Using constraint programming framework for Semiqualitative Reasoning

[Piera95]. N. Piera. Current Trends in Qualitative Reasoning and Applications, Monografla CIMNE, 33. International Center for Numerical Methods in Engineering, Barcelona. [Piera87]. N. Piera. Connectius de logiques no estandard com a operadors d'agregació en classificació multivariable i reconeixement de formes. Ph. D. Thesis Universitat Politecnica de Catalunya, Barcelona. [Raiman86]. O. Raiman. Order of Magnitude Reasoning. Proceedings of AAAI Conference, Philadelphia, 100-104. (Schwei7.er&Sklar83]. B. Schweizer and A. Sklar. Probalistic Metric Spaces, North-Holland, Amsterdam. [Travé-Massuyes&Piera89]. L. Travé-Massuyes and N. Piera. Toe Orders of Magnitude Models as Qualitative Algebras. Proceedings 11th IJCAl, Detroit, 1261-1266. [Travé-Massuyes et al.97]. L. Travé-Massuyes, Ph. Dague and F. GueITin. Le Raisonnement Qualitatifpour les Sciences de l'lngenieur, Ed. Hermes, Paris. 74 Using constraint programming framework for Semiqualitative Reasoning R.M. Gasea, J.A. Ortega, M. Toro, J. Torres and J.M. Cordero Departamento de Lenguajes y Sistemas Informáticos. Universidad de Sevilla Avda. Reina Mercedes s/n. Sevilla (Spain) {gasea ,jaortega, mtoro,jtorres,cordero }©lsi. us.es Abstract A semiqualitative model is the representation of the world by means of qualitative and quantitative knowledge. It is motivated by the lack of quantitative knowledge in determined parameters or variables of the model. We wish to obtain conclusions and generalization derived from these specific models .. In this work, we show as semiqualitative models may be transformed to interval constraint satisfaction problems(ICSP). The inference process in an ICSP is based in combining constraint propagation and bronch and bound algorithms. The interval domains of the variables are to propagate through the constraints. A defined operator must exist for every qualitative knowledge. lt transforms this knowledge to an interval constraint. The application of the constraint programming framework to a ICSP allows the obtaining of conclusions in a automatic way. Keywords: Qualitative reasoning, Constraint Programming, Consistency techniques. 1 Introduction Different communities have studied the qua litative representation of the world and they have proposed formalisms to qualitatively rea son about these representations. The main m tivations are the lack of quantitative knowledge and the excess of them that may obtain conclu sions and explanations understandable by hu mans. Generally the real models are not pure qualitative or pure quantitative but are nor mally composed of quantitative and qualita tive knowledge. lt is known as semiqualitative model. Ali this knowledge must be considered when these models are studied. In the eighties, the main concepts of the quali tative techniques appeared in the area of Arti ficial Intelligence(AJ), by means of the publication of the systems ENVISION [DeKleer84], QSJM[Kuipers86] and QPT[Forbus84]. Diff rent monographs have been published in the 90s [Weld90),[Faltings92],[Kuipers94],(Piera95], [Dague95],[Trave97], that reflect the topics and the clifferent developed techniques in qualita tive reasoning(QR). This qualitative know ledge is useful to understand, in a simple way, some of the properties of the models, ther fore the simplicity is its principal property. lt have been applied in different tasks, such as su pervision and diagnosis of chemical industrial process[Penalva91l[Bousson93](Chang93J, ma rine motor (Moreno93), the control [Lepetit87], analysis of dynamical systems (Aracil93] [Gasca98], software analysis [Xanthakis94] and conceptual design of structures in engineering [Bozzo98]. In a majority of the approaches to modeling qualitative reasoning in Al, it is as sumed explicitly or implicitly that qualitative 75 \1