Reasoning about cyclic space: axiomatic and computational aspects

Authors:
Philippe Balbiani;Jean-François Condotta;Gérard Ligozat
Affiliations:
Institut de Recherche en Informatique de Toulouse, Toulouse Cedex, France;Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, Orsay Cedex, France;Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, Orsay Cedex, France
Venue:
Spatial cognition III
Year:
2003

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Abstract

In this paper we propose models of the axioms for linear and cyclic orders. First, we describe explicitly the relations between linear and cyclic models, from a logical point of view. The second part of the paper is concerned with qualitative constraints: we study the cyclic point algebra. This formalism is based on ternary relations which allow to express cyclic orientations. We give some results of complexity about the consistency problem in this formalism. The last part of the paper is devoted to conceptual spaces. The notion of a conceptual space is related to the complexity properties of temporal and spatial qualitative formalisms, including the cyclic point algebra.