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A second Pretabular Classical Relevant LogicAssadollah Fallahi92/9/27 (Pretabular) A (B A)(A (B C)) (B (A C))(A (B C)) ((A B) (A C))

A ~ ~ A~ ~ A A(A B) (~ B ~ A) A A(A B) ((B C) (A C))(A (B C)) (B (A C))(A (B C)) ((A B) (A C))

A ~ ~ A~ ~ A A(A B) (~ B ~ A) TabularCL, 3, n ... Non-tabular, Int, R, K, T, B, S1, ... S4, S5 S5. . 1932 1951 LC 1959 1970 RM 1952 1971 Pretabular, S5T + 4 + 5+K=S5(A B) (B A)+Int=LCA (A A)+R=RM 1. 2. A B {~AB, ~A&B}[(A B) (~AB)] [(A B) (~A&B)]RM : 1. Locally tabularS5, LC, RMA {A , F}(A A) (A F) S5A B {T , B}[(A B) B] [(A B) T]LCS4D4510KK422 ()()S4.3D4.334K4.3K.3 ()()GrzInt33GLB ()() : 3 = (A B) (B A)LC = Int + (A B) (B A)

1 1 1 1 : Validity-preserving operations:Generated subframesReductions (p-morphisms)Disjoint unions 1971RM = R + A (A A) 1971RM = R + A (A A) 2008 R2 () 1971RM = R + A (A A) 2008 R2 () 2012 KRKR = R + A & ~A B 1971RM = R + A (A A) 2008 R2 () 2012 KRKR = R + A & ~A B : 1971RM = R + A (A A) 2008 R2 () 2012 KRKR = R + A & ~A B ((A B) ~A) ((A B) B) ((A B) T) ((A B) F) ((A B) t)

: 1971RM = R + A (A A) 2008 R2 () 2012 KRKR = R + A & ~A B ((A B) ~A) ((A B) B) ((A B) T) ((A B) F) ((A B) t)

A B { ~A, B, T, F, t } : 1971RM = R + A (A A) 2008 R2 () 2012 KRKR = R + A & ~A B T = A ~AF = A & ~At = p(p p)((A B) ~A) ((A B) B) ((A B) T) ((A B) F) ((A B) t)

A B { ~A, B, T, F, t } : + KR = R + A & ~A B3 = (A B) (B A)LC = Int + (A B) (B A)A =df (~ A A) KR5 = KR3 + (A t) (T (A A))(A B) =df ~ (A ~ B)[(A B) T] [(A B) F] [(A B) (~A & B)] [(A B) ((~A & B) f)] KR3 S4.3 :. . . - KR3 = KR + A & B (~A & B A)A B {T , F , ~A&B , (~A&B)f }

KR5 KR5 KR3.2 = KR3 + A A + (A B) (( f B) A) KR5 KR3.2 = KR3 + A A + (A B) (( f B) A) KR3.1 = KR3 + [(A (A A)) A] A KR3.5 KR3.2 = KR3 + A A + (A B) (( f B) A) KR3.1 = KR3 + [(A (A A)) A] AA =df (A + A) = (~ A A);A =df (A A) = ~ (A ~ A).f =df ~ t(A B) =df (~ A B).g1gg 1 1 1

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