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Art der Veröffentlichung: Doktorarbeit
Autor: T. Mossakowski
Titel: Representations, hierarchies and graphs of institutions
Erscheinungsjahr: 1996
Hochschule: Universität Bremen
Abstract / Kurzbeschreibung: For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of representation and embedding between logical systems, which are formalized as institutions here. Different kinds of representations will lead to a looser or tighter connection of the institutions, with more or less good possibilities of faithfully embedding the semantics and of re-using proof support.

In the second part, we then perform a detailed ``empirical'' study of the relations among various well-known institutions of total, order-sorted and partial algebras and first-order structures (all with Horn style, i.e. universally quantified conditional, axioms). We thus obtain a graph of institutions, with different kinds of edges according to the different kinds of representations between institutions studied in the first part.

We also prove some separation results, leading to a hierarchy of institutions, which in turn naturally leads to five subgraphs of the above graph of institutions. They correspond to five different levels of expressiveness in the hierarchy, which can be characterized by different kinds of conditional generation principles.

We introduce a systematic notation for institutions of total, order-sorted and partial algebras and first-order structures. The notation closely follows the combination of features that are present in the respective institution. This raises the question whether these combinations of features can be made mathematically precise in some way. In the third part, we therefore study the combination of institutions with the help of so-called parchments (which are certain algebraic presentations of institutions) and parchment morphisms.
PostScript Version: http://www.informatik.uni-bremen.de/~till/papers/phd.ps
Anmerkung / Hinweis: Also appeared as book in Logos Verlag
Status: Other
Letzte Aktualisierung: 04. 05. 2004

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