On consistent functions for neighborhood systems
| Autor: | En-Bing Lin, Yu Ru Syau, Churn-Jung Liau |
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| Rok vydání: | 2020 |
| Předmět: |
Generality
Pure mathematics Applied Mathematics Closure (topology) Modal logic 02 engineering and technology Theoretical Computer Science Morphism Modal Artificial Intelligence 020204 information systems Bounded function 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Invariant (mathematics) Software Mathematics |
| Zdroj: | International Journal of Approximate Reasoning. 121:39-58 |
| ISSN: | 0888-613X |
| DOI: | 10.1016/j.ijar.2020.03.002 |
| Popis: | In this paper, we propose a definition of system-consistent (sys-consistent) functions for neighborhood systems and compare it with a previous definition of granule-based consistent (gra-consistent) functions in the literature. We show that sys-consistency achieves the same level of generality as gra-consistency in the sense that the former subsumes all existing definitions of consistent functions that are known to be special cases of the latter. Then, we prove that sys-consistent functions are structure-preserving mappings with respect to interior and closure operators on neighborhood systems, whereas gra-consistent functions are not. In addition, we connect consistent functions with well-known model-theoretic notions of bisimulations and bounded morphisms in modal logic. As a consequence, this implies that properties described by modal formulas remain invariant under consistent mappings. Finally, we show that most (albeit not all) of the above-mentioned results still hold for some variants and extensions of the basic definition. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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