TOPOLOGICAL REASONING AND THE LOGIC OF KNOWLEDGE

We present a bimodal logic suitable for formalizing reasoning about po ints and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces, and we o btain complete axiomatizations for the sentences which hold in these i nterpretations. In addition, we axiomatize the validities of the small er class of topological spaces in a system we call topologic. We also prove decidability for these two systems. Our results on topologic rel ate early work of McKinsey on topological interpretations of S4 with r ecent work of Georgatos on topologic. Some of the results of this pape r were presented (Moss and Parikh, 1992) at the 1992 conference on The oretical Aspects of Reasoning about Knowledge.