Merging DEL and ETL

There are two approaches to merging temporal and epistemic models. The first one consists in starting with a temporal model and enriching it with epistemic dimension (as temporal epistemic logic), while the second one is supposed to start with an epistemic model introducing temporal dimension (dynamic epistemic logic, epistemic temporal logic). The proposed evolutionary epistemic model (EEM) is based on the standard epistemic model with an evolutionary relation. EEM captures knowledge changes in terms of the evolution of worlds included in different epistemic contexts. Unlike other temporal-epistemic models, EEM is free from the concept of history and enriched with quantification operators over the worlds’ evolution stages.

We contrast Bonanno's ‘Belief Revision in a Temporal Framework’ (Bonanno, 2008) with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of van Benthem et al. (2006b) with relational substitutions (van Benthem, 2004) for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences (Grove, 1988; Board, 2002; Baltag and Smets, 2006, 2008b), prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update (Baltag and Smets, 2008b) and preference substitution (van Benthem, 2004).

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective.

In this paper we show how to formalise false-belief tasks like the Sally-Anne task and the second-order chocolate task in Dynamic Epistemic Logic (DEL). False-belief tasks are used to test the strength of the Theory of Mind (ToM) of humans, that is, a human’s ability to attribute mental states to other agents. Having a ToM is known to be essential to human social intelligence, and hence likely to be essential to social intelligence of artificial agents as well. It is therefore important to find ways of implementing a ToM in artificial agents, and to show that such agents can then solve false-belief tasks. In this paper, the approach is to use DEL as a formal framework for representing ToM, and use reasoning in DEL to solve false-belief tasks. In addition to formalising several false-belief tasks in DEL, the paper introduces some extensions of DEL itself: edge-conditioned event models and observability propositions. These extensions are introduced to provide better formalisations of the false-belief tasks, but expected to have independent future interest.

We show that dynamic epistemic logic (DEL) is a substructural logic and that it is an extension of the update logic introduced in the companion article [12]. We identify axioms and inference rules that completely characterize the DEL product update, and we provide a sequent calculus for DEL. Finally, we show that DEL with a finite number of atomic events is as expressive as epistemic logic. In parallel, we provide a sequent calculus for update logic which turns out to be a generalization of the non-associative Lambek calculus.

The paper analyzes 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 latter, 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 behavior of said maps.

Epistemic Logic and Information Update

In dynamical multi-agent systems, agents are controlled by protocols. In choosing a class of formal protocols, an implicit choice is made concerning the types of agents, actions and dynamics representable. This paper investigates one such choice: An intensional protocol class for agent control in dynamic epistemic logic (DEL), called ‘DEL dynamical systems’. After illustrating how such protocols may be used in formalizing and analyzing information dynamics, the types of epistemic temporal models that they may generate are characterized. This facilitates a formal comparison with the only other formal protocol framework in dynamic epistemic logic, namely the extensional ‘DEL protocols’. The paper concludes with a conceptual comparison, highlighting modeling tasks where DEL dynamical systems are natural.

In this article we present dynamic epistemic logic in the content of topological semantics. Dynamic epistemic logic is a brunch of modern logic which close related to computer science. We show that the DEL under topological semantics is of highly similarity with that DEL under relational semantics. First we give some preliminary background of topological semantics. Then we introduce the concept of 2-topological space, by which we can study the knowledge and interaction between different agents. Finally, we define information update in topological model. Instead of the path “update as deleting worlds” used in relational semantics, here we view update as increasing open set. We prove the two ways of update is equivalent, show that the DEL in topological semantics as a nature extension of that DEL in relational semantics.

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, indeed, 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 [15] give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates. Our closing observations are on recent developments that link the ‘standard’ topic of (theory) belief revision [1] to the dynamic epistemic logics introduced here.

Dynamic Epistemic Logics are a set of multimodal logics that deal with knowledge and change. We argue that the theory for this formalism is mature enough to start a practical implementation, while at the same time having a sizable amount of theoretical expansions. We also claim that these two factors make it an attractive formalism for new features in games featuring an agent’s internal model, like planning for gathering information, acting without revealing one’s goals or feeding possibly false information to a set of agents to influence their beliefs, augmenting already existing mechanisms.

Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.

Supervisory control theory deals with problems related to the existence and the synthesis of supervisors. The role of a supervisor in a system is to control and restrict the behavior of this system in order to realize a specific behavior. When there are multiple supervisors, such systems are in fact multi-agent systems. The results of supervisory control theory are usually expressed in terms of operations like intersection and inclusion between formal languages. We reformulate them in terms of model checking problems in an epistemic temporal logic. Our reformulations are very close to natural language expressions and highlight their underlying intuitions. From an applied perspective, they pave the way for applying model checking techniques developed for epistemic temporal logics to the problems of supervisory control theory.

Multi-agent system (MAS) requires coordination mechanisms to facilitate dynamic collaboration of the intelligent components, with the goal of meeting local and global objectives. This paper deals with the issue of using dynamic epistemic default logic to offer a natural way of communication policies for the management of inter-agent exchanges in MAS. We first explore the communication protocols in MAS that operate in dynamic and highly uncertain environments, and then we add the constrained default sets to realize the extension of dynamic epistemic logic theory and restrict the agent’s inference behavior via constrained epistemic default reasoning. We also specify and reason the characteristic of the dynamic updating when agent meets incompatible knowledge in the logical framework that show the usefulness of logical tools carried out in the dynamic process of information acquisition.

Propositional Dynamic Epistemic Logic (DEL) provides an expressive framework for epistemic planning, but lacks desirable features that are standard in first-order planning languages (such as problem-independent action representations via action schemas). A recent epistemic planning formalism based on First-Order Dynamic Epistemic Logic (FODEL) combines the strengths of DEL (higher-order epistemics) with those of first-order languages (lifted representation), yielding benefits in terms of expressiveness and representational succinctness. This paper studies the plan existence problem for FODEL planning, showing that while the problem is generally undecidable, the cases of single-agent planning and multi-agent planning with non-modal preconditions are decidable.