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INTRO LOGIC

INTRO LOGIC. Derivations in PL 5. DAY 26. Exam 4 Topics. 6 derivations in Predicate Logic 15 points each, plus 10 free points universal derivation [Exercise Set C] existential-out [Exercise Set D] negation rules [Exercise Set E] multiple quantifiers [Exercise Set F]

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INTRO LOGIC

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  1. INTRO LOGIC Derivations in PL5 DAY 26

  2. Exam 4 Topics • 6 derivations in Predicate Logic • 15 points each, plus 10 free points • universal derivation [Exercise Set C] • existential-out [Exercise Set D] • negation rules [Exercise Set E] • multiple quantifiers [Exercise Set F] • polyadic quantifiers [Exercise Set G] • polyadic quantifiers [Exercise Set G]

  3. Example 1 (repeated from last lecture) 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

  4. Example 2 • there is a F who R’s every G/ every G is R’ed by some F or other (1) x(Fx & y(Gy  Rxy)) Pr (2) : x(Gx y(Fy & Ryx))

  5. (1) x(Fx & y(Gy  Rxy)) Pr (2) : x(Gx y(Fy & Ryx)) UD (3) : Gay(Fy & Rya) CD (4) Ga As (5) : y(Fy & Rya) D(ID) (6) y(Fy & Rya) As (7) :  DD (9) Fb & y(Gy  Rby) 1, O (8) y(Fy & Rya) 6, O (10) Fb 9, &O (11) y(Gy  Rby) (12) (Fb & Rba) 8, O (13) Ga  Rba 11, O (14) Fb Rba 12, &O (15) Rba 4,13, O (16) Rba 10,14 O (17)  15,16, I

  6. Example 3 • there is a G who R’s no F/ every F is dis-R’ed by at least one G (1) x(Gx & y(Fy & Rxy)) Pr (2) : x(Fx y(Gy & Ryx))

  7. (1) x(Gx & y(Fy & Rxy)) Pr (2) : x(Fx y(Gy & Ryx)) UD (3) : Fay(Gy & Rya) CD (4) Fa As (5) : y(Gy & Rya) D (ID) (6) y(Gy & Rya) As (7) :  DD (8) Gb & y(Fy & Rby) 1, O (9) y(Gy & Rya) 6, O (10) Gb 8, &O (11) y(Fy & Rby) (12) (Gb & Rba) 9, O (13) y(Fy & Rby) 11, O (14) Gb Rba 12, &O (15) (Fa & Rba) 13, O (16) Fa Rba 15, &O (17) Rba 10,1, O (18) Rba 4,16, O (19)  17,18, I

  8. GOOD LUCK ON EXAM 4! GOOD LUCK ON THE FINALS! HAVE A GREAT SUMMER! GO SOX!

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