Untangled: A Complete Dynamic Topological Logic
Keywords:KRR: Geometric, Spatial, and Temporal Reasoning, KRR: Action, Change, and Causality, GTEP: Coordination and Collaboration, MAS: Agent-Based Simulation and Emergent Behavior, MAS: Coordination and Collaboration, PRS: Model-Based Reasoning, PRS: Optimization of Spatio-Temporal Systems
AbstractDynamical systems are general models of change or movement over time with a broad area of applicability to many branches of science, including computer science and AI. Dynamic topological logic (DTL) is a formal framework for symbolic reasoning about dynamical systems. 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.
How to Cite
Fernández-Duque, D., & Montacute, Y. (2023). Untangled: A Complete Dynamic Topological Logic. Proceedings of the AAAI Conference on Artificial Intelligence, 37(5), 6355-6362. https://doi.org/10.1609/aaai.v37i5.25782
AAAI Technical Track on Knowledge Representation and Reasoning