The logic of Chance Discovery (CD) as well as mathematical models for CD, by the nature of the term chance, are hard to formalize, which poses challenging problems for mathematization of the area. It does not completely prevent us though from studying the logical laws which chance discovery and related notions should abide, especially in a carefully chosen and reasonably expressive mathematical formalism. The framework, the authors suggest11 This research is supported by Engineering and Physical Sciences Research Council (EPSRC), UK, grant EP/F014406/1. in this paper, is based on a well-developed area of modal logic, more precisely on Kripke-Hintikka semantics, with a notable distinction: unlike some other hybridization schemes, it leads to decidable logics, while still preserving high expressive power. We demonstrate our approach by an example of the Logic of Discovery and Knowledge, where a regular modal language is augmented with higher level operators intended to model some contrasting aspects of Chance Discovery: uncertain necessity of discovery and local common knowledge within contexts admitting branching time.