arXiv subjects

Hans van Ditmarsch

Publications and source records attributed to Hans van Ditmarsch.

At least 19 recordsLinked to original sources

arXiv2026

Axiomatisation for an asynchronous epistemic logic with sending and receiving messages

We investigate a logic for asynchronous announcements wherein the sending of the messages by the environment is separated from their reception by the individual agents. Both come with different modalities. In the logical semantics, formulas are interpreted in a world of a Kripke model but given a history of prior announcements and receptions that already happened. An axiomatisation AA for such a logic has been given in prior work, for the formulas that are valid when interpreted in the Kripke model before any such announcements have taken place. This axiomatisation is a reduction system wherein one can show that every formula is equivalent to a purely epistemic formula without dynamic modalities for announcements and receptions. We propose a generalisation AA* of this axiomatisation, for the formulas that are valid when interpreted in the Kripke model given any history of prior announcements and receptions of announcements. It does not extend the axiomatisation AA, for example it is no longer valid that nobody has received any message. Unlike AA, this axiomatisation AA* is infinitary and it is not a reduction system.

cs.LO↗

arXiv2026

The Dynamic Turn in Paraconsistency

In this work we propose a dynamic turn in paraconsistency. We introduce AMLFI1, the action model extension of the paraconsistent logic LFI1. A special case is PALFI1, a paraconsistent logic of public announcements. It corresponds to another, recently published, paraconsistent public announcement logic: the differences in their axiomatizations are mutually admissible. We also introduce UMLFI1, that extends AMLFI1 with factual change. Soundness and completeness are proven for all logics, and all extend the epistemic paraconsistent logics KLFI1, KB4LFI1 and S5LFI1, known from the literature. With such dynamic epistemic paraconsistent logics we can formalize obtaining and resolving provisional contradictions.

cs.LO↗

arXiv2026

Resolving Asynchronous Distributed Knowledge

There are by now various epistemic modal logics with intersection modalities for distributed knowledge and intersection update modalities for dynamic phenomena like agents sharing (all their) information, agents receiving information from other agents, and full information protocols. One of those is the logic of Resolving Distributed Knowledge, by Agotnes and Wang. It has distributed knowledge modalities for arbitrary subsets of the set of all agents and it also has so-called resolution modalities for arbitrary subsets of agents sharing their knowledge. In that logic, the agents not involved in the knowledge sharing are aware of the agents sharing knowledge, agents are memory-less, and the kind of dynamics represents synchronous updates, where there is common awareness of the global clock. In contrast, in this contribution we present a logic for Resolving Asynchronous Distributed Knowledge. It is an asynchronous generalization of the synchronous logic of resolving distributed knowledge. The logical semantics is history-based: truth is not only with respect to a given world in a model, but also with respect to a given history of prior resolutions, of which each individual agent can only observe a part. In particular, an agent is unaware of resolutions for groups of agents not including her. As is to be expected, this comes with many technical complications, for example concerning the axiomatization. The synchronous axioms relating resolution to distributed knowledge are now invalid. The modelling advantages of such an asynchronous novel logic, for distributed computing and similar areas, are however substantial and a major asset.

cs.LO↗

arXiv2026

History of the Muddy Children Puzzle

The Muddy Children Puzzle is a puzzle about knowledge and ignorance that has been inspiring for the development of epistemic logic. Who came up with it first? This is unclear. We trace the origin of the Muddy Children Puzzle through logical and literary publications over the past two centuries. The puzzle inspired a numerous variations such as involving numbers or coloured hats. We also present a novel hats puzzle involving self-reference.

cs.AI↗

arXiv2026

Self-Correcting Gossip Protocols

We investigate self-correcting gossip protocols with errors. In distributed computing, protocols with errors have been widely investigated in temporal epistemic logics. Instead, we propose a dynamic epistemic logic. We show how to correct transmission errors due to faulty messages without a central authority coordinating protocol execution, how this affects optimality, and how this compares to bounded memory and full information protocols.

cs.LO↗

arXiv2025

Hypergraph Semantics for Doxastic Logics

Simplicial models have become a crucial tool for studying distributed computing. These models, however, are only able to account for the knowledge, but not for the beliefs of agents. We present a new semantics for logics of belief. Our semantics is based on directed hypergraphs, a generalization of ordinary directed graphs in which edges are able to connect more than two vertices. Directed hypergraph models preserve the characteristic features of simplicial models for epistemic logic, while also being able to account for the beliefs of agents. We provide systems of both consistent belief and merely introspective belief. The completeness of our axiomatizations is established by the construction of canonical hypergraph models. We also present direct conversions between doxastic Kripke models and directed hypergraph models.

cs.LO↗

arXiv2025

Modal Logic for Simulation, Refinement, and Mutual Ignorance

Simulation and refinement are variations of the bisimulation relation, where in the former we keep only atoms and forth, and in the latter only atoms and back. Quantifying over simulations and refinements captures the effects of information change in a multi-agent system. In the case of quantification over refinements, we are looking at all the ways the agents in a system can become more informed. Similarly, in the case of quantification over simulations, we are dealing with all the ways the agents can become less informed, or in other words, could have been less informed, as we are at liberty how to interpret time in dynamic epistemic logic. While quantification over refinements has been well explored in the literature, quantification over simulations has received considerably less attention. In this paper, we explore the relationship between refinements and simulations. To this end, we also employ the notion of mutual factual ignorance that allows us to capture the state of a model before agents have learnt any factual information. In particular, we consider the extensions of multi-modal logic with the simulation and refinement modalities, as well as modalities for mutual factual ignorance. We provide reduction-based axiomatizations for several of the resulting logics that are built extending one another in a modular fashion.

cs.LO↗

arXiv2025

Muddy Waters

In the 2013 Advent calender of the Berlin Mathematics Research Center MATH+, Gerhard Woeginger presents a novel hat problem with an uncommon initial announcement. Although the information given is insufficient for the hat bearers to learn their colour, they are informed that the colours have been chosen so that they can learn their colour. We formalize this announcement in public announcement logic and in an extension of public announcement logic with fixpoints.

cs.LO↗

arXiv2025

Satisfiability of Quantified Boolean Announcements

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 communication protocols. However, quantifying over quite simple informative events, public announcements, is not computable: such an arbitrary public announcement logic, APAL, has an undecidable satisfiability problem. Here we consider even simpler informative events called Boolean announcements, where announcements are restricted to be a Boolean combination of atomic propositions. The logic is called Boolean arbitrary public announcement logic, BAPAL. A companion paper provides a complete finitary axiomatization, and related expressivity results, for BAPAL. In this work the satisfiability problem for BAPAL is shown to decidable, and also that BAPAL does not have the finite model property.

cs.LO↗

arXiv2024

A Logic for Repair and State Recovery in Byzantine Fault-tolerant Multi-agent Systems

We provide an epistemic logical language and semantics for the modeling and analysis of byzantine fault-tolerant multi-agent systems. This not only facilitates reasoning about the agents' fault status but also supports model updates for implementing repair and state recovery. For each agent, besides the standard knowledge modality our logic provides an additional modality called hope, which is capable of expressing that the agent is correct (not faulty), and also dynamic modalities enabling change of the agents' correctness status. These dynamic modalities are interpreted as model updates that come in three flavours: fully public, more private, or involving factual change. We provide complete axiomatizations for all these variants in the form of reduction systems: formulas with dynamic modalities are equivalent to formulas without. Therefore, they have the same expressivity as the logic of knowledge and hope. Multiple examples are provided to demonstrate the utility and flexibility of our logic for modeling a wide range of repair and state recovery techniques that have been implemented in the context of fault-detection, isolation, and recovery (FDIR) approaches in fault-tolerant distributed computing with byzantine agents.

cs.DC↗

arXiv2024

Bisimulation for Impure Simplicial Complexes

As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the vertex set. A maximal simplex is called a facet. Impure simplicial complexes represent that some agents (processes) are dead. It is known that impure simplicial complexes categorically correspond to so-called partial epistemic (Kripke) models. In this contribution, we define a notion of bisimulation to compare impure simplicial complexes and show that it has the Hennessy-Milner property. These results are for a logical language including atoms that express whether agents are alive or dead. Without these atoms no reasonable standard notion of bisimulation exists, as we amply justify by counterexamples, because such a restricted language is insufficiently expressive.

cs.LO↗

arXiv2024

The Undecidability of Quantified Announcements

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 group of agents (this group may be a proper subset of the set of all agents) all of which are simultaneously (and publicly) making known announcements. So this is more restrictive than APAL. Finally, CAL is as GAL except that we now quantify over anything the agents not in that group may announce simultaneously as well. The logic CAL therefore has some features of game logic and of ATL. We show that when there are multiple agents in the language, the satisfiability problem is undecidable for APAL, GAL, and CAL. In the single agent case, the satisfiability problem is decidable for all three logics. This paper corrects an error to the submitted version of Undecidability of Quantified Announcements, identified by Yuta Asami . The nature of the error was in the definition of the formula $cga(X)$ (see Subsection 5.2) which is corrected in this version.

cs.LO↗

arXiv2024

Boolean Observation Games

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. It does not control the given, fixed, value of variables. Boolean observation games are a generalization of Boolean games, a well-studied subclass of strategic games but with complete information, and wherein each player controls the value of its variables. In Boolean observation games, player goals describe multi-agent knowledge of variables. As in classical strategic games, players choose their strategies simultaneously and therefore observation games capture aspects of both imperfect and incomplete information. They require reasoning about sets of outcomes given sets of indistinguishable valuations of variables. An outcome relation between such sets determines what the Nash equilibria are. We present various outcome relations, including a qualitative variant of ex-post equilibrium. We identify conditions under which, given an outcome relation, Nash equilibria are guaranteed to exist. We also study the complexity of checking for the existence of Nash equilibria and of verifying if a strategy profile is a Nash equilibrium. We further study the subclass of Boolean observation games with `knowing whether' goal formulas, for which the satisfaction does not depend on the value of variables. We show that each such Boolean observation game corresponds to a Boolean game and vice versa, by a different correspondence, and that both correspondences are precise in terms of existence of Nash equilibria.

cs.GT↗

arXiv2023

Impure Simplicial Complexes: Complete Axiomatization

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 (agents) are alive, whereas impure simplicial complexes describe message passing in synchronous systems where processes may be dead (have crashed). Properties of impure simplicial complexes can be described in a three-valued multi-agent epistemic logic where the third value represents formulae that are undefined, e.g., the knowledge and local propositions of dead agents. In this work we present an axiomatization for the logic of the class of impure complexes and show soundness and completeness. The completeness proof involves the novel construction of the canonical simplicial model and requires a careful manipulation of undefined formulae.

cs.LO↗

arXiv2023

On Two- and Three-valued Semantics for Impure Simplicial Complexes

Simplicial complexes are a convenient semantic primitive to reason about processes (agents) communicating with each other in synchronous and asynchronous computation. Impure simplicial complexes distinguish active processes from crashed ones, in other words, agents that are alive from agents that are dead. In order to rule out that dead agents reason about themselves and about other agents, three-valued epistemic semantics have been proposed where, in addition to the usual values true and false, the third value stands for undefined: the knowledge of dead agents is undefined and so are the propositional variables describing their local state. Other semantics for impure complexes are two-valued where a dead agent knows everything. Different choices in designing a semantics produce different three-valued semantics, and also different two-valued semantics. In this work, we categorize the available choices by discounting the bad ones, identifying the equivalent ones, and connecting the non-equivalent ones via a translation. The main result of the paper is identifying the main relevant distinction to be the number of truth values and bridging this difference by means of a novel embedding from three- into two-valued semantics. This translation also enables us to highlight quite fundamental modeling differences underpinning various two- and three-valued approaches in this area of combinatorial topology. In particular, pure complexes can be defined as those invariant under the translation.

cs.DC↗

arXiv2023

Communication Pattern Logic: Epistemic and Topological Views

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 might fail: an agent is certain about the messages it receives, but it may be uncertain about the messages other agents have received. In a dynamic epistemic logic with distributed knowledge and with modalities for communication patterns, the latter are interpreted by updating Kripke models. We propose an axiomatization of communication pattern logic, and we show that collective bisimilarity (comparing models on their distributed knowledge) is preserved when updating models with communication patterns. We can also interpret communication patterns by updating simplicial complexes, a well-known topological framework for distributed computing. We show that the different semantics correspond, and propose collective bisimulation between simplicial complexes.

cs.DC↗

arXiv2023

Comparing the Update Expressivity of Communication Patterns and Action Models

Any kind of dynamics in dynamic epistemic logic can be represented as an action model. Right? Wrong! In this contribution we prove that the update expressivity of communication patterns is incomparable to that of action models. Action models, as update mechanisms, were proposed by Baltag, Moss, and Solecki in 1998 and have remained the nearly universally accepted update mechanism in dynamic epistemic logics since then. Alternatives, such as arrow updates that were proposed by Kooi and Renne in 2011, have update equivalent action models. More recently, the picture is shifting. Communication patterns are update mechanisms originally proposed in some form or other by Agotnes and Wang in 2017 (as resolving distributed knowledge), by Baltag and Smets in 2020 (as reading events), and by Velazquez, Castaneda, and Rosenblueth in 2021 (as communication patterns). All these logics have the same expressivity as the base logic of distributed knowledge. However, their update expressivity, the relation between pointed epistemic models induced by such an update, was conjectured to be different from that of action model logic. Indeed, we show that action model logic and communication pattern logic are incomparable in update expressivity. We also show that, given a history-based semantics and when restricted to (static) interpreted systems, action model logic is (strictly) more update expressive than communication pattern logic. Our results are relevant for distributed computing wherein oblivious models involve arbitrary iteration of communication patterns.

cs.LO↗

arXiv2023

Wanted Dead or Alive : Epistemic logic for impure simplicial complexes

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 processes are alive, by Goubault et al. In our semantics, given a designated face in a complex, a formula can only be true or false there if it is defined. The following are undefined: dead processes cannot know or be ignorant of any proposition, and live processes cannot know or be ignorant of factual propositions involving processes they know to be dead. The semantics are therefore three-valued, with undefined as the third value. We propose an axiomatization that is a version of the modal logic S5. We also show that impure simplicial complexes correspond to certain Kripke models where agents' accessibility relations are equivalence relations on a subset of the domain only. This work extends a WoLLIC 21 conference publication with the same title.

cs.DC↗