unit2 - Hardegree, Intermediate Logic ; Unit 2: Derivations...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Hardegree, Intermediate Logic ; Unit 2: Derivations in Function Logic 1 of 14 UNIT 2: DERIVATIONS IN FUNCTION LOGIC 1. EXERCISE SET A (Review of Predicate Logic) For each of the following arguments, construct a formal derivation of the conclusion (indicated by "/") from the premises. 1. f x(Fx Gx) / f xFx f xGx 2. f x(Fx Gx) ; ~F x(Gx & Hx) / ~F x(Fx & Hx) 3. F xFx F x ~ Gx / f x[Fx ~f xGx] 4. f x[Fx ~f xGx] / F xFx F x ~ Gx 5. F x ~F y(Fy & Ryx) / f x(Fx F y ~ Rxy) 6. f x F yRxy ; f x f y[Rxy Rxx] ; f x[Rxx f yRyx] / f x f yRxy 7. f x F yRxy ; f x[ F yRxy F yRyx] ; f x f y[Ryx f yRyx] / f x f yRxy 2. EXERCISE SET B 1.A. For each of the following three formulas, list the formula that is obtained by a single application of the rule Universal Elimination ( f O), using the singular term f(a) . 1.B. For each of the following three formulas, list the formula that is obtained by successive applications of the rule Universal Elimination ( f O), substituting f(a) for x and s(a,b) for y . (1) f x f y(Rxy Rxx) (2) f x f y{(Nx & Ny) N[p(x,y)]} (3) f x f y(R[x,m(y)] R[m(y),x]) 2.A. For each of the following three formulas, list every (non-trivial) formula that can be obtained by a single application of the rule Existential Introduction ( F I). (1) R[a , f(a)] (2) R[f(a) , f(a)] (3) R[s(a) , p(a,b)] 2.B. For each formula obtained in 2.A, list every (non-trivial) formula that can be obtained by one further application of F I. Hardegree, Intermediate Logic ; Unit 2: Derivations in Function Logic 2 of 14 3. EXERCISE SET C Directions For All Derivation Exercises . For each of the following, construct a formal derivation of the conclusion (indicated by "/") from the premises (if any). In cases in which two formulas are separated by '//', construct a derivation of each formula from the other. 1. P[f(b)] / f xP[f(x)] 2. P[f(b)] / f xPx 3. f xF[f(x)] / f xFx 4. F x(Fx Hx) ; F[p(a,b)] / H[p(a,b)] 5. F x(Fx Hx) ; F[p(a,b)] / f xHx 6. F x(Fx Hx) ; ~ H[f(a)] / ~ F[f(a)] 7. F x(Fx Hx) ; ~ H[f(a)] / ~F xFx 8. F x(Fx Gx) ; F x[(Fx & Gx) ~ Hx] ; H[p(a,b)] / f x(Hx & ~ Fx) 9. F x(Fx Gx) ; F x(Gx Hx) ; F[m(a)] / f x(Gx & Hx) 10. F x(Fx Gx) ; F x(Gx Hx) ; F[m(a)] / f xG[m(x)] & f xH[m(x)] 11. F x{R[x,s(a)] ~ R[x,p(a,b)]} ; R[s(a),s(a)] / f x ~ R[x,p(a,b)] 12. f xR[x,f(n)] F xR[x,f(n)] ; ~ R[g(n),f(n)] / ~ R[f(n),f(n)] 13. F x(Fx Rxx) ; F[p(c,d)] / f xR[x,p(c,d)] 14. F x(Fx Rxx) ; F x ~ R[m(a),x] / ~ F[m(a)] 15. F x{Fx F yRxy} ; F[g(a)] / R[g(a),g(a)] 16. f xR[f(a),x] F xR[x,f(a)] ; ~ R[g(b),f(a)] / ~ R[f(a),f(a)] Hardegree, Intermediate Logic ; Unit 2: Derivations in Function Logic 3 of 14 4. EXERCISE SET D 17. f x[ F yRxy f yRyx] ; R[f(a,b),f(a,b)] / R[g(a,b),f(a,b)] 18. f x(Rxx Fx) ; f x f y(Rxy Rxx) ; ~ F[g(a,b)] / ~ R[g(a,b),b] 19. f x(Fx Gx) ; f xM[m(x),x)] / f x{Fx F y{Gy & M[m(x),y]}} 20. f x f y{(Nx & Ny) N[p(x,y)]} ; F x{Nx &...
View Full Document

Page1 / 14

unit2 - Hardegree, Intermediate Logic ; Unit 2: Derivations...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online