D As DD

  9. Example 1 (repeated) every F is G ; no G is H / no F is H (1) x(Fx  Gx) Pr (2) x(Gx & Hx) Pr (3) : x(Fx & Hx) D (4) x(Fx & Hx) As (5) :  DD (6) x(Gx & Hx) 2, O (7) Fa & Ha 4, O (8) Fa  Ga 1, O (9) (Ga & Ha) 6, O (10) Fa 7, &O (11) Ha (12) Ga 8,10, O (13) Ga Ha 9, &O (14) Ha 12,13, O (15)  11,14, I

  10. Example 2 (repeated) if someone is F, then someone is unH/ if anyone is F, then not-everyone is H (1) xFx yHy Pr (2) : x(Fx yHy) UD (3) : FayHy CD (4) Fa As (5) : yHy ID (6) yHy As (7) :  DD (8) xFx 4, I (9) yHy 1,8, O (10) Hb 9, O (11) Hb 6, O (12)  10,11 O

  11. Example 3 there is someone whom everyone R’s/ everyone R’s someone or other (1) xyRyx Pr (2) : xyRxy UD (3) : yRay D(ID) (4) yRay As (5) :  DD (6) yRyb 1, O (7) yRay 4, O (8) Rab 6, O (9) Rab 7, O (10)  8,9, I

  12. Example 4 there is someone who R’s no-one/ everyone is dis-R’ed by someone or other (1) xyRxy Pr (2) : xyRyx UD (3) : yRya D(ID) (4) yRya As (5) :  DD (6) yRby 1, O (7) yRya 4, O (8) yRby 6, O (9) Rba 7, O (10) Rba 8, O (11)  9,10, I

  13. Example 5 (1) xy(Fy  Rxy) Pr • there is someone who R’s every F/ every F is R’ed by someone or other (2) : x(Fx yRyx) UD (3) : FayRya CD (4) Fa As (5) : yRya D(ID) (6) yRya As (7) :  DD (8) y(Fy  Rby) 1, O (9) yRya 6, O (10) Fa  Rba 8, O (11) Rba 9, O (12) Rba 4,10, O (13)  11,12, I

  14. Example 6 (1) x(Fx & yRxy) Pr (2) : xy(Fy & Ryx) UD • there is some F who R’s no-one/ everyone is dis-R’ed by some F or other (3) : y(Fy & Rya) D(ID) (4) y(Fy & Rya) As (5) :  DD (6) Fb & yRby 1, O (7) y(Fy & Rya) 4, O (8) Fb 6, &O (9) yRby (10) (Fb & Rba) 7, O (11) yRby 9, O (12) Fb Rba 10, &O (13) Rba 11, O (14) Rba 8,12 O (15)  13,14, I

  15. THE END