Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

Dynamic Epistemic Logic (DEL) deals with the representation and the study in a multi-agent setting of knowledge and belief change. It can express in a uniform way epistemic statements about: 1. what is true about an initial situation 2. what is true about an event occurring in this situation 3. what is true about the resulting situation after the event has occurred. We axiomatize within the DEL framework what we can infer about (iii) given (i) and (ii). Given three formulas (...) φ,φ' and φ" describing respectively (i), (ii) and (iii), we also show how to build a formula φ ? φ' which captures all the information which can be inferred about (iii) from φ and φ'. We show how our results extend to other modal logics than K. In our proofs and definitions, we resort to a large extent to the normal form formulas for modal logic originally introduced by Kit Fine. In a companion paper (Aucher, 2012), we axiomatize what we can infer about (ii) given (i) and (iii), and what we can infer about (i) given (ii) and (iii), and show how to build two formulas φ ? φ" and φ' ? φ" which capture respectively all the information which can be inferred about (ii) from φ and φ", and all the information which can be inferred about (i) from φ' and φ". (shrink)

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.

We present a theory of actions based on a theory of events in branching time, in which "particular" or "token" actions are taken to be sets of transitions from their initial states to the outcomes. We also present a simple theory of composition of events by which composite events can be formed out of other events. Various kinds of actions, including instantaneous group actions and sequential group actions, are introduced by way of composition, and an extended stit theory of agency (...) is proposed, in which the stit operators are combined or equipped with reified group actions. (shrink)

In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the (...) core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization of PAL without the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding of PAL and can be adapted to other dynamic epistemic logics. (shrink)

We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hillbert-style (...) axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for MLSR is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic. (shrink)

Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...) observation, interaction and belief revision in scientific communities. The presented sound and complete system provides the formal tools for qualitative analysis of the social dynamics of scientific inquiry. Furthermore, this paper includes detailed suggestions for future applications of the framework. (shrink)

Questions are triggers for explicit events of ‘issue management’. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multi-agent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.

Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (‘revoke’) the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what the requirements are for revocable belief revision. By this we not merely (...) mean recovering belief in non-modal propositions, as in the recovery principle for belief contraction, but recovering belief in modal propositions: beliefs about beliefs. These requirements are almost never met, a surprising result. (shrink)

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well‐known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two‐level approach to obligations is tested first against standard scenarios of contrary‐to‐duty obligations, leading also to a generalization for the Kanger‐Anderson reduction of deontic logic. Next, the priority framework is applied to model (...) two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two‐level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are not commonly known, and propose a semantics-driven logical framework to reason about knowledge in such scenarios. In particular, we introduce the notion of epistemic expectation models and a propositional dynamic logic-style epistemic logic for (...) reasoning about knowledge via matching agentsÊ expectations to their observations. It is shown how epistemic expectation models can be obtained from epistemic protocols. Furthermore, a characterization is presented of the effective equivalence of epistemic protocols. We introduce a new logic that incorporates updates of protocols and that can model reasoning about knowledge and observations. Finally, the framework is extended to incorporate fact-changing actions, and a worked-out example is given. © 2013 Elsevier B.V. (shrink)

• We study a new composition operation on (epistemic) multiagent models and update actions that takes vocabulary extensions into account.

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic ). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of \ is that (...) it can only encode public announcements. \ can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic ), with action model logic ). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both \ and \, and a sound and complete axiomatization is given for both. (shrink)

We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and (...) completeness results for these systems. (shrink)

This paper is part of an on-going programme on the study of the logical aspects of social network formation. It recalls the so-called social network model, discussing the properties of a notion of closeness between agents ; then introduces an extended social network model in which different agents might assign different values to different traits, discussing the properties of the notion of weighted closeness that arises. These notions are used to define social network creation operations by means of a threshold (...) strategy. The paper studies the properties of the social networks the updates create, providing sound and complete axiom systems for formal languages describing these updates’ effects. (shrink)

This paper provides a sound and complete proof system for a language that adds to Dynamic Epistemic Logic a discrete previous-time operator as well as single symbol formulas that partially reveal the most recent event that occurred. The completeness theorem is by filtration followed by model unraveling and other model transformations. Decidability follows from the completeness proof. The degree to which it is important to include the additional single symbol formulas is addressed in a discussion about the difficulties of the (...) completeness for a language that only adds the previous-time operator to DEL. Discussion is also given regarding the completeness for a language obtained by removing common knowledge operators from. (shrink)

This is the second paper in a two-part series introducing logics for reasoning about the dynamics of knowledge and beliefs. Part I introduced different logical systems that can be used to reason about the knowledge and beliefs of a group of agents. In this second paper, I show how to adapt these logical systems to reason about the knowledge and beliefs of a group of agents during the course of a social interaction or rational inquiry. Inference, communication and observation are (...) typical examples of informative events, which have been subjected to a logical analysis. The main goal of this article is to introduce the key conceptual and technical issues that drive much of the research in this area. (shrink)

We propose a general framework for dynamic epistemic logics. It consists of a generic language for DELs and a class of structures, called model transition systems, that describe model transformations in a static way. An MTS can be viewed as a two-layered Kripke model and consequently inherits standard concepts such as bisimulation and bounded morphism from the ordinary Kripke models. In the second half of this article we add the global operator to the language, which enables us to define the (...) notions of a canonical MTS and canonicity of a DEL formula for a property of MTSs. Using these notions, we clarify correspondences between axioms of DELs and properties of MTSs. (shrink)

We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents’ local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is ‘perfect’. We show that the class of recognizable languages has good closure (...) properties, leading to a Kleene-type theorem using what we call regular knowledge expressions. These automata model distributed causal knowledge in the following way: each agent in the system has a partial knowledge of the temporal evolution of the system, and every time agents synchronize, they update each other’s knowledge, resulting in a more up-to-date view of the system state. Hence we show that these automata can be used to solve the satisfiability problem for a natural epistemic temporal logic for local properties. Finally, we characterize the class of languages recognized by epistemic automata as the regular consistent languages studied in concurrency theory. (shrink)

This paper surveys the interface between the two major logical trends that describe agents’ intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to “merge” DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491–526, 2009) and Hoshi (Epistemic dynamics and protocol information. Ph.D. thesis, Stanford University Stanford, 2009a). The merged framework provides a (...) systematic comparison between these two logical systems and studies new logics of intelligent interaction. This paper presents the main results and the recent developments at the interface between DEL and ETL. (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)

Past public announcement operators have been defined in Hoshi and Yap :259–281, 2009) and Yap, to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic, and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model \ to a filtrated submodel of (...) the canonical model for \. Here \ is the minimal normal modal logic together with \ axioms for the universal operator U. This yields a highly general pre-announcement version of \ that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL. Indeed, we find that our reverse announcement operators cannot be represented by product update, and that they have an intimate connection with the knowledge forgetting of Zhang and Zhou :1525–1537, 2009). We show that the logic resulting from adding reverse announcements to PAL is sound and complete. (shrink)

The problem of perception is the problem of explaining how perceptual knowledge is possible. The skeptic has a simple solution: it is not possible. I analyze the weaknesses of one type of skeptical reasoning by making explicit a dynamic epistemic principle from dynamic epistemic logic that is implicitly used in debating the problem, with the aim of offering a novel diagnosis to this skeptical argument. I argue that prominent modest foundationalist responses to perceptual skepticism can be understood as rejecting the (...) dynamic assumption made by the skeptic, that there are independent reasons to doubt the truth of such a principle in the context of skeptical reasoning, and that making the dynamic principle explicit allows for a better understanding of at least one objection to modest foundationalism. (shrink)

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. (shrink)

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we (...) provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007 ). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically. (shrink)