A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations

• Autorzy: Burrieza A. , Ojeda-Aciego M.
• Języki publikacji: EN

Abstrakty

EN

Non-classical logics have proven to be an adequate framework to formalize knowledge representation. In this paper we focus on a multimodal approach to formalize order-of-magnitude qualitative reasoning, extending the recently introduced system MQ, by means of a certain notion of negligibility relation which satisfies a number of intuitively plausible properties, as well as a minimal axiom system allowing for interaction among the different qualitative relations. The main aim is to show the completeness of the formal system introduced. Moreover, we consider some definability results and discuss possible directions for further research.

Słowa kluczowe

EN

multimodal logic; non-classical logics; order-of-magnitude qualitative reasoning

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2005
• Tom: Vol. 68, nr 1/2
• Strony: 21--46
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Burrieza A.

• Dept. Filosofia. Univeridad de Malaga. Spain

autor

Ojeda-Aciego M.

• Dept. Matemática Aplicada. Universidad de Málaga. Spain

Bibliografia

• [1] Bennett, B.: Modal logics for qualitative spatial reasoning, Bulletin of the IGPL, 3(1), 1995, 1–22.
• [2] Bennett, B., Cohn, A., Wolter, F., Zakharyaschev, M.: Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning, Applied Intelligence, 17(3), 2002, 239 – 251.
• [3] Burgess, J. P.: Basic Tense Logic, in: Handbook of Philosophical Logic: Volume II: Extensions of Classical Logic (D. Gabbay, F. Guenthner, Eds.), Reidel, Dordrecht, 1984, 89–133.
• [4] Burrieza, A., Ojeda-Aciego, M.: A multimodal logic approach to order of magnitude qualitative reasoning, Lect. Notes in Artificial Intelligence, 3040, 2004, 431–440.
• [5] Dague, P.: Numeric Reasoning with Relative Orders of Magnitude, Proc. 11th National Conference on Artificial Intelligence, The AAAI Press/The MIT Press, 1993, 541–547.
• [6] Dague, P.: Symbolic Reasoning with Relative Orders of Magnitude, Proc. 13th Intl. Joint Conference on Artificial Intelligence,Morgan Kaufmann, 1993, 1509–1515.
• [7] Mavrovouniotis, M., Stephanopoulos, G.: Reasoning with Orders of Magnitude and Approximate Relations, Proc. 6th National Conference on Artificial Intelligence, The AAAI Press/The MIT Press, 1987.
• [8] Raiman, O.: Order of Magnitude Reasoning, Artificial Intelligence, 51, 1991, 11–38.
• [9] Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connections, Proc. of the 3rd Intl Conf on Principles of Knowledge Representation and Reasoning, 1992, 165–176.
• [10] Sánchez,M., Prats, F., Piera, N.: Una formalizaci´on de relaciones de comparabilidad en modelos cualitativos, Boleíın de la AEPIA (Bulletin of the Spanish Association for AI), 6, 1996, 15–22.
• [11] Shults, B., Kuipers, B.: Proving properties of continuous systems: qualitative simulation and temporal logic, Artificial Intelligence, 92, 1997, 91–129.
• [12] Travé-Massuyès, L., Prats, F., Sánchez, M., Agell, N.: Consistent relative and absolute order-of-magnitude models, Proc. Qualitative Reasoning 2002 Conference, 2002.
• [13] Wolter, F., Zakharyaschev, M.: Qualitative spatio-temporal representation and reasoning: a computational perspective, in: Exploring Artificial Intelligence in the New Millenium (G. Lakemeyer, B. Nebel, Eds.), Morgan Kaufmann, 2002.