act04ans

Fall CIS Assured programming with formal methods Act. 04 solution ACST Example . With respect to Example 2 . 9 in our text, draw a diagram for the relation J ( Obs ) . Labelallthefeaturesinthediagramtofullydescribethestructure. Discuss, foreachgivenpropo- sitions, when will it be true with respect to the model. Note : The Kripke model in this example is h W 2 , I 2 , J 2 i , where W 2 = { A , B , C , D } and the primiti- ive propositions are p , q , r and s . The interpretation function I is defined via the following: I 2 ( p ) = { A , C } , I 2 ( q ) = { A , B , D } , I 2 ( r ) = ∅ , I 2 ( S ) = { A , B , C , D } . In addition, there is an observer Obj (a primitive principal) where J 2 ( Obj ) = {( A , A ) , ( B , B ) , ( C , D ) , ( D , D )} . Answer Let M 29 = h W 2 , I 2 , J 2 i be the model. The graph of the relations J (Obs) is shown below: Figure : The graph of the relation J ( Obs ) Remark Table 2 . 2 given in the supplement (select from ACST) illustrates that two different observers can have different “perceptions” in the model. For example, one’s view is specified according to the x = 0 column whereas another’s view is specified by x = 1 column. Andrew C. Lee EECS Dept, Syracuse University