Optimal CSP OCSP=<Y, g, CSP> Decision variables y with domain d Utility function g(Y:Dy→>界 CSP is over variables <XY> Find Leading arg max g(Y) Y∈by st.3XE Dyst C(X,Y)is True Frequently we encode C in propositional logic e g0 is a multi-attribute utility function that is preferentially independent 3/17/2004 copyright Brian Williams, 2002 CSP Frequently in Propositional Logic (mode(E1)=ok implies ( thrust(E1)=on if and only if flow(V1)=on and flow(V2)=on))and (mode (E1)= ok or mode (E1)= unknown) and not(mode(E1)=ok and mode(E1)=unknown) V1 V2 E1 copyright Brian Williams, 20023/17/2004 copyright Brian Williams, 2002 5 Optimal CSP OCSP= <Y, g, CSP> ƒ Decision variables Y with domain DY ƒ Utility function g(Y): DY → ℜ ƒ CSP is over variables <X,Y> Find Leading arg max g(Y) Y ∈ Dy s.t. ∃ X ∈ DY s.t. C(X,Y) is True Î Frequently we encode C in propositional logic Î g() is a multi-attribute utility function that is preferentially independent. 3/17/2004 copyright Brian Williams, 2002 6 CSP Frequently in Propositional Logic (mode(E1) = ok implies (thrust(E1) = on if and only if flow(V1) = on and flow(V2) = on)) and (mode(E1) = ok or mode(E1) = unknown) and not (mode(E1) = ok and mode(E1) = unknown) E1 V1 V2