H.P. van Ditmarsch

Model Checking Russian Cards

We implement a specific protocol for bit exchange among card-playing agents in three different state-of-the-art epistemic model checkers and compare the results.

What can we achieve by arbitrary announcements?: A dynamic take on Fitch's knowability

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: □ϕ expresses that ϕ is true after an arbitrary announcement ψ. As this includes the trivial announcement ⊤, one might as well say that □ϕ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ⋄ϕ expresses that there is an announcement after which ϕ. This gives a perspective on Fitchs knowability issues: for which formulas ϕ does it hold that ϕ → ⋄Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.

Concurrent Dynamic Epistemic Logic

When giving an analysis of knowledge in multiagent systems, one needs a framework in which higher-order information and its dynamics can both be represented. A recent tradition starting in original work by Plaza treats all of knowledge, higher-order knowledge, and its dynamics on the same foot. Our work is in that tradition. It also fits in approaches that not only dynamize the epistemics, but also epistemize the dynamics: the actions that (groups of) agents perform are epistemic actions. Different agents may have different information about which action is taking place, including higher-order information. We demonstrate that such information changes require subtle descriptions. Our contribution is to provide a complete axiomatization for an action language of van Ditmarsch, where an action is interpreted as a relation between epistemic states (pointed models) and sets of epistemic states. The applicability of the framework is found in every context where multiagent strategic decision making is at stake, and already demonstrated in game-like scenarios such as Cluedo and card games.

Sum and Product in Dynamic Epistemic Logic

The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. 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 analyse one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that becomes false because it is announced. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking and the complexity is experimentally investigated for several representations and parameter settings.

Concurrent dynamic epistemic logic for MAS

When giving an analysis of knowledge in multiagent systems, one needs a framework in which higher-order information and its dynamics can both be represented. A recent tradition starting in original work by Plaza treats all of knowledge, higher-order knowledge, and its dynamics on the same foot. Our work is in that tradition. It also fits in approaches that not only dynamize the epistemics, but also epistemize the dynamics: the actions that (groups of) agents perform are epistemic actions. Different agents may have different information about which action is taking place, including higher-order information. We demonstrate that such information changes require subtle descriptions. The contribution of our paper is that it provides a complete axiomatization for an action language of van Ditmarsch, where an action is interpreted as a relation between states and sets of states. The applicability of the framework is found in every context where multiagent strategic decision making is at stake, and already demonstrated in game-like scenarios such as Cluedo and card games.

Model checking sum and product

We model the well-known Sum-and-Product problem in a modal logic, and verify its solution in a model checker. The modal logic is public announcement logic. The riddle is then implemented and its solution verified in the epistemic model checker DEMO.

Playing cards with Hintikka An introduction to dynamic epistemic logic

This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in Hintikka’s ‘Knowledge and Belief ’ (1962) give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates.

Restricted permutations and queue jumping

A connection between permutations that avoid 4231 and a certain queuing discipline is established. It is proved that a more restrictive queuing discipline corresponds to avoiding both 4231 and 42513, and enumeration results for such permutations are given.

Permuting machines and priority queues

Machines whose sole function is to re-order their input data are considered. Every such machine defines a set of allowable input-output pairs of permutations. These sets are studied in terms of the minimal disallowed pairs (the basis). Some allowable sets with small bases are considered including the one defined by a priority queue machine. For more complex machines defined by two or more priority queues in series or parallel, the basis is proved to be infinite.