Rough Dialogue and Implication Lattices

• Autorzy: Chakraborty M.K. , Banerjee M.
• Języki publikacji: EN

Abstrakty

EN

A dialogue is an `activity' by a pair of agents to arrive at some kind of understanding over a concept/belief/piece of information etc. represented by a subset (the extension) in some universe of discourse. The universe is partitioned into two different sets of granules (equivalence classes) representing the perceptions of the agents. So, there are two approximation spaces at the beginning. A third approximation space arises out of superimposition of the two partitions. A dialogue is a finite process of gradual enhancement of the two base subsets of the agents, in their `common' approximation space. Through this process, various kinds of overlap may emerge between the two final subsets. A first introduction of the idea of a dialogue in rough context was made in [6]. This paper further develops the notion and focusses upon the study of the above-mentioned overlaps in a systematic manner. Given two sets A and B in an approximation space, there are nine possible inclusion relations among the sets lo(A), A, up(A), lo(B), B and up(B) where lo and up denote the lower and upper approximation operators respectively. There are five resulting equivalence classes and the quotient set forms a lattice by implication ordering. That is, of the nine relations, only five are independent and they form an implication or entailment lattice. Starting with this basic lattice other implication lattices are formed. Relationship of these lattices with the various overlap conditions between the final pair of sets arrived at after a dialogue is studied. Finally, examples are given, one of which relates dialogues in rough context with rough belief revision [3] - in a line similar to the approach of [5].

Słowa kluczowe

EN

rough sets; negotiation; modal system S5; belief change

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 75, nr 1-4
• Strony: 123--139
• Opis fizyczny: bibliogr. 12 poz., rys.

Twórcy

autor

Chakraborty M.K.

autor

Banerjee M.

• Departtment of Mathematics and Statistics Indian Institute of Technology Kanpur 208016, India,

Bibliografia

• [1] Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet functions for contraction and revision, J. Symb. Logic, 50, 1985, 510-530.
• [2] Banerjee, M.: Logic for rough truth, Fund. Informaticae, 71(2-3), 2006, 139-151.
• [3] Banerjee, M.: Rough belief change, Transactions of Rough Sets V, LNCS 4100, 2006, 25-38.
• [4] Banerjee, M., Chakraborty, M. K.: A category for rough sets, Foundations of Computing and Decision Sciences, 18(3-4), 1993, 167-180.
• [5] Booth, R.: A negotiation style framework for non-prioritised revision, Proc. 8th Conf. on Theoretical Aspects of Rationality and Knowledge (TARK-2001), Italy (J. van Benthem, Ed.),Morgan Kaufmann, 137-150, 2001.
• [6] Chakraborty, M. K., Banerjee,M.: Dialogue in rough context, LNAI 3066, Proc. Int. Conf. on Rough Sets and Current Trends in Computing (RSCTC 2004), Sweden (S. Tsumoto, Ed.), Springer-Verlag, 295-299, 2004.
• [7] Gärdenfors, P., Rott, H.: Belief revision, in: Handbook of Logic in AI and Logic Programming, Vol.4: Epistemic and Temporal Reasoning (D. M. Gabbay, C. J. Hogger, J. A. Robinson, Eds.), Clarendon, 1995, 35-132.
• [8] Hughes, G. E., Cresswell, M. J.: A New Introduction to Modal Logic, Routledge, 1996.
• [9] Pawlak, Z.: Rough sets, Int. J. Comp. Inf. Sci., 11, 1982, 341-356.
• [10] Pawlak, Z.: Rough logic, Bull. Polish Acad. Sc. (Tech. Sc.), 35(5-6), 1987, 253-258.
• [11] Walton, D. N., Krabbe, E. C. W.: Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning, SUNY Press, 1995.
• [12] Wooldridge, M., Parsons, S.: Languages for negotiation, Proc. 14th European Conf. on AI (ECAI-2000), Germany (W. Horn, Ed.), John Wiley, 393-400, 2000.