A Logic of Blockchain Updates

Blockchains are distributed data structures that are used to achieve consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts (like Ethereum). Although blockchains gained a lot of popularity recently, there is no logic-based model for blockchains available. We introduce BCL, a dynamic logic to reason about blockchain updates, and show that BCL is sound and complete with respect to a simple blockchain model

Symbolic Model Checking for Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing DEL methods. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update

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

Knowing Values and Public Inspection

We present a basic dynamic epistemic logic of "knowing the value". Analogous to public announcement in standard DEL, we study "public inspection", a new dynamic operator which updates the agents' knowledge about the values of constants. We provide a sound and strongly complete axiomatization for the single and multi-agent case, making use of the well-known Armstrong axioms for dependencies in databases

Reachability of Five Gossip Protocols

Gossip protocols use point-to-point communication to spread information within a network until every agent knows everything. Each agent starts with her own piece of information (‘secret’) and in each call two agents will exchange all secrets they currently know. Depending on the protocol, this leads to different distributions of secrets among the agents during its execution. We investigate which distributions of secrets are reachable when using several distributed epistemic gossip protocols from the literature. Surprisingly, a protocol may reach the distribution where all agents know all secrets, but not all other distributions. The five protocols we consider are called 햠햭햸, 햫햭햲, 햢햮, 햳햮햪, and 햲햯햨. We find that 햳햮햪 and 햠햭햸 reach the same distributions but all other protocols reach different sets of distributions, with some inclusions. Additionally, we show that all distributions are subreachable with all five protocols: any distribution can be reached, if there are enough additional agents

The undecidability of arbitrary arrow update logic

Arbitrary Arrow Update Logic is a dynamic modal logic with a modality to quantify over arrow updates. Some properties of this logic have already been established, but until now it remained an open question whether the logic's satisfiability problem is decidable. Here, we show by a reduction of the tiling problem that the satisfiability problem of Arbitrary Arrow Update Logic is co-RE hard, and therefore undecidable