Corpus ID: 14231450

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

  title={Transition Constraints: A Study on the Computational Complexity of Qualitative Change},
  author={M. Westphal and J. Hu{\'e} and S. W{\"o}lfl and B. Nebel},
Many formalisms discussed in the literature on qualitative spatial reasoning are designed for expressing static spatial constraints only. However, dynamic situations arise in virtually all applications of these formalisms, which makes it necessary to study variants and extensions dealing with change. This paper presents a study on the computational complexity of qualitative change. More precisely, we discuss the reasoning task of finding a solution to a temporal sequence of static reasoning… Expand
Ordering Spatio-Temporal Sequences to Meet Transition Constraints: Complexity and Framework
This paper shows that the problem of ordering a sequence of qualitative spatial configurations to meet certain transition constraints is \(\mathcal{NP}\)-complete for the well known languages of RCC-8, Interval Algebra, and Block Algebra. Expand
The Implication of Patchwork and Compactness in Qualitative Spatio-Temporal Reasoning
We study the qualitative spatiotemporal logic that results by combining the propositional temporal logic (PTL) with a qualitative spatial constraint language, namely, theL1 logic, and investigate theExpand
On Ordering Spatio-Temporal Sequences to meet Transition Constraints
Time and space are fundamental concepts of study in Artificial Intelligence and, in particular, Knowledge Representation. In this paper, we investigate the task of ordering a temporal sequence ofExpand
Minimality of Combined Qualitative Constraint Networks
It is proved that the topological temporal sequences of constant-size regions over the subclass SRCC8 check this property, and the complexity of the satisfiability decision of relations as well as the enumeration of satisfiable basic relations is studied. Expand
Temporal Sequences of Qualitative Information: Reasoning about the Topology of Constant-Size Moving Regions
This work presents a general approach for reasoning about temporal sequences of qualitative information that is generally more efficient than existing techniques and identifies its three maximal tractable sub-classes containing all basic relations. Expand
Checking the Consistency of Combined Qualitative Constraint Networks
This work identifies sufficient conditions ensuring the polynomiality of consistency checking, and uses them to find tractable subclasses in constraint networks over combined qualitative formalisms. Expand
Séquences temporelles d’informations qualitatives : raisonner sur la topologie de régions mobiles de taille constante
Nous presentons une approche generale pour le raison-nement sur des sequences temporelles d'informations quali-tatives. Cette approche, qui s'appuie sur le cadre recemment introduit desExpand
Towards a Synergy of Qualitative Spatio-Temporal Reasoning and Smart Environments for Assisting the Elderly at Home∗
Applications of smart environments are ever-increasing due to their possibilities of contributing towards an independent and active lifestyle for different user groups. An example of such anExpand
Algorithmic Contributions to Qualitative Constraint-based Spatial and Temporal Reasoning. (Contributions Algorithmiques au Raisonnement Spatial et Temporel basé sur des Contraintes Qualitatives)
Le raisonnement spatial et temporel qualitatif est un domaine principal d’etudes de l’intelligence artificielle et, en particulier, du domaine de la representation des connaissances, qui traite desExpand
Décision de la cohérence des réseaux de contraintes qualitatives combinés
Nous etudions le probleme de la decision de la coherence de reseaux de contraintes dans le cadre de combinaisons de formalismes qualitatifs. Nous proposons un cadre formel qui englobe lesExpand


Infinite Qualitative Simulations by Means of Constraint Programming
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitativeExpand
Qualitative Spatio-Temporal Reasoning with RCC-8 and Allen's Interval Calculus: Computational Complexity
This work starts with the spatial calculus RCC-8 and Allen's interval calculus in order to construct a qualitative spatio-temporal calculus and shows that satisfiability is still in NP. Expand
Temporalizing Cardinal Directions: From Constraint Satisfaction to Planning
This paper investigates a constraint formalism which temporalizes the cardinal direction calculus with respect to Allen's interval algebra, and shows how continuous changes can be represented as operations to objects in grid-like structures. Expand
Temporalizing Spatial Calculi: On Generalized Neighborhood Graphs
This paper investigates how calculi discussed in the field of qualitative spatial reasoning can be temporalized in order to gain reasoning formalisms that can be used to express spatial configurations and their dynamics and introduces a generalized concept of neighborhood graph, which allows for reasoning about objects in such dynamic settings. Expand
Qualitative Temporal and Spatial Reasoning Revisited
This article studies the ‘local-to-global’ property by making use of a recently established connection of this property with universal algebra and shows that this property is equivalent to the presence of a so-called quasi near-unanimity (QNU) polymorphism of the constraint language. Expand
Qualitative Spatial Reasoning with Conceptual Neighborhoods for Agent Control
It is demonstrated that conceptual neighborhoods allow resolution of conflicting information by model-based relaxation of spatial constraints and the problem of automatically deriving neighborhood structures can be addressed if the relations of a calculus can be modeled in another calculus for which the neighborhood structure is known. Expand
Qualitative Spatial Reasoning with Cardinal Directions
An algebraic method is used to formalize the meaning of cardinal directions and two examples of systems to determine and reason with cardinal directions are discussed in some detail and results from a prototype are given. Expand
Dominance Diagrams: A Tool for Qualitative Reasoning About Continuous Systems
  • A. Galton
  • Mathematics, Computer Science
  • Fundam. Informaticae
  • 2001
By adding a representation of dominance between qualitative states to CNDs, it is possible to reason more effectively about the temporal incidence of the qualitative states represented in the diagrams; in addition, dominance turns out to be of importance in determining the structure of composite diagrams formed as the product of existing diagrams. Expand
A Qualitative Model for Space
This work describes a systematic representation that builds spatial maps based on local qualitative relations between objects that is free of subjective bias, and is complete in the qualitative sense of distinguishing all overlap/ tangency/nocontact geometries. Expand
Exact and approximate reasoning about temporal relations 1
This paper addresses a fundamental reasoning task that arises in applications of the algebra: Given (possibly indefinite) knowledge about the relationships between intervals, find all feasible relationships between two intervals, called the minimal labels problem. Expand