Inference rule application

Using frameworks to define the meaning of the very modeling constructs themselves— and even to define and encapsulate known inference rules—is very similar to the approach in Larch [Guttag90], Their application to Catalysis modeling constructs, UML stereotype-based extension, and new modeling constructs and notations is described in [D Souza97a],... 

ABSTRACT Smart structures usually incorporate some control schemes that allow them to react against disturbances. In mechanics we have in mind suppression of mechanical vibrations with possible applications on noise and vibration isolation. A model problem of a smart beam with embedded piezoelectric sensors and actuators is used in this paper. Vibration suppression is realized by using active control. Classical mathematical control usually gives good results for linear feedback laws under given assumptions. The design of nonlinear controllers based on fuzzy inference rules is proposed and tested in this chapter. 

Fuzzy inference rules systematize existing experience, available in terms of linguistic rules, and can be used for the realization of nonlinear controllers. The feedback is based on fuzzy inference and may be nonlinear and complicated. Knowledge or experience on the controlled system is required for the application of this technique. Since the linguistic rules are difficult to be explained and formulated for multi-input, multi-output systems, most applications are based on multi-input, single-output controllers. 

There are very many statements tliat are provably true and hence have the status of theorems within the knowledge repository. All of these are built by applying the inference rule to unproven data statements and proving their correctness by resolution. Tliese theorems are later used to support correctness reasoning about tlie specification of tlie application when it is presented. 

Tlie inference rule can now be applied to the specification data for the application being specified and, as before, tlie correctness of each offered tuple is proved by resolution (now with reference to all the compiler tlieorems, used as lemnias) prior to being included in tlie repository. As before, tlie repository now includes a representation of the application tlie compiler could be removed because every proof that might require to reference tliis knowledge will instead reference a lower-level tlieorem, preserved as an application lemma, in the repository. 

In each step in tliis multi-level process, the inference rule essentially activates what has previously been built. Tlierefore, if the last build was the appUcation specification, we can offer data (since that is what the application expects), and activate tlie application with tliat data, using the inference rule. Tliis will illustrate the functional behaviour actually captured in the specification, which may or may not be the same as eitlier what tlie specifier intended or wliat the client wanted There is an analogy to testing tlie correctness of a program with data, but here it is tlie correctness of the behaviour defined by tlie specification tliat is being tested by reasoning tliat is, without any code having been written. 

If the application compilation completes without error, tlien the inference rule can be applied to tlie animation data for tlie application. As before, tlie correctness of each offered data tuple can be proved by resolution prior to being included in the repository. This is the final animation step. Each proof may refer to any of the application tlieorems, used as lemmas. At tliis stage, of course, we do not attempt to remove tlie representation of the application. Because tlie same process is used, only the data being different, even the animation is provable and traceable back to the rule of inference and the original axioms tlirough tlie sequence of intermediate proof steps and leimnas. 

Generalize into properties, if possible, the examples where X is of a size equal to or less than some integer n, where n is the largest size where this leads to properties without recursion and without redundancy of information. Set m to A2 + d, where d is the decomposition decrement. The most useful generalization technique is the maximally repeated application of the replacing-a-constant-by-a-variable inductive inference rule to an example this often requires a subsequent specialization by introduction of a body to the resulting unit clause. 

Rules seemingly have the same format as IF.. THEN.. statements in any other conventional computer language. The major difference is that the latter statements are constructed to be executed sequentially and always in the same order, whereas expert system rules are meant as little independent pieces of knowledge. It is the task of the inference engine to recognize the applicable rules. This may be different in different situations. There is no preset order in which the rules must be executed. Clarity of the rule base is an essential characteristic because it must be possible to control and follow the system on reasoning errors. The structuring of rules into rule sets favours comprehensibility and allows a more efficient consultation of the system. Because of the natural resemblance to real expertise, rule-based expert systems are the most popular. Many of the earlier developed systems are pure rule-based systems. 

The user interface, the interpreter, and the inference engine together comprise the ES shell or a skeletal system. As these components are largely independent of the specific application, all that is needed to create a working ES from the shell is to feed it with rules and facts. 

The proof that —— Ag a (y2 0) 41,42,43 Ag is even longer so we shall skip several formal steps which are purely applications of rules of inference of the propositional calculus with identity. We start working back by ... 

General rules are not easy to infer from the existing literature, especially concerning particle production, since most of the fiterature reports deal only with genetic requirements for particle formation and have not investigated the effect of nutrient levels on particle productivity. Also, in most of the cases the process was not intended for industrial application, and the use of serum containing medium at laboratory scale is still ubiquitous. 

Fuzzy Logic Control The application of fuzzy logic to process control requires the concepts of fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form... 

On the basis of the state correlation diagram depicted in Figure 1, which connects the different stereoisomers of the pentacoordinate fragment [Rh(NH3)4Cl] +, Vanquickenbome etal. infer the main characteristics of the complicated photochemical mechanism in [Rh(NH3)4Cl2]+ and related complexes. This work gave the first evidence that the formulation of electronic selection rules was underlying the photosubstitution mechanism in d and d complexes. In principle, this idea was applicable to any complex with any coordination number. However, at this stage the... 

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