On Decidability of a Logic for Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility

  • Joanna Golińska-Pilarek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7519)

Abstract

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMRN for order-of-magnitude reasoning with the bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMRN by showing that the logic has the strong finite model property.

Keywords

multi-modal logic qualitative reasoning order-of-magnitude reasoning bidirectional negligibility knowledge representation decidability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burrieza, A., Ojeda-Aciego, M.: A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) CAEPIA/TTIA 2003. LNCS (LNAI), vol. 3040, pp. 431–440. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Burrieza, A., Ojeda-Aciego, M.: A multimodal logic approach to order of magnitude qualitative reasoning with comparability and negligibility relations. Fundamenta Informaticae 68(1-2), 21–46 (2005)MathSciNetMATHGoogle Scholar
  3. 3.
    Burrieza, A., Muñoz, E., Ojeda-Aciego, M.: Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility. In: Marín, R., Onaindía, E., Bugarín, A., Santos, J. (eds.) CAEPIA 2005. LNCS (LNAI), vol. 4177, pp. 370–378. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Burrieza, A., Muñoz-Velasco, E., Ojeda-Aciego, M.: A Logic for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance. In: Borrajo, D., Castillo, L., Corchado, J.M. (eds.) CAEPIA 2007. LNCS (LNAI), vol. 4788, pp. 210–219. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Golińska-Pilarek, J., Mora, A., Muñoz-Velasco, E.: An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance. In: Ho, T.-B., Zhou, Z.-H. (eds.) PRICAI 2008. LNCS (LNAI), vol. 5351, pp. 128–139. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Golińska-Pilarek, J., Muñoz-Velasco, E.: Relational approach for a logic for order-of-magnitude qualitative reasoning with negligibility, non-closeness and distance. Logic Journal of IGPL 17(4), 375–394 (2009)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Golińska-Pilarek, J., Muñoz-Velasco, E.: Dual tableau for a multimodal logic for order-of-magnitude qualitative reasoning with bidirectional negligibility. International Journal of Computer Mathematics 86(10-11), 1707–1718 (2009)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Orłowska, E., Golińska-Pilarek, J.: Dual Tableaux: Foundations, Methodology, Case Studies. Trends in Logic 36. Springer (2011)Google Scholar
  9. 9.
    Raiman, O.: Order of magnitude reasoning. Artificial Intelligence 51(1-3), 11–38 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joanna Golińska-Pilarek
    • 1
  1. 1.Institute of PhilosophyUniversity of WarsawPoland

Personalised recommendations