Abstract
A brief introduction to basic modifiers is given. Any modifier with its dual and the corresponding negation form a DeMorgan triple similar to that of t-norms, t-conorms, and negation. The lattice structure of the unit interval with the usual partial order is similar to that of the set of all membership functions. This structure has a certain connection to implication, by means of the subsethood of fuzzy sets, and it is possible to create a similar expression for modifiers as the axiom of reflexivity is in modal logic. Also, other connections to modal logics can be found. This motivates to develop a formal semantics to modifier logic by means of that of modal logic. Actually, this kind of logic is so-called metalogic concerning either true or false statements about properties of modifiers. This version is based on graded possibility operations. Hence, semantic tools for weakening modifiers are derived. The corresponding things for substantiating modifiers are constructed by means of duality. Finally, some outlines for modifier systems are considered.
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
Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)
Dombi, J.: A fuzzy halmazok operátorainak szerkezete a többtényezós döntések szempontjából. Kandidátusi Értekezés, Hungarian Academy of Sciences, Szeged (1993)
Dombi, J.: Theoretical Concepts of Modifiers and Hedges. In: Niskanen, V.A., Kortelainen, J. (eds.) On the Edge of Fuzziness. Acta Universitatis Lappeenrantaensis, vol. 179 (2004)
Habson, B., Gärdenfors, P.: A guide to intensional semantics. In: Modality, Morality and Other Problems of Sense and Nonsense: Essays Dedicated to Sören Halldén, CWK Gleerup Bokförlag, Lund (1973)
Hughes, G.E., Cresswell, M.J.: An Introduction to Modal Logic (reprint). Methuen and Co., London (1985)
Kripke, S.A.: Semantical considerations on modal logic. Acta Philosophica Fennica, Fasc. XVI (1963)
Lakoff, G.: Hedges: A study in meaning criteria and the logic of fuzzy concepts. The Journal of Philosophical Logic 2 (1973)
Lemmon, E.J.: An Introduction to Modal Logic. In: Segerberg, K. (ed.) American Philosophical Quarterly, Monograph No. 11, Basil Blackwell, Oxford (1977)
Mattila, J.K.: Modeling fuzziness by Kripke structures. In: Terano, T., Sugeno, M., Mukaidono, M., Shigemasu, K. (eds.) Fuzzy Engineering toward Human Friendly Systems, Proc. of IFES ’91, Yokohama, Japan, Nov. 13 - 15, 1991, vol. 2,
Mattila, J.K.: On modifier logic. In: Zadeh, L.A., Kacprzyk, J. (eds.) Fuzzy Logic for Management of Uncertainty, John Wiley & Sons, Inc., New York (1992)
Mattila, J.K.: Completeness of propositional modifier logic. Research Report 55, Lappeenranta University of Technology, Department of Information Technology (1995)
Mattila, J.K.: Modifier Logics Based on Graded Modalities. Journal of Advanced Computational Intelligence and Intelligent Informatics 7(2) (2003)
Mattila, J.K.: Modifiers Based on Some t-norms in Fuzzy Logic. Soft Computing 8(10), 663–667 (2004)
Mattila, J.K.: On Łukasiewicz Modifier Logic. Journal of Advanced Computational Intelligence and Intelligent Informatics 9(5) (2005)
Resconi, G., Klir, G.J., St. Clair, U.H.: Uncertainty and modal logic. In: Proceedings of Fifth International Fuzzy Systems Association World Congress’93, Seoul, Korea, July 4 - 9, 1993, vol. I (1993)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8 (1965)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Mattila, J.K. (2007). Possibility Based Modal Semantics for Graded Modifiers. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-72950-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
eBook Packages: Computer ScienceComputer Science (R0)