Spatial logics with connectedness predicates
Roman Kontchakov (Birkbeck College London), Ian Pratt-Hartmann, (Department of Computer Science, Manchester University), Frank Wolter, (Department of Computer Science, University of Liverpool), Michael, Zakharyaschev (Birkbeck College London)
TL;DR
This paper explores the extension of quantifier-free spatial logics with connectedness predicates, analyzing how these additions impact the computational complexity of spatial reasoning in AI.
Contribution
It introduces connectedness and component-counting predicates into spatial logics and characterizes their computational complexity.
Findings
Connectedness constraints can raise complexity from NP to PSpace and ExpTime.
Allowing component counting increases complexity to NExpTime.
The study provides a detailed complexity analysis for these extended logics.
Abstract
We consider quantifier-free spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of these logics and show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime.
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