Variable value

Rules may represent either guidelines based on experience, or compact descriptions of events, processes, and behaviors with the details and assumptions omitted. In either case, there is a degree of uncertainty associated with the appHcation of the rule to a given situation. Rule-based systems allow for expHcit ways of representing and dealing with uncertainty. This includes the representation of the uncertainty of individual rules, as weU as the computation of the uncertainty of a final conclusion based on the uncertainty of individual rules, and uncertainty in the data. There are numerous approaches to uncertainty within the rule-based paradigm (2,35,36). One of these approaches is based on what are called certainty factors. In this approach, a certainty factor (CF) can be associated with variable—value pairs, and with individual rules. The certainty of conclusions is then computed based on the CF of the preconditions and the CF for the rule. For example, consider the foUowing example. 

The entries in the table are arranged in order of increasing reaction coordinate or distance along the reaction path (the reaction coordinate is a composite variable spanning all of the degrees of freedom of the potential energy surface). The energy and optimized variable values are listed for each point (in this case, as Cartesian coordinates). The first and last entries correspond to the final points on each side of the reaction path. 

Record—The elements (fields) may be of different types and may be accessed at random fields and their types are assigned at declaration and may not be changed field values are assigned as are variable values. 

The observation of dependent variable values (in functional experiments this is cellular response) as they happen (i.e., as the agonist or antagonist binds to the receptor and as the cell responds) is referred to as real time. In contrast, a response chosen at a single point in time is referred to as stop-time experimentation. There are certain experimental formats that must utilize stop-time measurement of responses since the preparation is irreparably altered by the process of measuring response. For example, measurement of gene activation through reporter molecules necessitates lysis of the cell. Therefore, only one... 

A strict kinetic limitation based on the gas-phase reactant can be modeled using a variable value for h although experience shows that a first order rate expressions with n=l often provides an excellent fit to experimental data regardless of the underlying reaction mechanism. A site-competition model such as Equation (10.12) can also be used. 

Turbulent flame-front regime. Eddy-like contortions of fhe flame preheaf and burned gases zones give rise to "ouf of fronf" islands and peninsula sfructures of intermediate progress variable values. Scalar transport becomes gradient-like. 

Because the independent variable values are fixed for the problem, we may simplify notation by looking at u as a function of the variable 0 From now on we will therefore write u(X, 0) as u(0). 

Our ability to make these distinctions rests on the fact that we know the direction that the branching generation imposes on the updating of the variables. If we were not solving the problem in such a way that all the variables are explicitly determined by the branching, then these distinctions would not be so clear. For example, if some variable values were the result of solving an auxiliary linear program that involved these constraints, we could not classify the variables this way. 

The last step in the preceding argument, the use of our knowledge about flowshop scheduling, turns what had been a mainly syntactic criterion over the tree structure of the example, into a criterion based on state variables of (jc, y). The state variable values, the completion times of the various flowshop machines, are accessible before the subtrees beneath jc and y have been generated. Indeed, they determine the relationships between the respective elements of the subtrees (jcm, yu). If we can formalize the process of showing that the pair (jc, y) identified with our syntactic criterion, satisfies the eonditions for equivalence or dominance, wc will in the process have generated a new equivalence rule. 

In Section II, we presented the computational model involved in branching from a node, cr, to a node aa,. In this model, it was necessary to interpret the alphabet symbol a, and ascribe it to a set of properties. In the same way, we have to interpret o- as a state of the flowshop, and for convenience, we assigned a set of state variables to tr that facilitated the calculation of the lower-bound value and any existing dominance or equivalence conditions. Thus, we must be able to manipulate the variable values associated with state and alphabet symbols. To do this, we can use the distinguishing feature of first-order predicates, i.e., the ability to parameterize over their arguments. We can use two place predicates, or binary predicates, where the first place introduces a variable to hold the value of the property and the second holds the element of the language, or the string of which we require the value. Thus, if we want to extract the lower bound of a state o-, we can use the predicate Lower-bound Ig [cr]) to bind Ig to the value of the lower bound of cr. This idea extends easily to properties, which are indexed by more than just the state itself, for example, unit-completion-times, v, which are functions of both the state and a unit... 

Notice that the left-hand side of this rule contains two types of clauses. The first type is the variable values of the current state and those necessary to compute the new state, while the second, represented by = computes the value of the variable in the new state. This last clause enables the procedural information about how to compute the state variables to be attached to the reasoning. We must, however, be careful about how much of the computation we hide procedurally, and how much we make explicit in the rules. The level to which computation can be hidden will be a function of the theories we employ to try to obtain new dominance and equivalence conditions. If we do not hide the computation, we will be able to explicitly reason about it, and thus may find simplifications or redundancies in the computation that will lead to more computationally efficient procedures. 

The second type of implications involve clauses with the same state on the left- and right-hand sides of the implication, indicating the derivation of a state variable value from other variables in the state. 

This explicit inclusion of operationality allows us to declare explicitly some facts about the pair (x, y), such as their state variable values, as operational. This will not permit the explanation to stop at other partial solutions, whose states have not been declared operational thus we will use this approach. 

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