Untangled: A Complete Dynamic Topological Logic
Authors: David Fernández-Duque, Yoàv Montacute
AAAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | DTL can express various liveness and reachability conditions on such systems, but has the drawback that the only known axiomatisation requires an extended language. In this paper, we consider dynamic topological logic restricted to the class of scattered spaces. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original language of DTL. In particular, we show that the version of DTL based on the class of scattered spaces is finitely axiomatisable, and that the natural axiomatisation is sound and complete. |
| Researcher Affiliation | Academia | ICS of the Czech Academy of Sciences Ghent University 2University of Cambridge fernandez@cs.cas.cz, yoav.montacute@cl.cam.ac.uk |
| Pseudocode | No | The paper does not include pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for the described methodology is available. |
| Open Datasets | No | This paper is theoretical and does not involve training data or datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve validation data or dataset splits. |
| Hardware Specification | No | This paper is theoretical and does not describe experimental procedures, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | This paper is theoretical and does not describe experimental procedures, therefore no specific software dependencies with version numbers are listed. |
| Experiment Setup | No | This paper is theoretical and does not describe experiments with specific setup details or hyperparameters. |