Some uses of modal semirings
- We survey one branch of algebraic logic, namely modal semirings. They provide compact algebraic definitions of actions, with choice + and sequential composition · , together with modal operators box and diamond, parametrised by actions, that allow reasoning about successors and predecessors of states/worlds. Particular instances are homogeneous binary relations or sets of finite and infinite non-empty traces under fusing concatenation. As main examples of applications we present obstacle analysis for geographic wayfinders, Hoare Logic, O’Hearn’s Incorrectness Logic, General Correctness Logic, as well as the temporal logic CTL∗ and its sublogics CTL and LTL. We also give glimpses at Epistemic Logics of belief and knowledge, pointer structures plus Separation Logic and preference database queries. Finally, we briefly discuss some related algebraic approaches.
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| Author: | Bernhard Möller, Jules Desharnais |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1231611 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123161 |
| ISBN: | 978-3-031-88929-5OPAC |
| ISSN: | 0302-9743OPAC |
| Parent Title (English): | Recent Trends in Algebraic Development Techniques: 27th IFIP WG 1.3 International Workshop, WADT 2024, Enschede, The Netherlands, July 8, 2024, revised selected papers |
| Publisher: | Springer |
| Place of publication: | Cham |
| Editor: | Ionuț Țuțu |
| Type: | Conference Proceeding |
| Language: | English |
| Date of Publication (online): | 2025/06/27 |
| Year of first Publication: | 2025 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/27 |
| Tag: | algebraic semantics; assertion logics; semirings with modal operators; temporal logics |
| First Page: | 23 |
| Last Page: | 45 |
| Series: | Lecture Notes in Computer Science ; 15587 |
| DOI: | https://doi.org/10.1007/978-3-031-88930-1_2 |
| 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 |
| Licence (German): |  Deutsches Urheberrecht |
