Cheryl's Birthday

We present four logic puzzles and after that their solutions. Joseph Yeo designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for 'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other knowledge puzzles, and that can also be found on the webpage http://personal.us.es/hvd/lightbulb.html dedicated to the book.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Preservation of Semantic Properties during the Aggregation of Abstract Argumentation Frameworks

An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in a debate, we may wish to aggregate their individual argumentation frameworks to obtain a single such framework that reflects the consensus of the group. Even when agents disagree on many details, there may well be high-level agreement on important semantic properties, such as the acceptability of a given argument. Using techniques from social choice theory, we analyse under what circumstances such semantic properties agreed upon by the individual agents can be preserved under aggregation.Comment: In Proceedings TARK 2017, arXiv:1707.0825

A New Game Equivalence and its Modal Logic

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of "basic powers" which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching "instantial neighborhood game logic", and show how our analysis can be extended to a new game algebra and dynamic game logic.Comment: In Proceedings TARK 2017, arXiv:1707.0825