Logical representation

Thus, the conversion from a logical representation to a probability representation follows naturally from superposition and the von Misesian definition of probability. Simply replace tlie component identifier by its failure probability and combine probabilities according to the logical operations. 

Figure 28.3 Fuzzy logic representation of the disintegration time of a tablet as Low or High.

By substituting Eq. (9) into Eq. (10), one obtains three simultaneous equations with three unknowns which can be solved numerically. The power series representation of the three values of W y can be approximated in several ways. For systems with only one acid component (c.g, silica) and with the remaining components being basic, a logical representation is the asymmetric approximation. If we choose SiO2 to be component 1, then we set... 

Pyrolysis of fumarophycine (178) is reported to give the enamine (179), although expression (179a) may be a more logical representation of the product since an aziridinium ion intermediate must again be involved. 

A managed object is a logical representation of an element of hardware or software that the management system accesses for the purpose of monitor and control. 

Special care was taken to deliver a complete logical representation of chemical thermodynamics. As far as possible, derivations for the particular relationships have been provided to ensure a proper understanding and to avoid mistakes in their application. Many of these derivations have been put into the Appendix in order not to interrupt the flow of the text. 

A fault tree is a logical representation of the relationship or primary events that may cause the occurrence of a specified undesirable event, known as the top event, and it is depicted using a tree structure with normally OR and AND logic gates. The method is described in detail in Ref. [9], and an extensive list of publications on the method is available in Ref. [38]. 

Besides the mentioned advantages it should be noted that the creation of an appropriate logical representation of the product model is usually not a trivial task. It needs a lot of experience in the field of formal logic and their respective analyzing procedures. Furthermore, a gap remains between the real world product and the specified formal model. This gap can only be bridged with the help of the domain experts who should provide a crucial support within this first phase. 

Feature diagrams are a formal representation of product data with a precise semantics. Consequently, they define a unique mathematical model of the product data that consists of the hierarchical structure and additional logical formulas that specify the properties and links to aU product parts. The analyzing procedures presented here operate on purely logical representations of the product data. As a consequence, the structure and content of a feature diagram have to be transformed into an equivalent representation in logic. 

Based on the logical representation of the products, the wire harnesses, the costs and the expected sales, the optimization engine computed a set of cost-optimized wire harnesses, i.e. the optimality can be proven mathematically. Because of the... 

FIGURE 37.4 Logical representation of the algorithm of the modehng procedure. 

Fault tree analysis (FTA) provides a logical representation of many events and component failures that may combine to cause one critical event (e.g., pipeline explosion). It uses logic gates to show how basic events may combine to cause the critical top event. The top event would normally be a major hazard such as "pipeline SCC" as in the example shown in Fig. 12.10. The most commonly used tree symbols and gates used in the construction of fault trees are illustrated in Fig. 12.11 and briefly described here [12] ... 

Event tree analysis (ETA) is a logical representation of the various events that maybe triggered by an initiating event (e.g., a component failure). It uses branches to show the various possibilities that may arise at each step and it is often used to relate a failure event to various consequence models. It may also be used to quantify system-failure probabilities, where several contributory causes can only arise sequentially in time. 

A risk model often comprises a formal logical representation of the system. Fault- and event tree analysis is often building blocks in such a representation. Barriers, safety functions and/or layers of protection are typically represented by basic events. Probabilities are assigned to the outcome of the basic events, i.e., success or failure. A wide range of factors and conditions will influence the outcome of the basic events, and these need to be taken into account when assigning the basic event probabili-... 

The basic building blocks of a BCS are objects, which are logical representations of physical (computing and communicating) entities. An object is typed but not addressed (i.e., without an individual identifier we leave addressing to the lower-level (network) implementation). For instance, when a person is seriously sick, we care about whether a helicopter will come instead of which helicopter will come, under the simplest assumption that all helicopters share the same type helicopter. 

Convert the local models and their instances (containing the actual parameters of a design model) into a Frame-logic representation,... 

We will use the physical representation g/e) whenever implementation dependent properties of QCs based on atomic qubits are discussed. The logical representation will be used for considerations where the specific implementation is not relevant. The classical case would correspond to the situation that the qubit is prepared in one of these states. Therefore we will call the basis states 0) and 1) also classical basis states. However, quantum mechanically we can think of having the qubit in any arbitrary quantum superposition of the two basis states ... 

The experimental phase diagrams of oligomer systems will be discussed in the third part of this book. This part of the monograph has its own tasks so we ll concentrate on some general statements necessary for a logical representation of the data below. 

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