Abstract
We examine modal logical systems, with generalized operators, for the precise treatment of vague notions such as ‘often’, ‘a meaningful subset of a whole’, ‘most’, ‘generally’ etc. The intuition of ‘most’ as “all but for a ‘negligible’ set of exceptions” is made precise by means of filters. We examine a modal logic, with a new modality for a local version of ‘most’ and present a sound and complete axiom system. We also discuss some variants of this modal logic.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Barwise, J., Cooper, R.: Generalized quantifiers and natural language. Linguistics and Philosophy 4, 159–219 (1981)
Barwise, J., Feferman, S.: Model-Theoretic Logics. Springer, New York (1985)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Chang, C., Keisler, H.: Model Theory. North-Holland, Amsterdam (1973)
Carnielli, W., Veloso, P.: Ultrafilter logic and generic reasoning. In: Abstr. Workshop on Logic, Language, Information and Computation, Recife (1994)
Chandy, K., Lamport, L.: Distributed Snapshot: Determining Global States of Distributed Systems. ACM Transactions on Computer Systems 3, 63–75 (1985)
Enderton, H.: A Mathematical Introduction to Logic. Academic Press, New York (1972)
Goranko, V., Passy, S.: Using the Universal Modality: Gains and Questions. Journal of Logic and Computation 2, 5–30 (1992)
Osborne, M., Rubinstein, A.: A Course in Game Theory. MIT, Cambrige (1998)
Schelechta, K.: Default as generalized quantifiers. Journal of Logic and Computation 5, 473–494 (1995)
Turner, W.: Logics for Artificial Intelligence. Ellis Horwood, Chichester (1984)
Veloso, P.: On ‘almost all’ and some presuppositions. Manuscrito XXII, 469–505 (1999)
Veloso, P.: On modulated logics for ‘generally’. In: EBL 2003 (2003)
Venema, Y.: A crash course in arrow logic. In: Marx, M., Pólos, L., Masuch, M. (eds.) Arrow Logic and Multi-Modal logic, pp. 3–34. CSLI, Stanford (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benevides, M., Delgado, C., de Freitas, R.P., Veloso, P.A.S., Veloso, S.R.M. (2004). On Modalities for Vague Notions. In: Bazzan, A.L.C., Labidi, S. (eds) Advances in Artificial Intelligence – SBIA 2004. SBIA 2004. Lecture Notes in Computer Science(), vol 3171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28645-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-28645-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23237-7
Online ISBN: 978-3-540-28645-5
eBook Packages: Springer Book Archive