We propose a dynamic logic of lying, wherein a ‘lie that $\varphi $ ’ (where $\varphi $ 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 $\varphi $ . 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 two speaker perspectives: (Obs) an outside observer who is lying to an agent that is modelled in the system, and (Ag) an agent who is lying to another agent, and where both are modelled in the system. We distinguish three addressee perspectives: (Cred) the credulous agent who believes everything that it is told (even at the price of inconsistency), (Skep) the skeptical agent who only believes what it is told if that is consistent with its current beliefs, and (Rev) the belief revising agent who believes everything that it is told by consistently revising its current, possibly conflicting, 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 in the extension of that logic to belief revision. (shrink)

The paper gives a formal analysis of public lies, explains how public lying is related to public announcement, and describes the process of recoveries from false beliefs engendered by public lying. The framework treats two kinds of public lies: simple lying update and two-step lying, which consists of suggesting that the lie may be true followed by announcing the lie. It turns out that agents’ convictions of what is true are immune to the first kind, but can be shattered by (...) the second kind. Next, recovery from public lying is analyzed. Public lies that are accepted by an audience cannot be undone simply by announcing their negation. The paper proposes a recovery process that works well for restoring beliefs about facts but cannot be extended to beliefs about beliefs. The formal machinery of the paper consists of KD45 models and conditional neighbourhood models, with various update procedures on them. Completeness proofs for a number of reasoning systems (converse belief logic, public lies logic, lying and recovery logic, conditional neighbourhood logic, plus its dynamic version) are included. (shrink)

Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying 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, they outline the seven contributions to this special issue.

Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying 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, they outline the seven contributions to this special issue.

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 becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting of Gerbrandy’s logic of believed announcements, wherein agents may have or obtain incorrect beliefs. Our results are on the satisfiability and validity of instantiations of these semantically (...) defined categories, on iterated announcements, including arbitrarily often iterated announcements, and on syntactic characterization. We close with results for iterated announcements in the logic of knowledge, and for lying as private announcements to different agents. Detailed examples illustrate our lying concepts. (shrink)

In this article, we present a modal logic that extends the basic modal logic with two dynamic operators: copy ( ), which replicates the current model, labelling each copy with a different propositional symbol and respecting accessibility relations even between distinct copies; and remove ( ), which deletes paths in the model that satisfy certain intermediate conditions. We call the resulting logic. We study its computational complexity, and its relative expressivity with respect to (static) modal logics and, and the dynamic (...) epistemic Action Model Logic,. (shrink)

Dynamic epistemic logics provide an account of the evolution of agents’ belief and knowledge when they learn the occurrence of an event. These logics started to become popular about 20 years ago and by now there exists a huge number of publications about them. The present paper briefly summarises the existing body of literature, discusses some problems and shortcomings, and proposes some avenues for future research.

History based models suggest a process-based approach to epistemic and temporal reasoning. In this work, we introduce preferences to history based models. Motivated by game theoretical observations, we discuss how preferences can dynamically be updated in history based models. Following, we consider arrow update logic and event calculus, and give history based models for these logics. This allows us to relate dynamic logics of history based models to a broader framework.

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, (...) this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modular cut-free labelled (...) sequent calculus for the logic in the sense that our calculus can be regarded as a natural expansion of a labelled sequent calculus of iteration-free propositional dynamic logic. (shrink)

Communication within groups of agents has been lately the focus of research in dynamic epistemic logic. This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. The paper can be divided into two parts. In the first part, we present results on invariance and complexity of model checking. Moreover, we (...) compare partial communication with the public announcement and arrow update settings in terms of both language-expressivity and update-expressivity. Regarding the former, the three settings are equivalent, their languages being equally expressive. Regarding the latter, all three modes of communication are incomparable in terms of update-expressivity. In the second part, we shift our attention to strategic topic-based communication. We do so by extending the language with a modality that quantifies over the topics the agents can ‘talk about’, thus allowing a form of arbitrary partial communication. For this new framework, we provide a complete axiomatisation, showing also that the new language’s model checking problem is PSPACE-complete. Finally, we argue that, in terms of expressivity, this new language of arbitrary partial communication is incomparable to that of arbitrary public announcements and also to that of arbitrary arrow updates. (shrink)