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combined-problems.lisp
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(in-package "OSCAR")(setf *problems* (eval-when (:compile-toplevel :execute) (make-problem-list "Problem #1This is a case of collective rebutting defeatGiven premises: P justification = 1.0 A justification = 1.0Ultimate epistemic interests: R interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> Q strength = 1.0 pf-reason_2: {Q} ||=> R strength = 1.0 pf-reason_3: {C} ||=> ~R strength = 1.0 pf-reason_4: {B} ||=> C strength = 1.0 pf-reason_5: {A} ||=> B strength = 1.0Problem #2This is the same as #1 except that some reasons are backwards.Given premises: P justification = 1.0 A justification = 1.0Ultimate epistemic interests: R interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> Q strength = 1.0 pf-reason_2: {Q} ||=> R strength = 1.0 pf-reason_3: {A} ||=> B strength = 1.0 BACKWARDS PRIMA FACIE REASONS pf-reason_4: {} {C} ||=> ~R strength = 1.0 pf-reason_5: {} {B} ||=> C strength = 1.0Problem #3Figure 2Given premises: A justification = 1.0 B justification = 1.0 C justification = 1.0Ultimate epistemic interests: J interest = 1.0 K interest = 1.0 L interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A} ||=> D strength = 1.0 pf-reason_2: {D} ||=> G strength = 1.0 pf-reason_3: {B} ||=> E strength = 1.0 pf-reason_4: {C} ||=> F strength = 1.0 pf-reason_5: {I} ||=> L strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {G} ||=> J strength = 1.0 con-reason_2: {E} ||=> H strength = 1.0 con-reason_3: {H} ||=> K strength = 1.0 con-reason_4: {F} ||=> I strength = 1.0 con-reason_5: {F} ||=> (B @ E) strength = 1.0 con-reason_6: {H} ||=> (D @ G) strength = 1.0Problem #4Figure 3Given premises: A justification = 1.0 B justification = 1.0Ultimate epistemic interests: J interest = 1.0 K interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A} ||=> D strength = 1.0 pf-reason_2: {D} ||=> G strength = 1.0 pf-reason_3: {B} ||=> ~D strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {G} ||=> J strength = 1.0 con-reason_2: {~D} ||=> H strength = 1.0 con-reason_3: {H} ||=> K strength = 1.0Problem #5Figure 4Given premises: A justification = 1.0 B justification = 1.0 C justification = 1.0Ultimate epistemic interests: J interest = 1.0 K interest = 1.0 L interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A} ||=> D strength = 1.0 pf-reason_2: {D} ||=> G strength = 1.0 pf-reason_3: {B} ||=> ~D strength = 1.0 pf-reason_4: {C} ||=> D strength = 1.0 pf-reason_5: {I} ||=> L strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {G} ||=> J strength = 1.0 con-reason_2: {~D} ||=> H strength = 1.0 con-reason_3: {H} ||=> K strength = 1.0 con-reason_4: {D} ||=> I strength = 1.0Problem #6Figure 5Given premises: A justification = 1.0 B justification = 1.0 C justification = 1.0Ultimate epistemic interests: J interest = 1.0 K interest = 1.0 L interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A} ||=> D strength = 1.0 pf-reason_2: {D} ||=> G strength = 1.0 pf-reason_3: {B} ||=> ~D strength = 1.0 pf-reason_4: {C} ||=> F strength = 1.0 pf-reason_5: {I} ||=> L strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {G} ||=> J strength = 1.0 con-reason_2: {~D} ||=> H strength = 1.0 con-reason_3: {H} ||=> K strength = 1.0 con-reason_4: {F} ||=> I strength = 1.0 con-reason_5: {~D} ||=> M strength = 1.0 con-reason_6: {M} ||=> N strength = 1.0 con-reason_7: {N} ||=> (C @ F) strength = 1.0 con-reason_8: {F} ||=> (B @ ~D) strength = 1.0Problem #7Figure 7 -- self-defeatGiven premises: P justification = 1.0 Q justification = 1.0 S justification = 1.0Ultimate epistemic interests: T interest = 1.0 (R v ~T) interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> R strength = 1.0 pf-reason_2: {Q} ||=> ~R strength = 1.0 pf-reason_3: {S} ||=> T strength = 1.0Problem #8Figure 8 -- the lottery paradox paradoxGiven premises: P justification = 1.0Ultimate epistemic interests: ~T1 interest = 1.0 ~T2 interest = 1.0 ~T3 interest = 1.0 R interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {R} ||=> ~T1 strength = 1.0 pf-reason_2: {R} ||=> ~T2 strength = 1.0 pf-reason_3: {R} ||=> ~T3 strength = 1.0 pf-reason_4: {P} ||=> R strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {R , ~T1 , ~T2} ||=> T3 strength = 1.0 con-reason_2: {R , ~T2 , ~T3} ||=> T1 strength = 1.0 con-reason_3: {R , ~T1 , ~T3} ||=> T2 strength = 1.0 con-reason_4: {~T1 , ~T2 , ~T3} ||=> ~R strength = 1.0Problem #9Figure 8 -- the lottery paradox paradox using logicGiven premises: P justification = 1.0Ultimate epistemic interests: ~T1 interest = 1.0 ~T2 interest = 1.0 ~T3 interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {R} ||=> ~T1 strength = 1.0 pf-reason_2: {R} ||=> ~T2 strength = 1.0 pf-reason_3: {R} ||=> ~T3 strength = 1.0 pf-reason_4: {P} ||=> R strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {R} ||=> (T1 v (T2 v T3)) strength = 1.0Problem #10Figure 9 -- No nearest defeasible ancestor is defeated.Given premises: P justification = 1.0Ultimate epistemic interests: R interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> Q strength = 1.0 pf-reason_2: {Q} ||=> R strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {R} ||=> (P @ Q) strength = 1.0Problem #11figure 10 -- Robert and the pink elephant.Given premises: P justification = 1.0 Q justification = 1.0 R justification = 1.0Ultimate epistemic interests: U interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P , Q} ||=> S strength = 1.0 pf-reason_2: {R} ||=> T strength = 1.0 pf-reason_3: {S} ||=> U strength = 1.0 pf-reason_4: {V} ||=> ((P & Q) @ S) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {T , U} ||=> V strength = 1.0Problem #12figure 11 -- a simple case of ancestor defeat.Given premises: P justification = 1.0 Q justification = 1.0 R justification = 1.0Ultimate epistemic interests: W interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> S strength = 1.0 pf-reason_2: {S} ||=> U strength = 1.0 pf-reason_3: {Q} ||=> T strength = 1.0 pf-reason_4: {R} ||=> W strength = 1.0 pf-reason_5: {V} ||=> (S @ U) strength = 1.0 pf-reason_6: {U} ||=> (R @ W) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {S , T} ||=> V strength = 1.0Problem #13figure 12 -- a more complicated case of ancestor defeat.Given premises: P justification = 1.0 Q justification = 1.0 R justification = 1.0 X justification = 1.0Ultimate epistemic interests: W interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> S strength = 1.0 pf-reason_2: {S} ||=> U strength = 1.0 pf-reason_3: {Q} ||=> T strength = 1.0 pf-reason_4: {R} ||=> W strength = 1.0 pf-reason_5: {X} ||=> ~S strength = 1.0 pf-reason_6: {V} ||=> (S @ U) strength = 1.0 pf-reason_7: {U} ||=> (R @ W) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {S , T} ||=> V strength = 1.0Problem #14figure 13 -- a still more complicated case of ancestor defeat.Given premises: P justification = 1.0 Q justification = 1.0 R justification = 1.0 X justification = 1.0Ultimate epistemic interests: W interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P} ||=> S strength = 1.0 pf-reason_2: {S} ||=> U strength = 1.0 pf-reason_3: {Q} ||=> T strength = 1.0 pf-reason_4: {R} ||=> W strength = 1.0 pf-reason_5: {S} ||=> Y strength = 1.0 pf-reason_6: {X} ||=> ~S strength = 1.0 pf-reason_7: {V} ||=> (S @ U) strength = 1.0 pf-reason_8: {U} ||=> (R @ W) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {Y , T} ||=> V strength = 1.0Problem #15figure 14 -- a three-membered defeat cycle.Given premises: A justification = 1.0 P justification = 1.0 R justification = 1.0 T justification = 1.0Ultimate epistemic interests: B interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A} ||=> B strength = 1.0 pf-reason_2: {P} ||=> Q strength = 1.0 pf-reason_3: {R} ||=> S strength = 1.0 pf-reason_4: {T} ||=> U strength = 1.0 pf-reason_5: {Q} ||=> (R @ S) strength = 1.0 pf-reason_6: {S} ||=> (T @ U) strength = 1.0 pf-reason_7: {U} ||=> (P @ Q) strength = 1.0 pf-reason_8: {Q} ||=> (A @ B) strength = 1.0Problem #16figure 18 -- the paradox of the preface.Given premises: P1 justification = 1.0 P2 justification = 1.0 P3 justification = 1.0 S justification = 1.0 T justification = 1.0Ultimate epistemic interests: (Q1 & (Q2 & Q3)) interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P1} ||=> Q1 strength = 1.0 pf-reason_2: {P2} ||=> Q2 strength = 1.0 pf-reason_3: {P3} ||=> Q3 strength = 1.0 pf-reason_4: {S} ||=> R strength = 1.0 pf-reason_5: {T} ||=> ~(Q1 & (Q2 & Q3)) strength = 1.0 pf-reason_6: {S1} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 pf-reason_7: {S2} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 pf-reason_8: {S3} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_1: {Q1 , Q2} ||=> (Q1 & Q2) strength = 1.0 con-reason_2: {Q2 , Q3} ||=> (Q2 & Q3) strength = 1.0 con-reason_3: {Q1 , Q3} ||=> (Q1 & Q3) strength = 1.0 con-reason_4: {R , (Q1 & Q3)} ||=> S2 strength = 1.0 con-reason_5: {R , (Q2 & Q3)} ||=> S1 strength = 1.0 con-reason_6: {R , (Q1 & Q2)} ||=> S3 strength = 1.0 con-reason_7: {(Q1 & Q2) , ~(Q1 & (Q2 & Q3))} ||=> ~Q3 strength = 1.0 con-reason_8: {(Q2 & Q3) , ~(Q1 & (Q2 & Q3))} ||=> ~Q1 strength = 1.0 con-reason_9: {(Q1 & Q3) , ~(Q1 & (Q2 & Q3))} ||=> ~Q2 strength = 1.0 BACKWARDS CONCLUSIVE REASONS con-reason_11: {} {Q1 , Q2 , Q3} ||=> (Q1 & (Q2 & Q3)) strength = 1.0Problem #17figure 18 -- the paradox of the preface, using logic.Given premises: P1 justification = 1.0 P2 justification = 1.0 P3 justification = 1.0 S justification = 1.0 T justification = 1.0Ultimate epistemic interests: (Q1 & (Q2 & Q3)) interest = 1.0 FORWARDS PRIMA FACIE REASONS pf-reason_1: {P1} ||=> Q1 strength = 1.0 pf-reason_2: {P2} ||=> Q2 strength = 1.0 pf-reason_3: {P3} ||=> Q3 strength = 1.0 pf-reason_4: {S} ||=> R strength = 1.0 pf-reason_5: {T} ||=> ~(Q1 & (Q2 & Q3)) strength = 1.0 pf-reason_6: {S1} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 pf-reason_7: {S2} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 pf-reason_8: {S3} ||=> (T @ ~(Q1 & (Q2 & Q3))) strength = 1.0 FORWARDS CONCLUSIVE REASONS con-reason_4: {R , Q1 , Q3} ||=> S2 strength = 1.0 con-reason_5: {R , Q2 , Q3} ||=> S1 strength = 1.0 con-reason_6: {R , Q1 , Q2} ||=> S3 strength = 1.0Problem #18This uses contradiction-inversion.Given premises: B justification = 1 A justification = 1 C justification = 1Ultimate epistemic interests: Q interest = .7 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A , B} ||=> P strength = .7 pf-reason_2: {C} ||=> ~Q strength = .8 FORWARDS CONCLUSIVE REASONS con-reason_1: {P} ||=> Q strength = 1.0Problem #19Four-way collective defeat.Given premises: A1 justification = 1 B1 justification = 1 C1 justification = 1 D1 justification = 1Ultimate epistemic interests: P1 interest = .7 Q1 interest = .7 R1 interest = .7 S1 interest = .7 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A1} ||=> P1 strength = .7 pf-reason_2: {B1} ||=> Q1 strength = .7 pf-reason_3: {C1} ||=> R1 strength = .7 pf-reason_4: {D1} ||=> S1 strength = .7 FORWARDS CONCLUSIVE REASONS con-reason_1: {P1,Q1,R1} ||=> ~S1 strength = 1.0 con-reason_2: {P1,Q1,S1} ||=> ~R1 strength = 1.0 con-reason_3: {S1,Q1,R1} ||=> ~P1 strength = 1.0 con-reason_4: {P1,S1,R1} ||=> ~Q1 strength = 1.0Problem #20Two copies of four-way collective defeat.Given premises: A1 justification = 1 B1 justification = 1 C1 justification = 1 D1 justification = 1 A2 justification = 1 B2 justification = 1 C2 justification = 1 D2 justification = 1Ultimate epistemic interests: P1 interest = .7 Q1 interest = .7 R1 interest = .7 S1 interest = .7 P2 interest = .7 Q2 interest = .7 R2 interest = .7 S2 interest = .7 FORWARDS PRIMA FACIE REASONS pf-reason_1: {A1} ||=> P1 strength = .7 pf-reason_2: {B1} ||=> Q1 strength = .7 pf-reason_3: {C1} ||=> R1 strength = .7 pf-reason_4: {D1} ||=> S1 strength = .7 pf-reason_5: {A2} ||=> P2 strength = .7 pf-reason_6: {B2} ||=> Q2 strength = .7 pf-reason_7: {C2} ||=> R2 strength = .7 pf-reason_8: {D2} ||=> S2 strength = .7 FORWARDS CONCLUSIVE REASONS con-reason_1: {P1,Q1,R1} ||=> ~S1 strength = 1.0 con-reason_2: {P1,Q1,S1} ||=> ~R1 strength = 1.0 con-reason_3: {S1,Q1,R1} ||=> ~P1 strength = 1.0 con-reason_4: {P1,S1,R1} ||=> ~Q1 strength = 1.0 con-reason_5: {P2,Q2,R2} ||=> ~S2 strength = 1.0 con-reason_6: {P2,Q2,S2} ||=> ~R2 strength = 1.0 con-reason_7: {S2,Q2,R2} ||=> ~P2 strength = 1.0 con-reason_8: {P2,S2,R2} ||=> ~Q2 strength = 1.0Problem #21Given premises:Ultimate epistemic interests: ((p -> q) <-> (~q -> ~p)) interest = 1.0Problem #22Given premises:Ultimate epistemic interests: (~~p <-> p) interest = 1.0Problem #23Given premises:Ultimate epistemic interests: (~(p -> q) -> (q -> p)) interest = 1.0Problem #24Given premises:Ultimate epistemic interests: ((~p -> q) <-> (~q -> p)) interest = 1.0Problem #25Given premises:Ultimate epistemic interests: (((p v q) -> (p v r)) -> (p v (q -> r))) interest = 1.0Problem #26Given premises:Ultimate epistemic interests: (p v ~p) interest = 1.0Problem #27Given premises:Ultimate epistemic interests: (p v ~~~p) interest = 1.0Problem #28Given premises:Ultimate epistemic interests: (((p -> q) -> p) -> p) interest = 1.0Problem #29Given premises:Ultimate epistemic interests: (((p v q) & ((~p v q) & (p v ~q))) -> ~(~p v ~q)) interest = 1.0Problem #30Given premises: (q -> r) justification = 1.0 (r -> (p & q)) justification = 1.0 (p -> (q v r)) justification = 1.0Ultimate epistemic interests: (p <-> q) interest = 1.0Problem #31Given premises:Ultimate epistemic interests: (p <-> p) interest = 1.0Problem #32Given premises:Ultimate epistemic interests: (((p <-> q) <-> r) <-> (p <-> (q <-> r))) interest = 1.0Problem #33Given premises:Ultimate epistemic interests: ((p v (q & r)) <-> ((p v q) & (p v r))) interest = 1.0Problem #34Given premises:Ultimate epistemic interests: ((p <-> q) <-> ((q v ~p) & (~q v p))) interest = 1.0Problem #35Given premises:Ultimate epistemic interests: ((p <-> q) -> (~p v q)) interest = 1.0Problem #36Given premises:Ultimate epistemic interests: ((p -> q) v (q -> p)) interest = 1.0Problem #37Given premises:Ultimate epistemic interests: (((p & (q -> r)) -> s) <-> ((~p v (q v s)) & (~p v (~r v s)))) interest = 1.0Problem #41Given premises: (all x)(F x) justification = 1.0Ultimate epistemic interests: (some x)(F x) interest = 1.0Problem #42Given premises: (some x)(all y)(F x y) justification = 1.0Ultimate epistemic interests: (all y)(some x)(F x y) interest = 1.0Problem #43Given premises: (all x)((P x) -> ~(P x)) justification = 1.0Ultimate epistemic interests: ~(P a) interest = 1.0Problem #44Given premises: (all x)[(F x) -> ((H x) & ~(G x))] justification = 1.0Ultimate epistemic interests: ((G a) -> ~(F a)) interest = 1.0Problem #45Given premises: (all x)((H x) -> (G x)) justification = 1.0Ultimate epistemic interests: [((H a) -> (G a)) & ~(~(G b) & (H b))] interest = 1.0Problem #46Given premises: (all x)[(P x) <-> ((H x) & ~(P x))] justification = 1.0Ultimate epistemic interests: (all x)~(H x) interest = 1.0Problem #47Given premises: (all x)(F x) justification = 1.0 (all x)((F x) -> (G x)) justification = 1.0Ultimate epistemic interests: (all x)(G x) interest = 1.0Problem #48Given premises: (F a) justification = 1.0Ultimate epistemic interests: (some x)((F x) v (G x)) interest = 1.0Problem #49Given premises: (some x)(F x) justification = 1.0Ultimate epistemic interests: (some x)((F x) v (G x)) interest = 1.0Problem #50Given premises: (some x)((F x) v (G x)) justification = 1.0 ~(some x)(F x) justification = 1.0Ultimate epistemic interests: (some x)(G x) interest = 1.0Problem #51Given premises: [(some x)(F x) -> (all y)(G y)] justification = 1.0Ultimate epistemic interests: (all x)(all y)[(F x) -> (G y)] interest = 1.0Problem #52Given premises: (all x)[(F x) -> ((G x) -> (H x))] justification = 1.0Ultimate epistemic interests: [(all x)((F x) -> (G x)) -> (all x)((F x) -> (H x))] interest = 1.0Problem #53Given premises: (all x)[(F x) -> (some y)((F y) & (G x y))] justification = 1.0Ultimate epistemic interests: (all x)[(F x) -> (some y)(some z)((G x y) & (G y z))] interest = 1.0Problem #54Given premises: (all x)(some y)(R x y) justification = 1.0 (all x)(all y)((R x y) -> (R y x)) justification = 1.0 (all x)(all y)(all z)([(R x y) & (R y z)] -> (R x z)) justification = 1.0Ultimate epistemic interests: (all x)(R x x) interest = 1.0Problem #55Given premises:Ultimate epistemic interests: [(all x)(F x) -> (some x)(F x)] interest = 1.0Problem #56Given premises:Ultimate epistemic interests: (some x)[(F x) -> (all y)(F y)] interest = 1.0Problem #57Given premises:Ultimate epistemic interests: [(all x)(all y)((R x y) -> ~(R y x)) -> ~(some x)(R x x)] interest = 1.0Problem #58Given premises:Ultimate epistemic interests: ~(some x)(all y)((R x y) <-> ~(R y y)) interest = 1.0Problem #59Given premises:Ultimate epistemic interests: ~(all x)[((F x) v ~(F x)) -> ~((F x) v ~(F x))] interest = 1.0Problem #60Given premises:Ultimate epistemic interests: [(some x)((F x) v (G x)) <-> [(some x)(F x) v (some x)(G x)]] interest = 1.0Problem #61Given premises:Ultimate epistemic interests: [(all x)((F x) & (G x)) <-> [(all x)(F x) & (all x)(G x)]] interest = 1.0Problem #62Given premises:Ultimate epistemic interests: [(all x)((F x) -> (G x)) -> ((all x)(F x) -> (all x)(G x))] interest = 1.0Problem #63Given premises:Ultimate epistemic interests: [(P -> (all x)(F x)) <-> (all x)(P -> (F x))] interest = 1.0Problem #64Given premises:Ultimate epistemic interests: [(P -> (some x)(F x)) <-> (some x)(P -> (F x))] interest = 1.0Problem #65Given premises:Ultimate epistemic interests: [((all x)(F x) -> P) <-> (some x)((F x) -> P)] interest = 1.0Problem #66Given premises:Ultimate epistemic interests: (all x)((F x) v ~(F x)) interest = 1.0Problem #67Given premises:Ultimate epistemic interests: (some x)((F x) v ~(F x)) interest = 1.0Problem #68Given premises:Ultimate epistemic interests: (some y)((F a y) <-> (F y y)) interest = 1.0Problem #69Given premises:Ultimate epistemic interests: (all x)(some y)((F x y) <-> (F y y)) interest = 1.0Problem #70 Pelletier's problem 18Given premises:Ultimate epistemic interests: (some y)(all x)((F y) -> (F x)) interest = 1.0Problem #71 Pelletier's problem 19Given premises:Ultimate epistemic interests: (some x)(all y)(all z)(((P y) -> (Q z)) -> ((P x) -> (Q x))) interest = 1.0Problem #72 Pelletier's problem 20Given premises:Ultimate epistemic interests: [(all x)(all y)(some z)(all w)(((P x) & (Q y)) -> ((R z) & (S w))) -> ((some v1)(some u)((P v1) & (Q u)) -> (some s)(R s))] interest = 1.0Problem #73 Pelletier's problem 21Given premises: (some x)(p -> (F x)) justification = 1.0 (some x)((F x) -> p) justification = 1.0Ultimate epistemic interests: (some x)(p <-> (F x)) interest = 1.0Problem #74 Pelletier's problem 22Given premises:Ultimate epistemic interests: [(all x)(p <-> (F x)) -> (p <-> (all y)(F y))] interest = 1.0Problem #75 Pelletier's problem 23Given premises:Ultimate epistemic interests: [(all x)(p v (F x)) <-> (p v (all y)(F y))] interest = 1.0Problem #76 Pelletier's problem 24Given premises: ~(some x)((S x) & (Q x)) justification = 1.0 (all x)((P x) -> ((Q x) v (R x))) justification = 1.0 [~(some x)(P x) -> (some y)(Q y)] justification = 1.0 (all x)(((Q x) v (R x)) -> (S x)) justification = 1.0Ultimate epistemic interests: (some x)((P x) & (R x)) interest = 1.0Problem #77 Pelletier's problem 25Given premises: (some x)(P x) justification = 1.0 (all x)((F x) -> (~(G x) & (R x))) justification = 1.0 (all x)((P x) -> ((G x) & (F x))) justification = 1.0 [(all x)((P x) -> (Q x)) v (some y)((P y) & (R y))] justification = 1.0Ultimate epistemic interests: (some x)((Q x) & (P x)) interest = 1.0Problem #78 Pelletier's problem 26Given premises: [(some x)(P x) <-> (some y)(Q y)] justification = 1.0 (all x)(all y)(((P x) & (Q y)) -> ((R x) <-> (S y))) justification = 1.0Ultimate epistemic interests: [(all x)((P x) -> (R x)) <-> (all y)((Q y) -> (S y))] interest = 1.0Problem #79 Pelletier's problem 27Given premises: (some x)((F x) & ~(G x)) justification = 1.0 (all x)((F x) -> (H x)) justification = 1.0 (all x)(((J x) & (I x)) -> (F x)) justification = 1.0 [(some x)((H x) & ~(G x)) -> (all y)((I y) -> ~(H y))] justification = 1.0Ultimate epistemic interests: (all x)((J x) -> ~(I x)) interest = 1.0Problem #80 Pelletier's problem 28Given premises: (all x)[(P x) -> (all x)(Q x)] justification = 1.0 [(all x)((Q x) v (R x)) -> (some y)((Q y) & (S y))] justification = 1.0 [(some x)(S x) -> (all x)((F x) -> (G x))] justification = 1.0Ultimate epistemic interests: (all x)[((P x) & (F x)) -> (G x)] interest = 1.0Problem #81 Pelletier's problem 29Given premises: [(some x)(F x) & (some y)(G y)] justification = 1.0Ultimate epistemic interests: ([(all x)((F x) -> (H x)) & (all y)((G y) -> (J y))] <-> (all z)(all w)(((F z) & (G w)) -> ((H z) & (J w)))) interest = 1.0Problem #82 Pelletier's problem 30Given premises: (all x)(((F x) v (G x)) -> ~(H x)) justification = 1.0 (all x)(((G x) -> ~(I x)) -> ((F x) & (H x))) justification = 1.0Ultimate epistemic interests: (all x)(I x) interest = 1.0Problem #83 Pelletier's problem 31Given premises: ~(some x)((F x) & ((G x) v (H x))) justification = 1.0 (some x)((I x) & (F x)) justification = 1.0 (all x)(~(H x) -> (J x)) justification = 1.0Ultimate epistemic interests: (some x)((I x) & (J x)) interest = 1.0Problem #84 Pelletier's problem 32Given premises: (all x)(((F x) & ((G x) v (H x))) -> (I x)) justification = 1.0 (all x)(((I x) & (H x)) -> (J x)) justification = 1.0 (all x)((K x) -> (H x)) justification = 1.0Ultimate epistemic interests: (all x)(((F x) & (K x)) -> (J x)) interest = 1.0Problem #85 Pelletier's problem 33Given premises:Ultimate epistemic interests: [(all x)[((P a) & ((P x) -> (P b))) -> (P c)] <-> (all x)((~(P a) v ((P x) v (P c))) & (~(P a) v (~(P b) v (P c))))] interest = 1.0Problem #86 Half of Pelletier's problem 34Given premises:Ultimate epistemic interests: [[(some x)(all y)((P x) <-> (P y)) <-> ((some z)(Q z) <-> (all w)(Q w))] -> [(some u)(all v1)((Q u) <-> (Q v1)) <-> ((some r)(P r) <-> (all s)(P s))]] interest = 1.0Problem #87 Pelletier's problem 35Given premises:Ultimate epistemic interests: (some u)(some v1)[(P u v1) -> (all x)(all y)(P x y)] interest = 1.0Problem #88 Pelletier's problem 36Given premises: (all x)(some y)(F x y) justification = 1.0 (all x)(some z)(G x z) justification = 1.0 (all x)(all y)[((F x y) v (G x y)) -> (all z)(((F y z) v (G y z)) -> (H x z))] justification = 1.0Ultimate epistemic interests: (all x)(some y)(H x y) interest = 1.0Problem #89 Pelletier's problem 37Given premises: (all z)(some w)(all x)(some y)[[((P x z) -> (P y w)) & (P y z)] & [(P y w) -> (some u)(Q u w)]] justification = 1.0 (all x)(all z)[~(P x z) -> (some v1)(Q v1 z)] justification = 1.0 [(some y)(some s)(Q y s) -> (all x)(R x x)] justification = 1.0Ultimate epistemic interests: (all x)(some y)(R x y) interest = 1.0Problem #90 Pelletier's problem 38Given premises:Ultimate epistemic interests: [(all x)[[(P a) & ((P x) -> (some y)((P y) & (R x y)))] -> (some z)(some w)[(P z) & ((R x w) & (R w z))]] <-> (all x)[[(~(P a) v (P x)) v (some z)(some w)((P z) & ((R x w) & (R w z)))] & [~(P a) v (~(some y)((P y) & (R x y)) v (some z)(some w)((P z) & ((R x w) & (R w z))))]]] interest = 1.0Problem #91 Pelletier's problem 39Given premises:Ultimate epistemic interests: ~(some x)(all y)((F y x) <-> ~(F y y)) interest = 1.0Problem #92 Pelletier's problem 40Given premises:Ultimate epistemic interests: [(some y)(all x)((F x y) <-> (F x x)) -> ~(all z)(some w)(all v1)((F v1 w) <-> ~(F v1 z))] interest = 1.0Problem #93 Pelletier's problem 41Given premises: (all z)(some y)(all x)[(F x y) <-> ((F x z) & ~(F x x))] justification = 1.0Ultimate epistemic interests: ~(some z)(all x)(F x z) interest = 1.0Problem #94 Pelletier's problem 42Given premises:Ultimate epistemic interests: ~(some y)(all x)[(F x y) <-> ~(some z)((F x z) & (F z x))] interest = 1.0Problem #95 Pelletier's problem 43Given premises: (all x)(all y)[(Q x y) <-> (all z)((F z x) <-> (F z y))] justification = 1.0Ultimate epistemic interests: (all x)(all y)[(Q x y) <-> (Q y x)] interest = 1.0Problem #96 Pelletier's problem 44Given premises: (all x)[[(F x) -> (some y)((G y) & (H x y))] & (some y)((G y) & ~(H x y))] justification = 1.0 (some x)[(J x) & (all y)[(G y) -> (H x y)]] justification = 1.0Ultimate epistemic interests: (some x)((J x) & ~(F x)) interest = 1.0Problem #97 Pelletier's problem 45Given premises: (all x)[[(F x) & (all y)[((G y) & (H x y)) -> (J x y)]] -> (all y)[((G y) & (H x y)) -> (K y)]] justification = 1.0 ~(some y)((L y) & (K y)) justification = 1.0 (some x)[[(F x) & (all y)((H x y) -> (L y))] & (all y)(((G y) & (H x y)) -> (J x y))] justification = 1.0Ultimate epistemic interests: (some x)((F x) & ~(some y)((G y) & (H x y))) interest = 1.0Problem #98 Pelletier's problem 46Given premises: (all x)([(F x) & (all y)[((F y) & (H y x)) -> (G y)]] -> (G x)) justification = 1.0 [(some x)((F x) & ~(G x)) -> (some x)(((F x) & ~(G x)) & (all y)(((F y) & ~(G y)) -> (J x y)))] justification = 1.0 (all x)(all y)[[((F x) & (F y)) & (H x y)] -> ~(J y x)] justification = 1.0Ultimate epistemic interests: (all x)((F x) -> (G x)) interest = 1.0Problem #99 Pelletier's problem 47Given premises: (all x)((W x) -> (A x)) justification = 1.0 (all x)((F x) -> (A x)) justification = 1.0 (all x)((B x) -> (A x)) justification = 1.0 (all x)((C x) -> (A x)) justification = 1.0 (all x)((S x) -> (A x)) justification = 1.0 (some w0)(W w0) justification = 1.0 (some f0)(F f0) justification = 1.0 (some b0)(B b0) justification = 1.0 (some c0)(C c0) justification = 1.0 (some s0)(S s0) justification = 1.0 (some g0)(G g0) justification = 1.0 (all x)((G x) -> (P x)) justification = 1.0 (all x)[(A x) -> [(all w)((P w) -> (E x w)) v (all y)(((A y) & ((M y x) & (some z)((P z) & (E y z)))) -> (E x y))]] justification = 1.0 (all x)(all y)[((C x) & (B y)) -> (M x y)] justification = 1.0 (all x)(all y)[((S x) & (B y)) -> (M x y)] justification = 1.0 (all x)(all y)[((B x) & (F y)) -> (M x y)] justification = 1.0 (all x)(all y)[((F x) & (W y)) -> (M x y)] justification = 1.0 (all x)(all y)[((W x) & (F y)) -> ~(E x y)] justification = 1.0 (all x)(all y)[((W x) & (G y)) -> ~(E x y)] justification = 1.0 (all x)(all y)[((B x) & (C y)) -> (E x y)] justification = 1.0 (all x)(all y)[((B x) & (S y)) -> ~(E x y)] justification = 1.0 (all x)[(C x) -> (some y)((P y) & (E x y))] justification = 1.0 (all x)[(S x) -> (some y)((P y) & (E x y))] justification = 1.0Ultimate epistemic interests: (some x)(some y)[[(A x) & (A y)] & (some z)[(E x y) & ((G z) & (E y z))]] interest = 1.0Problem #100 Pelletier's problem 57Given premises: (F (g a b) (g b c)) justification = 1.0 (F (g b c) (g a c)) justification = 1.0 (all x)(all y)(all z)[[(F x y) & (F y z)] -> (F x z)] justification = 1.0Ultimate epistemic interests: (F (g a b) (g a c)) interest = 1.0Problem #102Given premises:Ultimate epistemic interests: [(all x)[((F a) & ((F x) -> (F (g x)))) -> (F (g (g x)))] -> (all x)[[(~(F a) v (F x)) v (F (g (g x)))] & [(~(F a) v ~(F (g x))) v (F (g (g x)))]]] interest = 1.0Problem #103 The unintuitive problemGiven premises: (all x)(all y)(all z)([(P x y) & (P y z)] -> (P x z)) justification = 1.0 (all x)(all y)(all z)([(Q x y) & (Q y z)] -> (Q x z)) justification = 1.0 (all x)(all y)((Q x y) -> (Q y x)) justification = 1.0 (all x)(all y)(~(P x y) -> (Q x y)) justification = 1.0 ~(P a b) justification = 1.0Ultimate epistemic interests: (Q c d) interest = 1.0Problem #104 Chang and Lee problem 3Given premises: (all x)(P x e x) justification = 1.0 (all x)(P e x x) justification = 1.0 (all x)(all y)(all z)(all u)(all v1)(all w)[((P x y u) & ((P y z v1) & (P u z w))) -> (P x v1 w)] justification = 1.0 (all x)(all y)(all z)(all u)(all v1)(all w)[((P x y u) & ((P y z v1) & (P x v1 w))) -> (P u z w)] justification = 1.0 (all x)(P x x e) justification = 1.0 (P a b c) justification = 1.0Ultimate epistemic interests: (P b a c) interest = 1.0")))(setq *comparison-log* '(OSCAR_3.31 0.23 0.23 10 0.95 ((104 35 37 78) (103 145 63 296) (102 21 30 44) (100 3 9 10) (99 623 145 471) (98 42 41 120) (97 13 33 42) (96 5 12 19) (95 13 40 46) (94 31 35 66) (93 6 18 24) (92 6 14 14) (91 2 8 8) (90 81 43 101) (89 15 25 47) (88 6 13 20) (87 7 12 14) (86 255 111 297) (85 16 31 45) (84 5 19 20) (83 4 16 17) (82 5 13 17) (81 16 39 47) (80 6 22 23) (79 12 26 27) (78 13 38 44) (77 3 12 13) (76 9 32 36) (75 10 19 27) (74 3 14 15) (73 9 17 27) (72 6 13 16) (71 10 13 24) (70 5 8 12) (69 3 5 5) (68 2 4 4) (67 2 4 4) (66 1 4 4) (65 6 16 18) (64 5 18 20) (63 5 15 17) (62 2 8 8) (61 6 17 21) (60 10 23 32) (59 3 6 6) (58 2 8 8) (57 2 7 7) (56 3 8 10) (55 1 4 4) (54 7 15 18) (53 7 21 23) (52 3 11 11) (51 3 9 9) (50 2 8 8) (49 3 5 6) (48 1 4 5) (47 3 6 6) (46 4 12 12) (45 2 5 5) (44 2 6 8) (43 1 3 3) (42 1 5 5) (41 2 3 3) (37 18 36 51) (36 1 5 7) (35 1 4 5) (34 5 18 24) (33 8 27 36) (32 28 80 95) (31 1 3 3) (30 4 18 18) (29 4 12 12) (28 2 4 5) (27 1 3 3) (26 2 3 3) (25 2 11 12) (24 4 11 15) (23 2 4 6) (22 1 3 3) (21 4 11 14) (20 23 24 32) (19 10 12 16) (18 3 7 8) (17 14 21 27) (16 17 21 29) (15 5 12 13) (14 7 13 14) (13 6 12 13) (12 3 10 11) (11 4 8 9) (10 3 4 5) (9 11 13 16) (8 9 9 13) (7 11 9 14) (6 8 16 19) (5 7 11 14) (4 4 8 10) (3 5 14 17) (2 4 7 10) (1 3 7 8))))