Modal Logic of Partitions

This thesis proposes “partitionistic elimination” in philosophical applications of modal logic based on possible world semantics to notions around information and to deontic reasoning. There are two common ideas in usages of possible worlds in philosophical logic relevant to information and agency. First, elimination of possibilities represents a condition of information acquisition and real choice. It has been usually unspecified how many possibilities are to be eliminated. Second, a partition of a set of possible worlds often represents epistemic options or choices toward an action. The thesis proposes to combine these ideas: use a partition in order to specify how many possible worlds are to be eliminated when information acquisition or action arises. Based on the proposal, the thesis develops semantics of a modal language whose logic is non-monotonic in general. An axiomatization of the basic logic of the semantics is shown. Completeness and finite model properties are proved. The thesis also characterizes some frame conditions, but a nested partition condition is not characterizable. The formal results are applied to the two areas of information and obligation. The first application of new modal logics is to the logic of questions and answers. Modal operators formally describe logical behavior of relevant informal concepts previously argued. A formal counterpart of the notion of complete and just complete information behaves to elucidate some examples related to Gricean conversational implicature. The notion of partial information is to be refined to three subclasses with different logical properties. The second application of partition