Sum and Product in Dynamic Epistemic Logic

The Sum-and-Product riddle was first published in [Fre69]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown. We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. We analyze one of the announcements towards the solution ...

• Type: Journal
• Year: 2008
• Where: LOGCOM
• Authors: Hans P. van Ditmarsch, Ji Ruan, Rineke Verbrugge
• Keywords: LOGCOM 2008, Public Announcements, Riddle, Sum-and-Product Riddle