Abstract
This work concentrates on the automated deduction of logics of order-of-magnitude reasoning. Specifically, a translation of the multimodal logic of qualitative order-of-magnitude reasoning into relational logics is provided; then, a sound and complete Rasiowa-Sikorski proof system is presented for the relational version of the language.
The first two authors are partially supported by projects TIC2003-9001-C02-01 and TIN2006-15455-C03-01.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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, vol. 4177, pp. 370–378. Springer, Heidelberg (2006)
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, vol. 3040, pp. 431–440. Springer, Heidelberg (2004)
Burrieza, A., Ojeda-Aciego, M.: A multimodal logic approach to order of magnitude qualitative reasoning with comparability and negligibility relations. Fundamenta Informaticae 68, 21–46 (2005)
Dague, P.: Symbolic reasoning with relative orders of magnitude. In: Proc. 13th Intl. Joint Conference on Artificial Intelligence, pp. 1509–1515. Morgan Kaufmann, San Francisco (1993)
Dallien, J., MacCaull, W.: RelDT—a dual tableaux system for relational logics (in press, 2005), Available from: http://logic.stfx.ca/reldt/
Formisano, A., Omodeo, E., Orłowska, E.: A PROLOG tool for relational translation of modal logics: A front-end for relational proof systems. In: Beckert, B. (ed.) Tableaux 2005 Position Papers and Tutorial Descriptions. Universität Koblenz-Landau, Fachberichte Informatik vol. 12, pp. 1-10 (2005), System available from http://www.di.univaq.it/TARSKI/transIt/
Gargov, G., Goranko, V.: Modal logic with names. Journal of Philosophical Logic 22, 607–636 (1993)
Golińska-Pilarek, J., Orłowska, E.: Tableaux and dual tableaux: Transformation of proofs (submitted, 2005)
MacCaull, W., Orłowska, E.: Correspondence results for relational proof systems with application to the Lambek calculus. Studia Logica 71, 279–304 (2002)
Orłowska, E.: Relational interpretation of modal logics. In: Andreka, H., Monk, D., Nemeti, I. (eds.) Algebraic Logic. Colloquia Mathematica Societatis Janos Bolyai, vol. 54, pp. 443–471. North Holland, Amsterdam (1988)
Orłowska, E.: Relational semantics for nonclassical logics: Formulas are relations. In: Wolenski, J. (ed.) Philosophical Logic in Poland, pp. 167–186. Kluwer, Dordrecht (1994)
Passy, S., Tinchev, T.: PDL with data constants. Information Processing Letters 20, 35–41 (1985)
Passy, S., Tinchev, T.: An essay in combinatory dynamic logic. Information and Computation 93, 263–332 (1991)
Rasiowa, H., Sikorski, R.: Mathematics of Metamathematics. Polish Scientific Publishers (1963)
Schmidt, R., Orłowska, E., Hustadt, U.: Two proof systems for Peirce algebras. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003. LNCS, vol. 3051, pp. 235–248. Springer, Heidelberg (2004)
Tarski, A.: On the calculus of relations. Journal of Symbolic Logic 6, 73–89 (1941)
Travé-Massuyès, L., Prats, F., Sánchez, M., Agell, N.: Consistent relative and absolute order-of-magnitude models. In: Proc. Qualitative Reasoning 2002 Conference (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burrieza, A., Ojeda-Aciego, M., Orłowska, E. (2006). Relational Approach to Order-of-Magnitude Reasoning. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds) Theory and Applications of Relational Structures as Knowledge Instruments II. Lecture Notes in Computer Science(), vol 4342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11964810_6
Download citation
DOI: https://doi.org/10.1007/11964810_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69223-2
Online ISBN: 978-3-540-69224-9
eBook Packages: Computer ScienceComputer Science (R0)