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Logics for Order-of-Magnitude Qualitative Reasoning: Formalizing Negligibility

  • Alfredo Burrieza
  • Emilio Muñoz-Velasco
  • Manuel Ojeda-Aciego
Chapter
Part of the Outstanding Contributions to Logic book series (OCTR, volume 17)

Abstract

Qualitative reasoning deals with information expressed in terms of qualitative classes and relations among them, such as comparability, negligibility or closeness. In this work, we focus on the different logic-based approaches to the notions of negligibility developed by our group.

Keywords

Qualitative reasoning Modal logic Negligibility Relational logic Dual tableaux Order of magnitude reasoning 

Notes

Acknowledgements

Some excerpts of the following works have been reprinted with permission:

\(\bullet \) A. Burrieza et al. Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility. Current Topics in Artificial Intelligence, Lecture Notes in Computer Science, Vol. 4177, pp. 370–378, Springer (2006). With permission of Springer.

\(\bullet \) A. Burrieza et al. A Logic for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance. Current Topics in Artificial Intelligence, Lecture Notes in Computer Science, Vol. 4788, pp. 210–219, Springer (2007). With permission of Springer.

\(\bullet \) A. Burrieza et al. A Propositional Dynamic Logic Approach for Order of Magnitude Reasoning. Advances in Artificial Intelligence—IBERAMIA 2008, Lecture Notes in Computer Science, Vol. 5290, pp. 11–20, Springer (2008). With permission of Springer.

\(\bullet \) A. Burrieza, M. Ojeda-Aciego. A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations. Fundamenta Informaticae 68(1-2), 21–46, IOS Press (2005). With permission of IOS Press.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alfredo Burrieza
    • 1
  • Emilio Muñoz-Velasco
    • 2
  • Manuel Ojeda-Aciego
    • 2
  1. 1.Dept FilosofíaUniversidad de MálagaMálagaSpain
  2. 2.Dept Matemática AplicadaUniversidad de MálagaMálagaSpain

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