Derivation schema

For a non-recursive property Pj, a normalized successful derivation is an instance of the following derivation schema ... 

In derivation schemas, however, the selected atom(s) for the next inference(s) is (are) underlined. 

Replacing opp by (p, this last goal may be rewritten more compactly, and the revised derivation schema continues as follows ... 

We may now justify Heuristic 13-1. When proving the involved property, say Fj, the derivation starting from the clause, say Ci, that is obtained from the generalized minimal disjunct necessarily succeeds, as shown in the following derivation schema ... 

To summarise in authentic tasks, we have established that stmcture-property relations can be described by a dynamic system of stmctures, properties and their interrelations. Within the limits of our study we have derived a generalised conceptual schema, which we expect to be useful to teach macro-micro problems in which stmcture-property relations can be explicitly used (Figs. 9.2, 9.3 and 9.4). The system of nested stmctures, systematically assigned to appropriate scales, and the properties of the different stmctural components reveal a conceptual schema necessary for macro-micro thinking. The system of relevant nested stmctures and the explicit relations between stmctures and properties form the backbone of macro-micro reasoning. Depending on the task, a number of different meso-levels are relevant and... 

Fig. 9.4 Conceptual schema of the design of a bullet-proof jacket derived from the experts consultation. An example of a structure-property relation is marked as a line...

The new conceptual schemas derived in the first part of this chapter could thus be used to design context-based units by a design research approach (Van den Akker,... 

My analytical contribution is to show how the Harrod-Domar model -more specifically, its Domar variant - can be derived from the multisectoral reproduction schema, with the multiplier and the monetary circuit as the key building blocks. These building blocks are defined using Leontief s input-output analysis, a model which has its origins in the Marxian economic tradition. 

The book is thus a series of steps, from the multiplier and its role in the reproduction schema in Chapter 2 to the Kalecki principle in Chapter 3 and a detailed consideration of the circuit of money in Chapter 4. Having built up a macro monetary model of the reproduction schema, in which both money and aggregate demand are featured, Chapter 5 derives the Domar growth model from these analytical foundations. The relevance of this growth model to Marxian theories of crisis is explored and further developed in Chapter 6. 

Under Marx s assumption, in Capital, volume 2, that prices and values are identical, and hence 1 of output is equal to an hour of labour time, this equation captures both an income and multiplier relationship. The equivalence between prices and values is embodied in the identity p = v such that the total employment of labour units (vQ) is equal to total money net income (pQ). Similarly, vF the total number of labour emits required to produce final demand, is equal to total money final demand (pF). Hence, the expression 1/1 — vh is an income/employment multiplier, in which the scalar vh represents the propensity to consume b, derived from the two-department schema.10 We shall refer to this as the Keyensian scalar multiplier, since although it is somewhat unusually defined according to worker consumption it retains the l/l h structure that is so common to economics textbooks. The simplicity of the Keynesian multiplier is retained in a two-department setting. 

These coefficients are derived from Table 4.3a, the input-output formulation of Marx s reproduction schema. 

An emphasis on borrowing, with the multiplier firmly located in Marx s reproduction schema, is provided by the Domar model of economic growth. Instead of providing a snapshot of each period of production, the schema can be developed over an extended number of periods thereby providing a more complete picture of economic growth over time. The contribution of the following analysis will be to derive the model developed by Domar (1947) from foundations that are consistent with Marx s multisectoral schema. Domar s model is particularly suitable for this purpose because it specifies the conditions required for balanced growth. In contrast to Harrod s variant of the model, in which actual investment is determined by an accelerator mechanism, in Domar s model the actual level of investment... 

The most basic proportions embedded in the reproduction schema are established under simple reproduction. This was touched on in our introduction to the schema in Chapter 2, and in establishing the mutual exchange which takes place between departments of production in the circulation of money (Chapter 4). These proportions can be formally derived, in Table 6.1, by displaying the elements of Marx s numerical example (Table 2.1) alongside the Marxian algebraic symbols.3... 

It can now be shown how this result can be derived using an input-output interpretation of the simple reproduction schema. Following the same procedure first introduced in Chapter 2, Table 6.2(a) re-expresses the numerical elements of Table 6.1 as an input-output table. 

Using Marx s reproduction schema, Kalecki derives an aggregate relationship between profits and capitalist expenditures.2 As demonstrated in Chapter 3, under the assumption of zero savings on the part of workers, an aggregate identity is established between profits, capitalist consumption and investment, which is shown as... 

The three-sector reproduction schema, explored in Tables 3.2-3.4, can be displayed algebraically, showing more precisely the way in which Kalecki s interpretation is derived from Marx s numerical example. Starting with... 

This type of scalar multiplier can also be derived from the two-sector Kaleckian schema, as shown by Nell (1988b 112), although this latter multiplier was not applied specifically to the circulation of money. A possible advantage of equation (4.23), since it is derived from an input-output model, is that it could be easily generalized to an n sector framework. 

Fiir die Bildung aller Derivate der Grundkorper waren nur noch be-kannte Biogencscschritte notwendig. Untersuchungen mit markierten Substanzen miissen zeigen, ob das diskutierte Schema von der Pflanze benutzt wird. 

Semantic Eye (Casher and Rzepa 2006) is a test-of-principle scheme for the semantic enrichment of journal articles. Rather unusually, it treats the PDF as the locus of semantic enrichment. The identifiers are mapped onto RDF triples that are then serialized as XML using Adobe s Extensible Metadata Platform (XMP) schema within the PDF. It uses InChls as identifiers for molecules and DOIs for the articles themselves. The idea is that the identifiers derived from the PDFs can be stored locally on a user s machine inside the PDFs, which are then mined by desktop indexing services, creating a sort of semantic intranet or semantic desktop. Exactly how the identifiers are assigned to the papers in the first place is left open to the user. 

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