A Generic Toolkit for n-ary Qualitative Temporal and Spatial Calculi

Temporal and spatial reasoning is a central task for numerous applications in many areas of artificial intelligence. For this task, numerous formalisms using the qualitative approach have been proposed. Clearly, these formalisms share a common algebraic structure. In this paper we propose and study a general definition of such formalisms by considering calculi based on basic relations of an arbitrary arity. We also describe the QAT (the qualitative algebra toolkit), a JAVA constraint programming library allowing to handle constraint networks based on those qualitative calculi

[1]  Peter van Beek,et al.  The Design and Experimental Analysis of Algorithms for Temporal Reasoning , 1995, J. Artif. Intell. Res..

[2]  Gérard Ligozat,et al.  What Is a Qualitative Calculus? A General Framework , 2004, PRICAI.

[3]  Peter van Beek,et al.  On the Conversion between Non-Binary and Binary Constraint Satisfaction Problems , 1998, AAAI/IAAI.

[4]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[5]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[6]  Krzysztof R. Apt,et al.  Principles of constraint programming , 2003 .

[7]  Christian Bessiere,et al.  A Simple Way to Improve Path Consistency Processing in Interval Algebra Networks , 1996, AAAI/IAAI, Vol. 1.

[8]  James F. Allen.  An Interval-Based Representation of Temporal Knowledge , 1981, IJCAI.

[9]  Jean-François Condotta,et al.  Spatial Reasoning About Points in a Multidimensional Setting , 2002, Applied Intelligence.

[10]  I. Hodkinson,et al.  Relation Algebras by Games , 2002 .

[11]  Gérard Ligozat,et al.  Weak Composition for Qualitative Spatial and Temporal Reasoning , 2005, CP.

[12]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[13]  Philippe Balbiani,et al.  A Model for Reasoning about Topologic Relations between cyclic intervals , 2000, KR.

[14]  Jean-François Condotta,et al.  On the consistency problem for the INDU calculus , 2006, J. Appl. Log..

[15]  Jean-François Condotta,et al.  Reasoning about Cyclic Space: Axiomatic and Computational Aspects , 2003, Spatial Cognition.

[16]  Anthony G. Cohn,et al.  A new approach to cyclic ordering of 2D orientations using ternary relation algebras , 2000, Artif. Intell..

[17]  Luis Fariñas del Cerro,et al.  A New Tractable Subclass of the Rectangle Algebra , 1999, IJCAI.

[18]  Gérard Ligozat,et al.  Reasoning about Cardinal Directions , 1998, J. Vis. Lang. Comput..

[19]  Henry A. Kautz,et al.  Constraint Propagation Algorithms for Temporal Reasoning , 1986, AAAI.

[20]  Abdul Sattar,et al.  INDU: An Interval and Duration Network , 1999, Australian Joint Conference on Artificial Intelligence.