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Manufacturing algebra and dynamics

Albrecht R.F., Canuto E.

Systems Science

2001

Vol. 27, nr 1

25-37

For system modeling we use two levels of abstraction: the logical structure (F, E(C), C) and algorithms on it in logical time, and the physical model structure (PROD, TRANS(ROUTE), ROUTE) for a model time T, being a subset of the set of intervals on R, the set of real numbers. PROD is a family of input-output objects modeling production modules, plants, processors of certain types. To PROD corresponds the family F of functions f, describing the functional behaviour of the PR < PROD. ROUTE is a set of transportation routes RT, connecting an output port of a PR with an input port of another PR. To RT corresponds an element c < C, C is the set of "connectors". TR transports a quantity z of items from the output port to the input port on route RT. This corresponds to a relation E(c) < E(C), c › z[c] in the logical structure. The set D of physical data on which the PR and TR operate is partitioned into a finite number of subsets, the "sorts", types, classes D(s). For our application, only the quantity q of elements of subsets U < D(s) is of interest, thus we consider q = card U, q < N0, the set of natural numbers with 0 included. The input- and output ports of a PR are physical storage objects ST < STORE, the set of storages under consideration. We assume, ST is dedicated to a sort s. A production module PR is located at a location l < L, input- and output storages of PR have locations (l, i) and (l, j). A storage content changes in the course of time. Thus, we have families of elements qslkt, k = i or j, t < T, to describe the states of all storages employed in a production process. The algebra of operations on such families is studied. In addition, variable structures and their control modules are considered.

On the structure of knowledge base systems.

Albrecht R.F.

Systems Science

1999

Vol. 25, nr 1

115-120

Presented is a framework for mathematical representation of knowledge, using set theoretical and algebraic structures. The basic concepts are generalized relations with valuated elements, decomposed into input-output parts, defining binary "knowledge modules", the output parts depending on the input parts, the dependences given either explicity or constructively as a result of "rule" applications. For given hierarchically structured "queries" or "premises" in the form of families of valuated objects together with logic functions to be applied to the valuations, a knowledge module deduces answers" or "conclusions" by matching the input patterns with corresponding output patterns and then performing algebraic computations with the selected objects according to the algebraic structure of the domains of the valuations. Introducing in addition uniform topologies on the domains of the valuations, the "perfect' matching can be generalized to an approximate matching. Further, the knowledge modules as input-output systems can be composed to complex systems.