A question about hierarchical systems (Q2724373)

The conceptual framework of the author consists of a syntax (equations), a semantics (solutions to the equations) and an environment where implementation takes place. A hierarchy is mirrored in the syntax as a partial order on associated quantities. A ``one-world semantics'' consists in compiling the various syntaxes along the hierarchy and interpreting only at the lowest level. The problem is that faults at lower levels are not filtered away in the superstructure and truth statements or adequateness of the model at this upper level may be abusively invalidated. A ``multi-world semantics'' where interpretation takes place at all levels is proposed but the problem (the question of the title) is to relate the different semantics in the hierarchy. Some way-outs are proposed: i) The use of invariants which would propagate meaning down the hierarchy and protect against irrelevant factors. ii) Refining the environment model so that the factors are handled seperately. This might allow a ``bottom-up'' propagation of information so that the higher levels can understand the messages from the base. iii) Ideal compilation, but it is not clear what is meant by ``ideal'' and the words compilation and translation are used equivalently on page 318 while they are given different meanings on page 322.NEWLINENEWLINENEWLINEReviewer's comments: ii) and iii) seem likely to be computationally demanding.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].