作业_7

作业_7 -...

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Unformatted text preview: 200628017029197 0 1. W={x1, x2, x3, x4, x5, x6} 0 R0 R(x1, x2), R(x1, x3), R(x2, x2), R(x2, x3), R(x3, x2), R(x4, x5), R(x5, x4), R(x5, x6) 0 L0 X x1 x2 x3 x4 x5 x6 { p} L( X ) {q} { p, q} { p} {q} {φ} p ; x5 ªo ¸ RcØr x cWo ª ¸o x5 q ; x5 y ∈W ( p ∨ q) R ( x5 , y ) 0 R ( x5 , x 4 ) x R ( x5 , x 6 ) 00 00 x4 x6 px qx qx px x5 x4 x6 x5 q; p 0 0 x4 0 x6 0 ( p ∨ q) ( p ∨ q) x5 ( p ∨ q) (SET)T ª ¸ o c. B0 U0 OI c 6 » zE PI c 6 » zE @ @ PIN0 Vª W ¸o o ~ V˜c cª No h » Ào ¸ , 2. d n SET ˜c cª Ko ~» h N áÀ o ¸ Kc» {Õ á c» ª á À· « OKc» {Õ á c» ª Iá À· « » h ˜c cª No ~ Ào ¸ 0 U0 Cert (U , PK U , t , σ ) {K UV }PK V {OI , h( PI )}K UV {K UB }PK B {PI , h( OI )}K UB σ ( SK U , h( OI ) , h( PI ) ) ¸h d o .ªc K UV x U 0 Vo ø-ªc ¸ σ ( SK U , h( OI ) , h( PI ) ) h( OI ) , h( PI¸ )o Ø-ªc 200628017029197 c »}~ N Vc»} ~ N cªK ¸ Ð c»}h ˜ áÀ k p~ U ¸ dX Ñ V Believes U said OI J0 U ¸ dX Ñ V Believes V canprove ( U said OI) to J cª ¸ CA˜ Ðk J0 CA 8 P sees Cert ( U , PK U , t , σ ) ⇒ P Believes U U V0 P Believes( J sees Cert ( U , PK U , t , σ ) ) ⇒ J Believes g Ò 0 match g mx h(m)0 match(m, h(m)) = true ª ¸Ð k H 0 ª ¸ Ð Hkc ª ¸ Ð m Hc k ª ¸ Ð h Hc k h(m)0 mx A Has m : A x : g (1)k ˜ªc ¸Ð (a) 0 : B1 : B2 : P ( sees Cert (U , PK U , t , σ ) ) ⇒ P Believes P Believes ( J sees Cert (U , PK U , t , σ ) ) U ⇒ P Believes ( J Believes B3 : B4 : U) ( P said x ) ∨ ( P sees x ) ⇒ P has x P Believes x ∧ ( x ⇒ y ) ⇒ P Believes y BAN g g Kailar 0 Kailar P Believes x ⇔ P CanProve x to P P CanProve x to P ∧ ( x ⇒ y ) ⇒ P CanProve y to P Kailar 0 cª BAN ˜ ¸Ðk P CanProve y to P ⇔ P Believes y cª ¸ Ð η k c(b)k H ª¸ Ð : B4 : P Believes x ∧ ( x ⇒ y ) ⇒ P Believes y C1 V Believes V U 200628017029197 C2 V Believes (U said h(m) ) ∧ V has m ∧ match(m, h(m)) ⇒ V Believes (U said m ) C3 V Believes ( J has h( Cert (U , PK U , t , σ ) ) ) ∧ J received Cert (U , PK U , t , σ ) ⇒ V Believes ( J sees Cert (U , PK U , t , σ ) ) (2) 0 ① V Believes ( U said OI ) 0 message-meaning rules R1 x C1 x D1 : V Believes (V U ) ∧ V sees { OI , h( PI )} K UV ⇒ V Believes (U said { OI , h( PI )} ) 0 belief rules R15 x D1 x V Believes (U said OI ) ② V Believes ( V CanProve (U said OI ) to J ) Kailar c»cª}˜h l €Ð ¸ ~À 5 cª ¸ Õ ” X c V x ª l ¸ ˆÐ “ Ü g ” A CanProve x to B c» }~ N Ax Bx cª ¸ x ¨” Õ x y ( y ≠ x )0 Bx Ax Bx J Believes (U said OI ) V → J : Cert (U , PK U , t , σ ) , Cert (V , PK V , t , σ ) −1 J → V : { h( Cert (U , PK U , t , σ ) )} PK J , Cert ( J , PK J , t , σ ) V → J : {{ OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J } PK V −1 J → V : {{ h( OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) ) )} PK V } PK J B1 x D2 : D3 : J sees Cert (U , PK U , t , σ ) ⇒ J Believes J sees Cert (V , PK V , t , σ ) ⇒ J Believes −1 U V 200628017029197 D4 : V sees Cert ( J , PK J , t , σ ) ⇒ V Believes J x message-meaning rules R2 x D4 x D5 : V sees { h( Cert (U , PK U , t , σ ) )} PK J −1 ⇒ V Believes ( J said h( Cert (U , PK U , t , σ ) ) ) x B3 x D5 x D6 : J said h( Cert (U , PK U , t , σ ) ) ⇒ J has h( Cert (U , PK U , t , σ ) ) B4 x D5 x D6 x D7 : V Believes ( J has h( Cert (U , PK U , t , σ ) ) ) x C 3 x D7 x J received Cert ( U , PK U , t , σ ) x D8 : x B2 x D8 x V Believes ( J sees Cert (U , PK U , t , σ ) ) D9 : P Believes ( J Believes U) x seeing rules R10 x D3 x D10 : J sees {{ OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J } PK V −1 ⇒ J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J seeing rules R9 x D11 : J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J ∧ J Believes J ⇒ J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} seeing rules R6 x D11 x D12 : 0 B3 x D12 x J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} ⇒ J sees OI D13 : J sees OI ⇒ J has OI 200628017029197 0 seeing rules R6 x D11 x D14 : J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} ⇒ J sees σ ( SK U , h( OI ) , h( PI ) ) B1 x B4 x D8 x D15 : V Believes ( J sees Cert (U , PK U , t , σ ) ) ⇒ V Believes ( J Believes U) x cª 3”. ˆ ¸Õ Kripke P W0 ª ¸ ÕR ˆ ” L0 200628017029197 e d q a c p, q p, q b W= { a , b , c , d , e } 0 p R0 R( a , b ), R( a , e ), R( b , c ), R( b , e ), R( e , e ), R( d , d ) L0 0 X a b c d e L( X ) { p, q} { p} { p, q} {q} {φ} ...
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