Papers by Hans van Ditmarsch
Outstanding Contributions to Logic, 2014
Lecture Notes in Computer Science, 2005
We model the well-known Sum-and-Product problem in a modal logic, and verify its solution in a mo... more 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. This logic contains operators for knowledge, but also 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. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. It involves reformulations to facilitate the computation.
Lecture Notes in Computer Science, 2012
Lecture Notes in Computer Science, 2015
Lecture Notes in Computer Science, 2014
We propose a dynamic logic of lying, wherein a 'lie that ϕ' (where ϕ is a formula in the logic) i... more We propose a dynamic logic of lying, wherein a 'lie that ϕ' (where ϕ is a formula in the logic) is an action in the sense of dynamic modal logic, that is interpreted as a state transformer relative to the formula ϕ. The states that are being transformed are pointed Kripke models encoding the uncertainty of agents about their beliefs. Lies can be about factual propositions but also about modal formulas, such as the beliefs of other agents or the belief consequences of the lies of other agents. We distinguish (i) an outside observer who is lying to an agent that is modelled in the system, from (ii) one agent who is lying to another agent, and where both are modelled in the system. For either case, we further distinguish (iii) the agent who believes everything that it is told (even at the price of inconsistency), from (iv) the agent who only believes what it is told if that is consistent with its current beliefs, and from (v) the agent who believes everything that it is told by consistently revising its current beliefs. The logics have complete axiomatizations, which can most elegantly be shown by way of their embedding in what is known as action model logic or the extension of that logic to belief revision.
In one hour, you will all be taken to your cells to be kept in solitary confinement, with no poss... more In one hour, you will all be taken to your cells to be kept in solitary confinement, with no possibility of communicating with any of your fellow inmates. Well, almost no possibility .... every night from now on, I will choose one of you at random, re-trieve you from your cell, and take you to ...
A CIP Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-5... more A CIP Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-5838-7 (HB) ISBN 978-1-4020-5839-4 (e-book) ISBN 978-1-4020-6908-6 (PB) Published by Springer, PO Box 17, 3300 AA Dordrecht, The Netherlands. Printed on acid-free paper ...
The Unity of Science in the Arabic Tradition, 2008
In this short contribution we briefly present life and times of Ibn Khaldūn, his magistral accomp... more In this short contribution we briefly present life and times of Ibn Khaldūn, his magistral accomplishment in the Muqaddimah, and present Muqaddimah fragments related to logic and epistemology from the perspective of modern modal logic.
Philosophy of Information, 2008
Uncertainty, Rationality, and Agency, 2005
We show how belief revision can be treated systematically in the format of dynamicepistemic logic... more We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.
Logic Journal of IGPL, 2013
We give a relation between a logic of knowledge and change, with a semantics on Kripke models, an... more We give a relation between a logic of knowledge and change, with a semantics on Kripke models, and a logic of knowledge and time, with a semantics on interpreted systems. In particular, given an epistemic state (pointed Kripke model with equivalence relations) and a formula in a dynamic epistemic logic (a logic describing the consequences of epistemic actions), we construct an interpreted system relative to that epistemic state and that formula that satisfies the translation of the formula into a temporal epistemic logic. The construction involves that the protocol that is implicit in the dynamic epistemic formula, i.e., the set of sequences of actions being executed to evaluate the formula, is made explicit. We first focus on the logic of knowledge and change that is known as public announcement logic, then generalize our results to a dynamic epistemic logic. When compared to Kripke (possible worlds) models, interpreted systems have at least two appealing features: a natural accessibility relation between domain objects, and an equally natural notion of dynamics, modelled by runs. The accessibility relation as we know it from the possible worlds model is in this case grounded; it has a direct and natural interpretation, as follows. In an interpreted system, the role of possible worlds is performed by global states, which are constituted by the agents' local states and the state of the environment. Each agent knows exactly its own local state and the possible local states of other agents: two global states are indistinguishable for an agent if his local compartment is the same. Secondly, an interpreted system defines a number of runs through such global states (i.e., a sequence of global states). Each run corresponds to a possible computation allowed by a protocol. In an object language with temporal and epistemic operators one can then express temporal properties such as liveness and temporal epistemic properties such as perfect recall.
Electronic Notes in Theoretical Computer Science, 2006
We implement a specific protocol for bit exchange among card-playing agents in three different st... more 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.
Logic Journal of IGPL, 2007
... van Ditmarsch. Apart from Mara very many others were closely involved in the organization of ... more ... van Ditmarsch. Apart from Mara very many others were closely involved in the organization of SICTTL, in particular the other members of the local organization committte Bélen Pérez-Lancho, and Ana Gil. Hans van Ditmarsch's ...
Advances in Intelligent and Soft Computing, 2011
Given an interpreted system, we investigate ways for two agents to communicate secrets by public ... more Given an interpreted system, we investigate ways for two agents to communicate secrets by public announcements. For card deals, the problem to keep all of your cards a secret (i) can be distinguished from the problem to keep some of your cards a secret (ii). For (i): we characterize a novel class of protocols consisting of two announcements, for the case where two agents both hold n cards and the third agent a single card; the communicating agents announce the sum of their cards modulo 2n + 1. For (ii): we show that the problem to keep at least one of your cards a secret is equivalent to the problem to keep your local state (hand of cards) a secret; we provide a large class of card deals for which exchange of secrets is possible; and we give an example for which there is no protocol of less than three announcements.
Advances in Intelligent and Soft Computing, 2012
Journal of Applied Non-Classical Logics, 2005
Lecture Notes in Computer Science, 2013
In public announcement logic it is assumed that all agents pay attention (listen to/observe) to t... more In public announcement logic it is assumed that all agents pay attention (listen to/observe) to the announcement. Weaker observational conditions can be modelled in event (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 called logic of announcements and attention. We give an axiomatization and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic . We exploit our logic to formalize the concept of joint attention that has been widely discussed in the philosophical and cognitive science literature. Finally, we extend our logic by integrating attention change.
Lecture Notes in Computer Science, 2013
Epistemic plausibility models are Kripke models agents use to reason about the knowledge and beli... more Epistemic plausibility models are Kripke models agents use to reason about the knowledge and beliefs of themselves and each other. Restricting ourselves to the single-agent case, we determine when such models are indistinguishable in the logical language containing conditional belief, i.e., we define a proper notion of bisimulation, and prove that bisimulation corresponds to logical equivalence on image-finite models. We relate our results to other epistemic notions, such as safe belief and degrees of belief. Our results imply that there are only finitely many non-bisimilar single-agent epistemic plausibility models on a finite set of propositions. This gives decidability for single-agent epistemic plausibility planning.
Advances in Intelligent and Soft Computing, 2012
Lecture Notes in Computer Science, 2007
Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators t... more 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 a labelled tableau-calculus for this logic. We also present an extension of the calculus for a logic of arbitrary announcements.
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Papers by Hans van Ditmarsch