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PRESENTATION Refinery Optimization Using Total Site (Pinch) Technology and Simulation Specification Data Sheets, CHEMPUTERS, Conference and Exhibition of Computer Technology for Chemical Engineers, Houston, TX, 14, 15 February 1996

That will take care of the Manage Consultants view, but you will also need to visit another binding: the popup button on the Journal Entries window. Find that popup now and take a look at its bindings. It has three, shown in Table 9 3:

Notice this more general rule does not require the specific values for Volume and Density that were required by the first rule Instead, it states a more general constraint on the values of these attributes PROLOG-EBG computes the weakest preimage of the target concept with respect to the explanation, using a general procedure called regression (Waldinger 1977) The regression procedure operates on a domain theory represented by an arbitrary set of Horn clauses It works iteratively backward through the explanation, first computing the weakest preimage of the target concept with respect to the final proof step in the explanation, then computing the weakest preimage of the resulting expressions with respect to the preceding step, and so on The procedure terminates when it has iterated over all steps :in the explanation, yielding the weakest precondition of the target concept with respect to the literals at the leaf nodes of the explanation A trace of this regression process is illustrated in Figure 113 In this figure, the explanation from Figure 112 is redrawn in standard (nonitalic) font The frontier of regressed expressions created at each step by the regression procedure is shown underlined in italics The process begins at the root of the tree, with the frontier initialized to the general target concept SafeToStack(x,y) The first step is to compute the weakest preimage of this frontier expression with respect to the final (top-most) inference rule in the explanation The rule in this case is SafeToStack(x, y) t Lighter(x, y), so the resulting weakest preimage is Lighter@, y) The process now continues by regressing the new frontier, {Lighter(x, y)], through the next Horn clause in the explanation, resulting in the regressed expressions (Weight(x, wx), LessThan(wx, wy), Weight(y, wy)} This indicates that the explanation will hold for any x and y such that the weight wx of x is less than the weight wy of y The regression of this frontier back to the leaf nodes of the explanation continues in this step-by-step fashion, finally.

FIGURE 113 Computing the weakest preimage of SafeToStack(0 bj 1, Obj2) with respect to the explanation The target concept is regressed from the root (conclusion) of the explanation, down to the leaves At each step (indicated by the dashed lines) the current frontier set of literals (underlined in italics) is regressed backward over one rule in the explanation When this process is completed, the conjunction of resulting literals constitutes the weakest preimage of the target concept with respect to the explanation This weakest preimage is shown by the italicized literals at the bottom of the figure

ac Consultant for Journal Entry.arrangedObjects ac Consultant for Journal Entry.arrangedObjects.consultantFirstName ac Journal Entry.selection.consultantForEntry

resulting in a set of generalized literals for the leaf nodes of the tree This final set of literals, shown at the bottom of Figure 113, forms the body of the final rule The heart of the regression procedure is the algorithm that at each step regresses the current frontier of expressions through a single Horn clause from the domain theory This algorithm is described and illustrated in Table 113 The illustrated example in this table corresponds to the bottommost single regression step of Figure 113 As shown in the table, the REGRESS algorithm operates by finding a substitution that unifies the head of the Horn clause rule with the corresponding literal in the frontier, replacing this expression in the frontier by the rule body, then applying a unifying substitution to the entire frontier The final Horn clause rule output by PROLOG-EBG formulated as follows: is The clause body is defined to be the weakest preconditions calculated by the above procedure The clause head is the target concept itself, with each substitution from each regression step (ie, the substitution Oh[ in Table 113) applied to it This substitution is necessary in order to keep consistent variable names between the head and body of the created clause, and to specialize the clause head when the