Semiring neighbours
- In 1996 Zhou and Hansen proposed a first-order interval logic called Neighbourhood Logic (NL) for specifying liveness and fairness of computing systems and also defining notions of real analysis in terms of expanding modalities. After that, Roy and Zhou presented a sound and relatively complete Duration Calculus as an extension of NL. We present an embedding of NL into an idempotent semiring of intervals. This embedding allows us to extend NL from single intervals to sets of intervals as well as to extend the approach to arbitrary idempotent semirings. We show that most of the required properties follow directly from Galois connections, hence we get the properties for free. As one important result we get that some of the axioms which were postulated for NL can be dropped since they are theorems in our generalisation. Furthermore, we present some possible interpretations for neighbours beyond intervals. Here we discuss for example reachability in graphs and applications to hybridIn 1996 Zhou and Hansen proposed a first-order interval logic called Neighbourhood Logic (NL) for specifying liveness and fairness of computing systems and also defining notions of real analysis in terms of expanding modalities. After that, Roy and Zhou presented a sound and relatively complete Duration Calculus as an extension of NL. We present an embedding of NL into an idempotent semiring of intervals. This embedding allows us to extend NL from single intervals to sets of intervals as well as to extend the approach to arbitrary idempotent semirings. We show that most of the required properties follow directly from Galois connections, hence we get the properties for free. As one important result we get that some of the axioms which were postulated for NL can be dropped since they are theorems in our generalisation. Furthermore, we present some possible interpretations for neighbours beyond intervals. Here we discuss for example reachability in graphs and applications to hybrid systems. At the end of the paper we add finite and infinite iteration to NL and extend idempotent semirigs to Kleene algebras and omega algebras. These extensions are useful for formulating repetitive properties and procedures like loops.…
Author: | Peter HöfnerGND |
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URN: | urn:nbn:de:bvb:384-opus4-1942 |
Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/243 |
Series (Serial Number): | Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2005-19) |
Publisher: | Institut für Informatik, Universität Augsburg |
Place of publication: | Augsburg |
Type: | Report |
Language: | English |
Year of first Publication: | 2005 |
Publishing Institution: | Universität Augsburg |
Release Date: | 2006/06/19 |
GND-Keyword: | Halbring |
Institutes: | Fakultät für Angewandte Informatik |
Fakultät für Angewandte Informatik / Institut für Informatik | |
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |