scholarly journals Reachability Games in Dynamic Epistemic Logic

2019 ◽  
Author(s):  
Bastien Maubert ◽  
Sophie Pinchinat ◽  
François Schwarzentruber
Keyword(s):  
Epistemic Logic ◽  
Imperfect Information ◽  
Dynamic Epistemic Logic ◽  
Perfect Information ◽  
Planning Problem ◽  
Multiplayer Games ◽  
Public Announcements ◽  
Action Models

We define reachability games based on Dynamic Epistemic Logic (DEL), where the players? actions are finely described as DEL action models. We first consider the setting where a controller with perfect information interacts with an environment and aims at reaching some desired state of knowledge regarding the observers of the system. We study the problem of existence of a strategy for the controller, which generalises the classic epistemic planning problem, and we solve it for several types of actions such as public announcements and public actions. We then consider a yet richer setting where observers themselves are players, whose strategies must be based on their observations. We establish several decidability and undecidability results for the problem of existence of a distributed strategy, depending on the type of actions the players can use, and relate them to results from the literature on multiplayer games with imperfect information.

scholarly journals Playing cards with Hintikka An introduction to dynamic epistemic logic

2005 ◽  
Vol 3 ◽  
Author(s):  
H. P. Ditmarsch ◽  
W. Van Der Hoek ◽  
B. P. Kooi
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Knowledge And Beliefs ◽  
Public Announcements

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.

Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic1

2020 ◽  
Vol 30 (6) ◽  
pp. 1213-1238
Author(s):  
Dominik Klein ◽  
Rasmus K Rendsvig
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Model Transformations ◽  
Continuous Mappings ◽  
Turing Completeness ◽  
Action Model ◽  
Free Case ◽  
Finite Action ◽  
Action Models ◽  
Turing Complete

Abstract The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the postcondition-free case. As upper bounds, it is shown that either 1 atom, 3 agents and preconditions of modal depth 18 or 1 atom, 7 agents and preconditions of modal depth 3 suffice for Turing completeness.

scholarly journals ARROW UPDATE LOGIC

2011 ◽  
Vol 4 (4) ◽  
pp. 536-559 ◽  
Author(s):  
BARTELD KOOI ◽  
BRYAN RENNE
Keyword(s):  
Epistemic Logic ◽  
Belief Change ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Epistemic Access ◽  
Multi Agent ◽  
Logic Approach ◽  
Action Models ◽  
Information Change ◽  
Update Logic

We presentArrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

scholarly journals THE EXPRESSIVITY OF FACTUAL CHANGE IN DYNAMIC EPISTEMIC LOGIC

2013 ◽  
Vol 7 (2) ◽  
pp. 208-221 ◽  
Author(s):  
LOUWE B. KUIJER
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Public Announcements

AbstractA commonly used dynamic epistemic logic is one obtained by adding commonknowledge and public announcements to a basic epistemic logic. It is known from Kooi (2007) that adding public substitutions to such a logic adds expressivity over the class K of models. Here I show that substitutions also add expressivity over the classes KD45, S4 and S5 of models. Since the combination of common knowledge, public announcements and substitutions, was shown in Kooi (2007) to be equally expressive to relativized common knowledge these results also show that relativized common knowledge is more expressive than common knowledge and public announcements over KD45, S4 and S5. These results therefore extend the result from van Benthem et al. (2006) that shows that relativized common knowledge is more expressive than common knowledge and public announcements over K.

Program models and semi-public environments

2016 ◽  
Vol 29 (7) ◽  
pp. 1071-1097
Author(s):  
Davide Grossi ◽  
Wiebe van der Hoek ◽  
Christos Moyzes ◽  
Michael Wooldridge
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Semantic Model ◽  
The World ◽  
Semantic Models ◽  
Action Models

Abstract We develop a logic for reasoning about semi-public environments , i.e. environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use program models for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e. change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.

scholarly journals Dynamic Epistemic Logic with Assignments, Concurrency and Communication Actions

2020 ◽  
Author(s):  
Mario Folhadela Benevides ◽  
Isaque Macalam Saab Lima
Keyword(s):  
Epistemic Logic ◽  
Reduction Method ◽  
Dynamic Epistemic Logic ◽  
Epistemic Action ◽  
Action Logic ◽  
Action Models

This work proposes an extension of Dynamic Epistemic Logic with Communication Actions by adding the notion of postconditions from Dynamic Epistemic Logic with Assigments to deal with boolean assignments to action models. Other concurrent logics, like Concurrent Epistemic Action Logic introduced by Ditmarsch, Hoek and Kooi, do not deal with boolean assignments. We present an axiomatization and show that the proof of soundness, completeness and decidability can be done using a reduction method.

scholarly journals DYNAMIC GRADED EPISTEMIC LOGIC

2019 ◽  
Vol 12 (4) ◽  
pp. 663-684
Author(s):  
MINGHUI MA ◽  
HANS VAN DITMARSCH
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Kripke Models ◽  
Public Events ◽  
Public Announcements ◽  
Event Models

AbstractGraded 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 give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

scholarly journals Concurrent Games in Dynamic Epistemic Logic

2020 ◽  
Author(s):  
Bastien Maubert ◽  
Sophie Pinchinat ◽  
Francois Schwarzentruber ◽  
Silvia Stranieri
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Infinite Game ◽  
Action Models ◽  
Individual Actions

Action models of Dynamic Epistemic Logic (DEL) represent precisely how actions are perceived by agents. DEL has recently been used to define infinite multi-player games, and it was shown that they can be solved in some cases. However, the dynamics being defined by the classic DEL update product for individual actions, only turn-based games have been considered so far. In this work we define a concurrent DEL product, propose a mechanism to resolve conflicts between actions, and define concurrent DEL games. As in the turn-based case, the obtained concurrent infinite game arenas can be finitely represented when all actions are public, or all are propositional. Thus we identify cases where the strategic epistemic logic ATL*K can be model checked on such games.

scholarly journals Small Undecidable Problems in Epistemic Planning

2018 ◽  
Author(s):  
Sébastien Lê Cong ◽  
Sophie Pinchinat ◽  
François Schwarzentruber
Keyword(s):  
Cellular Automata ◽  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Planning Problem ◽  
Reachability Problem ◽  
Public Action ◽  
Automatic Structure ◽  
The Common ◽  
Initial Knowledge

Epistemic planning extends classical planning with knowledge and is based on dynamic epistemic logic (DEL). The epistemic planning problem is undecidable in general. We exhibit a small undecidable subclass of epistemic planning over 2-agent S5 models with a fixed repertoire of one action, 6 propositions and a fixed goal. We furthermore consider a variant of the epistemic planning problem where the initial knowledge state is an automatic structure, hence possibly infinite. In that case, we show the epistemic planning problem with 1 public action and 2 propositions to be undecidable, while it is known to be decidable  with public actions over finite models. Our results are obtained by reducing the reachability problem over small universal cellular automata. While our reductions yield a goal formula that displays the common knowledge operator, we show, for each of our considered epistemic problems, a reduction into an epistemic planning problem for a common-knowledge-operator-free goal formula by using 2 additional actions.

scholarly journals A Four-Valued Dynamic Epistemic Logic

2020 ◽  
Vol 29 (4) ◽  
pp. 451-489
Author(s):  
Yuri David Santos
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Modal Logics ◽  
The Other ◽  
Other Hand ◽  
Public Announcements ◽  
Tableau System ◽  
The One ◽  
Available Information

Abstract Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents’ knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge—or more appropriately, belief—is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we present an intuition and possible application for many-valued modal logics, and on the other hand we develop a logic that models the dynamics of evidence in a simple and intuitively clear fashion.

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