作业_70

作业_70 -...

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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 ª š¹ R>cy x cf >¹ ªš 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 fÈ ( p ∨ q) (SET)8c ª¹>š B0 U0 OI n E Ñ z PI n E Ñ z @ @ PIN0 V> ª š f ¹ 6 Vª ˜8nH ¹ > š P ác , 2. SET ª ˜8nH ¹ > š P 6 á ´c ˆ ´ ˆ ª H¸c A náA n • Oˆ ª I H¸c A ´ náA n • 6á cª ˜8nH ¹ > š P 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 ) ) ¹ h Xšªc > K UV x U 0 V> d ¹ šªc σ ( SK U , h( OI ) , h( PI ) ) h( OI ) , h( PI¹ )> W šªc L 8 àn V0 Uh · P¶ 200628017029197 Vf6 nà ´ cªˆ H ¹ nf6 ˜ R × á• V Believes U said OI J0 U ¶µ { ð V Believes V canprove ( U said OI) to J cª ¹ CA¸ R× J0 CA 8 P sees Cert ( U , PK U , t , σ ) ⇒ P Believes U U P Believes( J sees Cert ( U , PK U , t , σ ) ) ⇒ J Believes W W 0 match W mx h(m)0 match(m, h(m)) = true ª ¹R × h W (1)× hªc ¹R (a) 0 ª ¹ R m hc × : : ª ¹ R h hc × h(m)0 B1 : B2 : P ( sees Cert (U , PK U , t , σ ) ) P Believes U P Believes ( J sees Cert (U , PK U , t , σ ) ) P Believes ( J Believes U) U) B3 : B4 : B5 : cª(b)× ˜ ¹R P Believes U P Believes (U Believes z) P Believes x ∧ P Believes y ∧ ( x, y P Believes x ∧ ( x : P Believes z z) P Believes z C1 C2 V Believes V U J Believes (U said h(m) ) ∧ J sees m ∧ match(m, h(m)) J Believes (U said m ) C3 (2) 0 V Believes (V sent x to J ) V Believes ( J sees x ) ① V Believes ( U said OI ) 0 message-meaning rules R1 x C1 x 200628017029197 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 n 6˜áU cf ¹H ` ªP ` cª ¹ R Ù x c V x ª ` ¹ XU “ N 3 ” A CanProve x to B 6à nf Ax Bx cª ¹ x x` U x y ( y ≠ x )0 Bx Ax Bx J Believes (U said OI ) V → J : Request, Cert (U , PK U , t , σ ) , Cert (V , PK V , t , σ ) J → V : Cert ( J , PK J , t , σ ) V → J : {{ OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J } PK V −1 B1 x D2 : D3 : D4 : J sees Cert (U , PK U , t , σ ) J sees Cert (V , PK V , t , σ ) V sees Cert ( J , PK J , t , σ ) J Believes J Believes V Believes U V J x V → J : Cert ( U , PK U , t , σ ) , Cert ( V , PK V , t , σ ) x D5 : V Believes ( J sees { Cert (U , PK U , t , σ ) , Cert (V , PK V , t , σ )} ) x B5 x seeing rules R6 x D5 x D6 : D7 : x B 2 x D6 x V Believes ( J sees Cert (U , PK U , t , σ ) ) V Believes ( J sees Cert (V , PK V , t , σ ) ) D8 : P Believes ( J Believes U) 200628017029197 0 B 2 x D7 x D9 : P Believes ( J Believes V) −1 x V → J : {{ OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) ) } PK J } PK V D10 : V Believes J sees {{ OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J } PK V −1 B4 x seeing rules R10 x D10 x D9 x D11 : V Believes ( J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} PK J ) B3 x D4 x V Believes ( J Believes J) J) x ( ) x B4 x seeing rules R9 x D11 x V Believes ( J Believes D12 : V Believes ( J sees { OI , h( PI ) , σ ( SK U , h( OI ) , h( PI ) )} ) B5 x seeing rules R6 x D12 x D13 : V Believes ( J sees OI ) D14 : V Believes ( J sees {σ ( SK U , h( OI ) , h( PI ) )} ) B4 x seeing rules R10 x D8 x D14 x D15 : V Believes ( J Believes (U said { h( OI ) , h( PI )} ) ) 0 B5 x belief rules R15 x D15 x D16 : V Believes ( J Believes (U said { h( OI )} ) ) 0 C2 x J Believes (U said { h( OI )} ) ∧ J sees OI ∧ match(OI , h(OI )) J Believes (U said OI ) 0 B4 x D13 x D16 x V Believes ( J Believes (U said OI ) ) 200628017029197 0 Kailar “m¨ ” A CanProve x to B 6à nf V Believes (V CanProve (U said OI ) to J ) 0 3Œ.ª 8¹ Qc Kripke 8˜ W. ª ¹ QR8 Œ L. e d q a c p, q p, q b * ª ¹Q Œ 8 0 p W= { a , b , c , d , e } 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} 0 4acª (¹ U. EG ( p ) 200628017029197 p s0 cª ¹ S ³ ¸ 6.2.3 0 p s1 Kripke 0 p s2 s3 EG ( c ª Þ )¹ 8R p i = 1 x y 1 ( true ) = p ∧ EX ( true ) = p 0 p x S1 = { s 0 , s1 , s 2 } i = 2 x y 2 ( true ) = 0 i = 1 x y 1 ( true ) = p ∧ EX ( true ) = p 0 p x S1 = { s 0 , s1 , s 2 } i = 2 x y 2 ( true ) = y ( y ( true ) ) = y ( p ) = p ∧ EX ( p ) 0 EX ( p ) x { s0 , ¹ sS1 }³ (ª S 2 = { s0 , s1 , s 2 } ∧ { s 0 , s1 } = { s 0 , s1 } i = 3 x y 3 ( true ) = y y 2 ( true ) = p ∧ EX ( p ∧ EX ( p ) ) 0 EX ( p ∧ EX ( p ) ) x ( ) { s0 } x S 3 = { s 0 , s1 , s 2 } ∧ { s 0 } = { s 0 } i = 4 x y 4 ( true ) = y y 3 ( true ) = p ∧ EX ( p ∧ EX ( p ∧ EX ( p ) ) ) 0 ( ) EX ( p ∧ EX ( p ∧ EX ( p ) ) ) S3 = S4 { s0R }Þ 8ª ¹ S 4 = { s0 , s1 , s 2 } ∧ { s 0 } = { s 0 } EG¹ ( R pÞ )c 8ª Kripke¹ 0Þ f cª R S 3 = { s0 } ...
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This note was uploaded on 10/20/2009 for the course CS G22 taught by Professor Sam during the Fall '06 term at Academy of Art University.

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