Paper:
A Modal Characterization of Visibility and Focus in Granular Reasoning
Yasuo Kudo* and Tetsuya Murai**
*Department of Computer Science and Systems Engineering, Muroran Institute of Technology, 27-1 Mizumoto, Muroran 050-8585, Japan
**Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-Ku, Sapporo 060-0814, Japan
We have proposed two key concepts – focus and visibility – as modalities of modal logic. Scott-Montague models that we have proposed represent properties of visibility and focus and the concept that p is visible as modal sentence vis p and p is clearly visible – or is in focus – as modal sentence cv p.
- [1] Z. Pawlak, “Rough Sets,” Int. Journal of Computer and Information Sciences, Vol.11, pp. 341-356, 1982. [2] Z. Pawlak, “Rough Sets: Theoretical Aspects of Reasoning about Data,” Kluwer, Dordrecht, 1991. [3] T. Y. Lin, “Granular Computing on Binary Relation, I & II,” Rough Sets in Knowledge Discovery 1: Methodology and Applications, L. Polkowski et al. (Eds.), Physica-Verlag, pp. 107-121, pp. 122-140, 1998. [4] A. Skowron, “Toward Intelligent Systems: Calculi of Information Granules,” New Frontiers in Artificial Intelligence, Terano et al. (Eds.), LNAI 2253, Springer, pp. 251-260, 2001. [5] T. Murai, M. Nakata, and Y. Sato, “A Note on Filtration and Granular Reasoning,” T. Terano et al. (Eds.), New Frontiers in Artificial Intelligence, LNAI 2253, Springer, pp. 385-389, 2001. [6] T. Murai, G. Resconi, M. Nakata, and Y. Sato, “Operations of Zooming In and Out on Possible Worlds for Semantic Fields,” E. Damiani et al. (Eds.), Knowledge-Based Intelligent Information Engineering Systems and Allied Technologies, pp. 1083-1087, 2002. [7] T. Murai, G. Resconi, M. Nakata, and Y. Sato, “Granular Reasoning Using Zooming In & Out: Part 2. Aristotle's Categorical Syllogism,” Electronic Notes in Theoretical Computer Science, Vol.82, Issue 4, 2003. [8] T. Murai, G. Resconi, M. Nakata, and Y. Sato, “Granular Reasoning Using Zooming In & Out: Part 1. Propositional Reasoning,” Rough sets, Fuzzy sets, Data mining, and Granular Computing, G. Wang et al. (Eds.), LNAI 2639, Springer, pp. 421-424, 2003. [9] Y. Kudo and T. Murai, “Visibility and Focus: An Extended Framework for Granular Reasoning,” Advances in Logic Based Intelligent Systems, K. Nakamatsu and J. M. Abe (Eds.), IOS Press, pp. 280-287, 2005. [10] Y. Kudo and T. Murai, “A Note on Granular Reasoning and Semantics of Four-Valued Logics,” Computing Anticipatory, Systems: CASYS'05 - Seventh Int. Conf., AIP Conf. Proc., Vol.839, pp. 453-460, 2006. [11] Y. Kudo and T. Murai, “A Modal Characterization of Granular Reasoning Based on Scott-Montague Models,” Proc. of SCIS2008 & ISIS2008, pp.991-995, 2008. [12] B. F. Chellas, “Modal Logic: An Introduction,” Cambridge University Press, 1980. [13] S. C. Kleene, “Introduction to Metamathematics,” North-Nostrand, 1952. [14] J. Hintikka, “Knowledge and Belief,” Cornell University Press, 1962. [15] A. N. Prior, “Past, Present and Future,” Clarendon Press, 1967.