# 第十九章 谓词逻辑

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. 1 . 0 3: x 1 ,x 2 0 c 1 3() f 1 (1) ,f 1 (2) f 2 (1) R 2 (1) R 2 (1) (f 2 (1) (f 1 (1) (x 1 ),f 1 (2) (x 2 )),c 1 ) - PowerPoint PPT Presentation

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• 1 03:x1,x20c13()f1(1),f1(2)f2(1)R2(1)R2(1)(f2(1)(f1(1)(x1),f1(2)(x2)),c1)x1,x2x1,x20x1,x20

• (1)(2)

• 19.1:X={x1,,xn,}xiC= {c1,,cn,}ci

• T(1)=,Tn={fni|ar(fni)=n}|Tn|0(|T(1)|0),19.1XCT(1)-IT(1)=I=XCT(1)I=, I0=XC(T0=)I1={(f1i,xj)|f1iT1,xjX}{(f1i,cj)|f1iT1,cjC} (f2i,xj,xk)|f2iT2,xj,xkX} (f2i,xj,ck)|f2iT2,xjX,ckC} (f2i,cj,xk)|f2iT2,xkX,cjC} (f2i,cj,ck)|f2iT2,cj,ckC} (fki,y1,y2,yk)|fkiTk,yiXC}

• nInIfki:IkIfki(a1,,ak)=(fki,a1,,ak)ajI (j=1,,k)fkiIik19.2:XCT(1)-IIIfniinXC,T(1)I

• C=,T=({f11,f21|ar(f11)=1, ar(f21)=2,I0I1I2

• 19.3:R=RnnRn ={Rni|ar(Rni)=n}19.4:RniRnRInRni(t1, ,tn)I(R0i),t1, ,tnI,RniinRIIYYC=, T(1)=,R=R0(R00)

• A={1,,100}A0.ciiR2iR2i(c1,0)R2i(c100,0)AxR2i(x,0)x

• :xxxR2i(x,0)xyR2i(y,0)xp(x)q(x)x (p(x)q(x))A={-2,-1,0,1,2},A0ciiR2(1)R2(1)(c-2,0)R2(1)(c-1,0)R2(1)(c0,0) R2(1)(c1,0)R2(1)(c2,0)

• AxR2(1)(x,0)xxxxR2(1)(x,0)xyR2(1)(y,0)xp(xp(x))x(p(x))

• xxx=xYP(Y) {F, }-Xxx:P(Y)P(Y)

• 19.5:() Y={Rn(t1, ,tn)|RnR,tiI, 1i n}{F,,x|xX}P(Y)P(Y)P(Y)F0x

• Fxx, ,

• 19.6:q=xp()pxpxxqpqxqxqxqxq qvar(q)var(q)=qqx

• AP(Y)Avar(A):(1)x(R11(x)yR21(x,y))(2)x(xR11(x)R21(x,y))R22(x,y):(1),yR21(x,y)xR11(x)yR21(x,y)xyxy,

• (2)x(xR11(x)R21(x,y))R22(x,y)(2)xR11(x)xxR11(x)R21(x,y)

• 19.7:p(x)P(Y)xt(z)z txpztpxtpxtp(x)xp(t(z))zpxpzzp(t(z))tpx,

• :x1R21(x1,x2)x3R22(x3,x1)f21(x1,x3)x1,x2f22(x2,x3)x1x2x2x1x1x2

• :p(x)pP(Y)()p(x)xp(x)xp(t)tp(x)xp(x2)=x1R21(x1,x2)x3R22(x3,x1)p(f22(x2,x3))=x1R21(x1, f22(x2,x3)) x3R22(x3,x1)p(x1)=x1R21(x1,x2)x3R22(x3,x1)p(f11(x2))=x1R21(x1, x2)) x3R22(x3,f11(x2))

• 19.8pP(Y)pd(p)l(p)(i)d(F)=l(F)=d(q)=l(q)=0qP(Y)(ii)d(p1p2)=max{d(p1),d(p2)} l(p1 p2)=1+max{ l(p1),l(p2)}

• :P256 1,2,6,7,8

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