# On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces

@inproceedings{Kontchakov2011OnTD, title={On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces}, author={Roman Kontchakov and Yavor Nenov and Ian Pratt-Hartmann and Michael Zakharyaschev}, booktitle={IJCAI}, year={2011} }

We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in R2…

## 13 Citations

Topological Logics with Connectedness over Euclidean Spaces

- MathematicsTOCL
- 2013

The results show, in particular, that spatial reasoning is much harder over Euclidean spaces than over arbitrary topological spaces.

Computability of Euclidean spatial logics

- Mathematics, Philosophy
- 2011

This work considers first-order and quantifier-free Euclidean spatial logics with primitives for topological relations and operations, the property of convexity and the ternary relation of being closer-than, and shows that the corresponding logics are undecidable.

Convex Solutions of RCC8 Networks

- MathematicsECAI
- 2012

It is shown that consistent RCC8 networks over 2n + 1 variables are guaranteed to have a convex solution in Euclidean spaces of n dimensions and higher, and it is proved that the bound is optimal for 2- and 3-dimensional spaces.

Reasoning about Topological and Cardinal Direction Relations Between 2-Dimensional Spatial Objects

- Computer Science, MathematicsJ. Artif. Intell. Res.
- 2014

This paper combines some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra and the Cardinal Direction Calculus for directional information to show that reasoning with topological and directional information is decidable and remains in NP.

Transition Constraints: A Study on the Computational Complexity of Qualitative Change

- Computer ScienceIJCAI
- 2013

This paper discusses the reasoning task of finding a solution to a temporal sequence of static reasoning problems where this sequence is subject to additional transition constraints, and shows how such transitions can be defined as relations and expressed within qualitative constraint formalisms.

Twenty Years of Topological Logic

- Philosophy
- 2013

Topological logics are formal systems for representing and manipulating information about the topological relationships between objects in space. Over the past two decades, these logics have been the…

Drawing Interactive Euler Diagrams from Region Connection Calculus Specifications

- Computer ScienceJ. Log. Lang. Inf.
- 2015

The improved local search and the hybrid method outperforms the local search from the literature and the gradient method for generating a diagram and both good results in terms of quality of drawings and stability are seen.

Probabilistic Region Connection Calculus

- Computer ScienceAAAI Spring Symposia
- 2015

A novel probabilistic model and specification language for spatial relations and a basic algorithm for answering queries about the probability of a relation to hold between two entities based on Markov Random Fields is shown.

RCC and the Theory of Simple Regions in ℝ2

- PhilosophyCOSIT
- 2013

It is proved that, in dimension two and with the standard semantics, a theory equivalent to RCC can be given without any reference to points at the semantic level also.

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