Journal of Logic and Computation, Volume 10, Issue 2, pp. 253-269: Abstract.
Two alternative notions of 'possibility' satisfying Halpern's conditions
K Su1, H Chen2 and D Ding3
1Department of Computer Science, Zhongshan University, Guangzhou, 510275, PRC, 2Department of Computer Science, Changsha Institute of Technology, Changsha, 410073, PRC, 3Department of Mathematics, Nanjing University, Nanjing, 210008, PRC
In this paper we give two alternative notions of possibility that satisfy Halpern's two conditions. One of the two notions, for the logic S4n, seems to behave in the same way as Halpern's original one; and the other has quite different properties from those of Halpern's. They exemplify that the answers are negative to the two questions proposed by Halpern, that is, whether his two conditions are sufficient to determine the notion of 'possibility' uniquely for a given logic and whether the results he proved for his three notions of possibility hold for any of those satisfying the two conditions.
Keywords: epistemic logic, knowledge, ignorance, only knowing.