Symbolic reasoning systems

The primary differences, then, between development of expert systems and more traditional software engineering are found in steps one and two, above. First, the problems chosen will involve symbolic reasoning, and will require the transfer of expertise from experts to a knowledge base. Second, rapid prototyping, the "try it and see how it works, then fix it or throw it away" approach will play an important role in system development. 

First, the application should involve symbolic reasoning. There is no point in trying to develop an expert system to perform numerical calculations, for example, Fourier transforms. 

This paper describes a new approach to building molecular models using methods of expert systems. We are applying symbolic reasoning to a problem previously only approached numerically. The goals of this project were to develop a rapid model builder that mimicked the manual process used by chemists. A further aim was to provide a justification for the model as a chemist would justify a particular conformation. The AIMS algorithm reported here is extremely fast and has a complexity that increases linearly with the number of atoms in the model. 

Third, the developer must determine that the problem is well suited to use of expert system technologies. If the problem is purely algorithmic or procedural in nature, then it can be addressed by conventional technologies more efficiently than by expert systems. If the type of problem requires symbolic reasoning, then the problem may be suitable for expert systems technology. 

The reason why we represent a FSM in terms of its variables rather than its domains (traditionnally called alphabets) is practical this model is the one which is directly implemented in symbolic verification systems. A complete discussion of its correspondance with the model on alphabets can be found in [17]. 

Since biological systems can reasonably cope with some of these problems, the intuition behind neural nets is that computing systems based on the architecture of the brain can better emulate human cognitive behavior than systems based on symbol manipulation. Unfortunately, the processing characteristics of the brain are as yet incompletely understood. Consequendy, computational systems based on brain architecture are highly simplified models of thek biological analogues. To make this distinction clear, neural nets are often referred to as artificial neural networks. 

Entropy is often described as a measure of disorder or randomness. While useful, these terms are subjective and should be used cautiously. It is better to think about entropic changes in terms of the change in the number of microstates of the system. Microstates are different ways in which molecules can be distributed. An increase in the number of possible microstates (i.e., disorder) results in an increase of entropy. Entropy treats tine randomness factor quantitatively. Rudolf Clausius gave it the symbol S for no particular reason. In general, the more random the state, the larger the number of its possible microstates, the more probable the state, thus the greater its entropy. 

A sutmnaty of the above shows various terms used for eaeh type of representation first (maero level, maeroscopic level, macroscopic world), second (sub-micro level, microscopic level, submicro level, submicroscopic level, molecular world, atomic world), and third (symbolic level, sy mbolic world, representational chemistry, algebraic system). In onr view, the system of terminology shonld be both as brief as possible and avoid any possible ambiguities of meaning. Conseqnently, sub-micro and snb-microscopic fall foul of our first criterion for they perhaps imply that snch a level can be seen through an optical microscope. For those reasons, we have decided to nse macro, submicro, symbolic for the individual types and triplet relationship to cover all three. The triplet relationship is a key model for chemical edncation. However, the authors in this book have been fiee to decide for themselves which conventions to use. Nevertheless, it is our intention to promote the terms macro, submicro, symbolic in all subsequent work and to discuss the value of the triplet relationship in chemical education. 

However, it mnst be noted that using this convention, equations for similar phenomena containing current densities mnst always be written in two different ways for anodic currents with the symbol i and for cathodic cnrrents with the symbol 111. For this reason, a mixed system is nsed in the following chapters All cnrrent densities (anodic as well as cathodic) are regarded as positive and denoted by the same symbol, i. In this way the same eqnations containing cnrrent densities can be used for all types of reactions. For the ion flnxes near the snrface of electrodes, the aforementioned signs are preserved (see Chapter 4). 

Since the integral is over time t, the resulting transform no longer depends on t, but instead is a function of the variable s which is introduced in the operand. Hence, the Laplace transform maps the function X(f) from the time domain into the s-domain. For this reason we will use the symbol when referring to Lap X t). To some extent, the variable s can be compared with the one which appears in the Fourier transform of periodic functions of time t (Section 40.3). While the Fourier domain can be associated with frequency, there is no obvious physical analogy for the Laplace domain. The Laplace transform plays an important role in the study of linear systems that often arise in mechanical, electrical and chemical kinetic systems. In particular, their interest lies in the transformation of linear differential equations with respect to time t into equations that only involve simple functions of s, such as polynomials, rational functions, etc. The latter are solved easily and the results can be transformed back to the original time domain. 

For historic reasons a number of different units of measurement have evolved to express quantity of the same thing. In the 1960s, many international scientific bodies recommended the standardisation of names and symbols and the adoption universally of a coherent set of units—the SI units (Systeme Internationale d Unites)— based on the definition of five basic units metre (m) kilogram (kg) second (s) ampere (A) mole (mol) and candela (cd). 

Structure trivial names and Strukturbericht symbols As a conclusion to the presentation of the rational nomenclature and symbolism of the intermetallic phases, it must be mentioned that a number of trivial names and symbols have been used and, due to historical reasons, are still in use both as indicators of a single phase in specific systems, or as descriptors of certain structural types or of families of different interrelated structural types. 

For fitting such a set of existing data, a much more reasonable approach has been used (P2). For the naphthalene oxidation system, major reactants and products are symbolized in Table III. In this table, letters in bold type represent species for which data were used in estimating the frequency factors and activation energies contained in the body of the table. Note that the rate equations have been reparameterized (Section III,B) to allow a better estimation of the two parameters. For the first entry of the table, then, a model involving only the first-order decomposition of naphthalene to phthalic anhydride and naphthoquinone was assumed. The parameter estimates obtained by a nonlinear-least-squares fit of these data, are seen to be relatively precise when compared to the standard errors of these estimates, s0. The residual mean square, using these best parameter estimates, is contained in the last column of the table. This quantity should estimate the variance of the experimental error if the model adequately fits the data (Section IV). The remainder of Table III, then, presents similar results for increasingly complex models, each of which entails several first-order decompositions. 

The names of the elements (and many of the symbols used to represent them) are traditional, rather than part of a logical system. The electrical charges that the ions usually carry can be reasoned out, but chemists do not work through such reasoning every time they want to use the charges or talk about them they simply know them as characteristic properties. 

Alternative technologies should also be considered, and the reasons for not using them should be justifiable. For example, database technology is not the right choice if a task requires reasoning that goes beyond retrieval of stored data based on well-defined criteria. At the same time, many problems that are stated in a symbolic way can be formulated mathematically, and in fact can be better solved numerically. For such problems, knowledge-based systems are not the appropriate answer. 

Figure 7.43. Predicted reaction path for the meteoric diagenetic system of the Floridan aquifer. These reaction path calculations agree reasonably well with observations, as shown by variousl symbols. Reaction path calculations of this nature can be applied to other modern meteoric diagenetic systems, and perhaps, with modifications to ancient systems now removed from original meteoric water. (After Plummer et al., 1983.)...

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