Syntactic generalization

In Section 7.2.1, we define a criterion for comparing logic algorithms in terms of generality. Since verifying this criterion is only semi-decidable, we introduce, in Section 7.2.2, a sound approximation of it, namely syntactic generalization. 

Intuitively, LAi(r) is less general than LA2(r) iff Bi is less often true than B2, More formally  

Being semantically more general ( ) is defined dually. Two logic algorithms, each more general than the other, are semantically equivalent (=). We use for and.  

Note that a semantic generalization relationship between two logic algorithms does not amount to a logical implication relationship between them. 

Comparing logic algorithms in terms of semantic generality can be a difficult task, and is only semi-decidable anyway. We thus define a particular case of this generality relation in terms of purely syntactic criteria. 

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Fig, 23. (a) The raw data of three distinct records and (b) their corresponding syntactic generalizations. (Reprinted from Bakshi and Stephanopoulos, Representation of Process Trends, Part IV, Computers and Chemical Engineering, 18(4), p. 303, Copyright (1994), with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB. UK). 

Let s first define syntactic generalization over conjunctions of literals, and then over logic algorithms ... 

Let us now relate the refinement operator gen to the syntactic generality relation ... 

Syntactic Cellular Polymers. Syntactic cellular polymer is produced by dispersing rigid, foamed, microscopic particles in a fluid polymer and then stabilizing the system. The particles are generally spheres or microhalloons of phenoHc resin, urea—formaldehyde resin, glass, or siUca, ranging 30—120 lm dia. Commercial microhalloons have densities of approximately 144 kg/m (9 lbs/fT). The fluid polymers used are the usual coating resins, eg, epoxy resin, polyesters, and urea—formaldehyde resin. 

Test results provides the hypothesis that syntactic foam is rate insensitive and that the static uniaxial strain stress-strain curve actually represents the general constitutive relation. Disagreement between the experimental data and the predicted behavior is greatest at low stresses (1 kbar) where experimental stresses are about double those predicted analytically. The discrepancy decreases at the higher stress levels and virtually disappears at and beyond 7 kbar. This range... 

Syntactic foams are obtained by mixing hollow micro- or macro-balloons, generally made of glass but sometimes of polymer, directly with a liquid resin, generally a thermoset. Some extend this definition to all composites with a foamed core. 

Syntactic foamed materials are classified as foamed plastics because they are formally similar in structure to cellular gas-expanded plastics in that they are heterophase, gas-solid systems. In general, however, they differ from ordinary foamed plastics in that they are not binary but tertiary systems because the filler and binder are made usually from different materials 3 5). 

Soviet scientists have developed a cold-cure EDS material87). Note that the epoxy binders used are in fact generally hot-cure oligomers (from the point of view of the functional groups used and the completion of cure). It turned out that the forced elastic limit and the compression elastic modulus of the matrix are the same for both hot and cold cures. The good mechanical properties of a cold cured syntactic foam seem to be due to strong intermolecular bonds. 

Syntactic foamed plastics are generally three component systems. For example, a syntactic system with 60% glass microspheres (bulk density of 300 kg/m3) consists... 

In general, the thermal conductivity of syntactic foams is the same as that of conventional chemical foamed polymers of the same apparent density 8> 115). 

In order to improve the properties of gas filled, particularly of syntactic, foams, a general theory covering their deterioration and deformation should be developed, along with continued technological research. The absence of reliable techniques for... 

The mechanical parameter of a highly filled syntactic foam must in general be analyzed taking into account the interactions at the binder—filler interface and the system s stresses since both of these factors are important for highly filled systems 8 W0). 

It is easy to see that these models are all based on the same (microstructural) principle, viz. that there is an elementary structural unit that can be described and then used for calculation. Remember that the corresponding unit cell for foamed polymers is the gas-structure element8 10). Microstructural models are a first approximation to a general theory describing the deformation and failure of gas-filled materials. However, this approximation cannot be extended to allow for all macroscopic properties of a syntactic foam to be calculated 166). In fact, the approximation works well only for the elastic moduli, it is satisfactory for strength properties, but deformation... 

Fillers with a density lower than that of epoxy can be used to provide reduced specific gravity in cured products. These are usually gas-filled microballoons. Although they generally bring about a significant increase in viscosity, the microballoon filled epoxies (sometimes called syntactic foam adhesives) are often used in marine applications where low density and buoyancy are important criteria. 

The second example (Scheme 8-2) is an elaboration of the first fragment, but formalized below as CML (chemical markup language) (3). We emphasize that this chapter is not meant to be an instructional manual for any given markup language, with CML here serving only to illustrate the general principles involved. Many other scientific applications of XML have been developed (3, 4), and syntactically, either of these examples could be replaced by other such modularized markup languages. 

Only isotropic gas-filled polymers based on RO will be wnsidered. Anisotropic (integral) and syntactic foams based on RO are discussed in general problems of the physical chemistry and technology of polymer foams based on high polymers and reactive oligomers are dealt with in ... 

Phenolic microbubbles generally yield lower-strength syntactic foams than do glass microbubbles of equal density. As bubble density decreases, relative strengths also decrease (7). The most important factor for use as deep-submergence buoys is the rate of water absorption under a given hydrostatic load. 

The third criterion, based on common relational characteristics, seems to be the most relevant one for successful problem solving (Riley et ah, 1983 Carpenter Moser, 1982). The essence of a problem can be represented in terms of a general description of the situation that eliminates both surface and syntactic features while preserving the relational ones. Such a general description allows the solver to recognize a problem s similarity to a canonical situation that is already well understood. 

The first step of the wrapper development process is to understand the given COM interface of a tool to be wrapped on the syntactical level. Therefore, its type hbrary is parsed and transformed, into a language-independent graph model, according to the schema in Fig. 5.60. Language independence is achieved, for example, by mapping specific COM data types to general ones. 

The general connection between an ADT and a production rule set was observed by Diercksen and Hall (1). However, they did not emphasise the need for a production rule to encapsulate both an ADT operation s syntactic and semantic content. 

Note that the version of VBA included with recent versions of Excel is a dialect of Visual BASIC. It is, at the same time, a subset and an extension, because it is specialized for use with a spreadsheet. Therefore, ifyouwantto learn more about VBA, consult books on VBA for Excel rather than those on Visual BASIC, because quite a few of the commands ofVisual BASIC do not exist in VBA, and vice versa. Of the many books available, useful early introductions are E. Boonin, UsingExcel Visual Basic for Applications, thefast and easy way to learn, Que (1996), and R. Jacobson, Microsoft Excel / Visual Basic, Step by Step, Microsoft Press (1995). As a general reference book use the Microsoft Excel / Visual Basic Programmer s Guide, Microsoft Press (1995). An extensive recent manual is J. Green, Excel 2000 VBA, Wrox Press (1999). Section 10.12 briefly summarizes the main syntactic features ofVBA. 

Another important distinction is based on density. For flotation, sandwich construction, thermal insulation, and ecomsmy, very low-density foams are preferred, often as low as 1 Ib/ft or less. Vinyl, polyolefin, and syntactic foams are generally of medium density. Structural foams are of medium to fairly high density and have a graded structure from solid skin to fairly low-density core. RIM foams are similar, often exhibiting a fairly high density. 

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