Hans van Ditmarsch

Hans van Ditmarsch
Open Universiteit Nederland | OU

About

263
Publications
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3,841
Citations
Citations since 2016
67 Research Items
1873 Citations
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2016201720182019202020212022050100150200250300
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Introduction
Skills and Expertise

Publications

Publications (263)
Article
Full-text available
Group announcement logic (GAL) and coalition announcement logic (CAL) allow us to reason about whether it is possible for groups and coalitions of agents to achieve their desired epistemic goals through truthful public communication. The difference between groups and coalitions in such a context is that the latter make their announcements in the pr...
Preprint
Full-text available
Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed under containment. Pure simplicial complexes describe message passing in asynchronous systems where all processes...
Chapter
It is known that without synchronization via a global clock one cannot obtain common knowledge by communication. Moreover, it is folklore that without exchanging higher-level information arbitrary higher-level shared knowledge cannot be achieved.Here we make this result precise. We use epistemic logic to formally define “everyone knows that everyon...
Article
Full-text available
In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic (AMSL), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public...
Conference Paper
Full-text available
Knowledge has long been identified as an inherent component of agents' decision-making in distributed systems. However, for agents in fault-tolerant distributed systems with fully byzantine agents, achieving knowledge is, in most cases, unreal-istic. If agents can both lie and themselves be mistaken, then a message received is generally not suffici...
Preprint
Full-text available
Public announcement logic(PAL) is an extension of epistemic logic (EL) with some reduction axioms. In this paper, we propose a cut-free labelled sequent calculus for PAL, which is an extension of that for EL with sequent rules adapted from the reduction axioms. This calculus admits cut and allows terminating proof search.
Preprint
We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full information protocol in distributed computing is the special case wherein all agents inform each other. We study this protocol in distributed computing models where communication mig...
Preprint
Full-text available
Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask whether it is possible to achieve some state of knowledge, and has important applications in synthesising secure...
Article
We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a fu...
Article
Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: SAPAL and SCAPAL. Such restrictions are relevant...
Preprint
Full-text available
We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent synchronous distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes , where all proces...
Preprint
Full-text available
We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional variables of which only it can observe the value, and it controls whether and to whom it can reveal that value. I...
Chapter
Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and als...
Article
Full-text available
In this paper, we propose three knowability logics LK, LK−, and LK=. In the single-agent case, LK is equally expressive as arbitrary public announcement logic APAL and public announcement logic PAL, whereas in the multi-agent case, LK is more expressive than PAL. In contrast, both LK− and LK= are equally expressive as classical propositional logic...
Article
Full-text available
Coalition announcement logic (CAL) is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we descr...
Chapter
We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes, where all processes are alive...
Article
Full-text available
In this article, we present a modal logic that extends the basic modal logic ML with two dynamic operators: copy (cp), which replicates the current model, labelling each copy with a different propositional symbol and respecting accessibility relations even between distinct copies; and remove (rm), which deletes paths in the model that satisfy certa...
Article
We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimu...
Preprint
Full-text available
Quantification over public announcements shifts the perspective from reasoning strictly about the results of a particular announcement to reasoning about the existence of an announcement that achieves some certain epistemic goal. Depending on the type of the quantification, we get different formalisms, the most known of which are arbitrary public a...
Preprint
Full-text available
We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimu...
Preprint
Full-text available
We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes, where all processes are alive...
Chapter
Full-text available
A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a telephone call wherein the caller and the callee exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore some protocols wherein the...
Article
In this paper we study the solvability of the equality negation task in a simple wait-free model where two processes communicate by reading and writing shared variables or exchanging messages. In this task, the two processes start with a private input value in the set {0,1,2}, and after communicating, each one must decide a binary output value, so...
Article
In the Russian cards problem, a group of communicating agents and an eavesdropper, Eve, draw cards from a deck. The agents then wish to inform each other about their hand without Eve learning any 'protected' information, typically in the sense of weak possibilistic security. We consider a weakening of this original problem, whereby the cards are li...
Chapter
Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: FSAPAL and SCAPAL; and another version quantifyin...
Preprint
Full-text available
A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a telephone call wherein the calling agents exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore protocols wherein the termination...
Article
The so-called gossip problem is a formal model of peer-to-peer communication. In order to perform such communication efficiently, it is important to keep track of what agents know about who holds what information at a given point in time. The knowledge that the agents possess depends strongly on the particular type of communication that is used. He...
Preprint
Full-text available
In this survey we review several dynamic epistemic logics with modalities representing quantification over information change. Of such logics we present typical axioms involving the relation between knowledge or belief and informative action, their relative expressivity, directions for applications, and what is known on the decidability and complex...
Article
Full-text available
We describe some recent trends in research on lying from a multidisciplinary perspective, including logic, philosophy, linguistics, psychology, cognitive science, behavioral economics, and artificial intelligence. Furthermore, we outline the seven contributions to this special issue of topiCS.
Preprint
Full-text available
Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and als...
Article
Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic l...
Chapter
Full-text available
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 a...
Preprint
Full-text available
Distributed dynamic gossip is a generalization of the classic telephone problem in which agents communicate to share secrets, with the additional twist that also telephone numbers are exchanged to determine who can call whom. Recent work focused on the success conditions of simple protocols such as "Learn New Secrets" (LNS) wherein an agent a may o...
Article
Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We g...
Article
Full-text available
We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomati...
Chapter
We present an epistemic logic ELF (Epistemic Logic with Filters) where knowledge does not require complete certainty. In this logic, instead of saying that an agent knows a particular fact if it is true in every accessible world, we say that it knows the fact if it is true in a sufficiently large set accessible worlds. On a technical level, we do t...
Article
Full-text available
The original publication of the article is missing the funding information.
Article
We define a Public Announcement Separation Logic (PASL) that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying its semantics and illustrating its interest for modelling systems, we provide a sound and complete tableau calculus that deals with resource, ag...
Chapter
Full-text available
A gossip protocol aims at arriving, by means of point-to-point communications (or telephone calls), at a situation in which every agent knows all the information initially present in the network. If it is forbidden to have more than one call at the same time, the protocol is called sequential. We generalise a method, that originates from the famous...
Article
Full-text available
A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting...
Article
In the past decades, forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning. In this paper, we study forgetting in multi-agent modal logics. We adopt the semantic definition of existential bisimulation quantifiers as that of forgetting. We resort to canonical formulas of modal logi...
Preprint
Full-text available
We propose a framework for strategic voting when a voter may lack knowledge about the preferences of other voters, or about other voters' knowledge about her own preference. In this setting we define notions of manipulation, equilibrium, and dominance, under uncertainty. We provide scenarios wherein the profile of true preferences is the same but t...
Article
Full-text available
Arbitrary public announcement logic (APAL) reasons about how the knowledge of a set of agents changes after true public announcements and after arbitrary announcements of true epistemic formulas. We consider a variant of arbitrary public announcement logic called positive arbitrary ublic announcement logic (PAPAL), which restricts arbitrary public...
Article
Full-text available
In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update modalities induce transformations (updates) of relational models. In AAUML the update modalities formalize the exe...
Article
Full-text available
Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi intuitively expressing that 'after every public announcement of a formula, formula phi is true.' The logic APAL is...
Conference Paper
We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulation-invariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature.
Article
Full-text available
We compare different epistemic notions in the presence of awareness of propositional variables: the logic of implicit knowledge (in which explicit knowledge is definable), the logic of explicit knowledge, and the logic of speculative knowledge. Speculative knowledge is a novel epistemic notion that permits reasoning about unawareness. These logics...
Conference Paper
Full-text available
We give combinatorial, computational and simulation results for well-known distributed protocols for gossiping on completely connected networks. The protocols consist of: making any call (ANY), only calling agents whose secret you do not know (" learn new secrets " LNS), and never repeating calls (" call once " CO). First, we show that these protoc...
Conference Paper
We propose an epistemic strategy logic with future and past time operators, called \(\text {SLKP}\), for Strategy Logic with Knowledge of the Past. With \(\text {SLKP}\) we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on th...
Article
Full-text available
In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \(\varphi \), while all the other agents observe that group G is informed, but are uncertain whether the...
Conference Paper
Full-text available
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...
Article
Full-text available
In this paper we introduce {\em global and local announcement logic} (GLAL), a dynamic epistemic logic with two distinct announcement operators -- $[\phi]^+_A$ and $[\phi]^-_A$ indexed to a subset $A$ of the set $Ag$ of all agents -- for global and local announcements respectively. The boundary case $[\phi]^+_{Ag}$ corresponds to the public announc...
Article
Full-text available
Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic...
Article
We propose a logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents. Additional to epistemic modalities, the logic therefore contains two types of dynamic modalities, for sending messages and for receiving messages. The semantics defines truth relative to the current state of receptio...
Chapter
Full-text available
Rohit Parikh has written on levels of knowledge (Parikh and Krasucki in Sadhana 17(1):167–191, 1992). Levels of knowledge are relevant for the analysis of gossip protocols. Gossip protocols describe the dissemination of information over a network. We present some examples of epistemic gossip protocols, wherein the agents or processes communicate wi...
Article
A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agen...
Article
In this paper we introduce arbitrary arrow update logic (AAUL). The logic AAUL takes arrow update logic, a dynamic epistemic logic where the accessibility relations of agents are updated rather than the set of possible worlds, and adds a quantifier over such arrow updates. We investigate the relative expressivity of AAUL compared to other logics, m...
Article
Arbitrary Arrow Update Logic is a dynamic modal logic that uses an arbitrary arrow update modality to quantify over all 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 that the satisfiability problem of Arbit...
Article
Full-text available
In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of (non-)cont...
Article
Full-text available
We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatization...
Article
Full-text available
We prove that modal logic formulated in a language with the cover modality is exponentially more succinct than the usual box-and-diamond version. In contrast with this, we show that adding the so-called public announcement operator to the latter results in a modal system that is exponentially more succinct than the one based on the cover modality.
Article
Full-text available
In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is...
Article
This paper demonstrates the undecidability of a number of logics with quantification over public announcements: arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). In APAL we consider the informative consequences of any announcement, in GAL we consider the informative consequences of a...
Article
Full-text available
A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. We consider distributed gossip protocols wherein the agents themselves instead of a global scheduler determine whom to call. In this paper the problem of designing and analyzing gossip protocols is given a dynamic twist by assuming that when a...
Conference Paper
We define an Epistemic Separation Logic, called ESL, that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying the semantics and the expressiveness of this logic, we provide a tableau calculus with labels and resource contraints that is sound and complete an...
Chapter
A rich man gives you two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much money as the other envelope. You may choose one envelope and keep the money. You pick one envelope, open it, and it contains 100 dollars. Now the rich man offers you the option to take the other envelope instead....
Chapter
At a trial a prisoner is sentenced to death by the judge. The verdict reads “You will be executed next week, but the day on which you will be executed will be a surprise to you.” The prisoner reasons as follows. “I cannot be executed on Friday, because in that case I would not be surprised. But given that Friday is eliminated, then I cannot be exec...
Chapter
Suppose you have made it to the final round of a game show. You can win a car that is behind one of three doors. The game show host asks you to pick a door. You choose door number 1. He tells you that he knows where the car is, and opens one of the remaining doors that does not have the car, say door number 3. Now he asks you whether you would like...
Chapter
A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light switch (and that is the only way in which they can communicate). The...
Chapter
You cannot see what is written on your own forehead. But you can see what is on the forehead of the person who you are talking to. In the original version of the riddle you only know your own number, but not the other’s number. In this version you only know the other’s number, but not your own number. Otherwise, there is no difference. After the an...
Chapter
Anne and Bill get to hear the following: “Given are two natural numbers. They are consecutive numbers. I am going to whisper one of these numbers to Anne and the other number to Bill.” This happens. Anne and Bill now have the following conversation. Anne: “I don’t know your number.” Bill: “I don’t know your number.” Anne: “I know your number.” Bill...
Chapter
From a pack of seven known cards 0, 1, 2, 3, 4, 5, 6 Alice and Bob each draw three cards and Cath gets the remaining card. All this is known. How can Alice and Bob openly inform each other about their cards, without Cath learning of any of their cards who holds it?
Chapter
A group of children has been playing outside and they are called back into the house by their father. The children gather round him. As one may imagine, some of them have become dirty from the play. In particular: they may have mud on their face. Children can only see whether other children are muddy, and not if there is any mud on their own face....
Chapter
Six friends each know a secret. They can call each other. In each call they exchange all the secrets they know. How many calls are needed for everyone to know all secrets?
Chapter
This 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 agents holding playing cards; and, mainly for the purpose of motivating the dynamics, we also briefly introduce the concepts of shared an...
Chapter
Six players are playing Cluedo. On the game board, Alice just landed in the kitchen. She says: “I suspect that Miss Scarlett did it, with a knife, in the kitchen.” Nobody shows her a card. Who committed the murder?
Chapter
Anne, Bill, and Cath all have a positive integer on their forehead. They can only see the foreheads of others. One of the numbers is the sum of the other two. All the previous is common knowledge. They now successively make the truthful announcements: 1. Anne: “I don’t know my number.” 2. Bill: “I don’t know my number.” 3. Cath: “I don’t know my nu...
Chapter
\(A\) says to \(S\) and \(P\) : I have chosen two integers \(x, y\) with \(1 < x < y\) and \(x+y \leq 100\) . In a moment I will inform \(S\) of their sum \(s = x+y\) , and I will inform \(P\) of their product \(p = xy\) . These announcements will remain secret. You are required to make an effort to determine the numbers \(x\) and \(y\) .