Traditional definitions of common ground in terms of iterative de re attitudes do not apply to conversations where at least one conversational participant is not acquainted with the other(s). I propose and compare two potential refinements of traditional definitions based on Abelard’s distinction between generality in sensu composito and in sensu diviso.

Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale (i.e., what levels of granularity) are useful for a rational agent? Where should these thresholds be placed given a rational agent’s preferences and risk-orientation? Do scale score assignments have any bearing on decision-making and if so, (...) how should scores be assigned? Given two possible states of nature , an ordered collection of alternatives from which one is to be selected depending on the probability that A is the case, a simple expected utility condition stipulates when adjacent alternatives are distinguishable and determines the threshold odds separating them. Threshold odds and utilities are mapped onto scale scores via a simple distance model. The placement of the thresholds reflects relative concern over decisional consequences given A versus consequences given ∼ A. Likewise, it is shown that scale scores reflect risk-aversion or risk-seeking not only with respect to A versus ∼ A but also with respect to the rank of the R j . Connections are drawn between this framework and rank-dependent expected utility (RDEU) theory. Implications are adumbrated for both machine and human decision-making. (shrink)

Salience reasoning, many have argued, can help solve coordination problems, but only if such reasoning is supplemented by higher-order predictions, e.g. beliefs about what others believe yet others will choose. In this paper, I will argue that this line of reasoning is self-undermining. Higher-order behavioral predictions defeat salience-based behavioral predictions. To anchor my argument in the philosophical literature, I will develop it in response and opposition to the popular Lewisian model of salience reasoning in coordination games. This model imports the (...) problematic higher-order beliefs by way of a ‘symmetric reasoning’ constraint. In the second part of this paper, I will argue that a player may employ salience reasoning only if she suspends judgment about what others believe yet others will do. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical (...) convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems. (shrink)

The purpose of this survey is twofold: (1) to place some centralthemes of epistemic logic in a general epistemological context,and (2) to outline a new framework for epistemic logic developedjointly with S. Andur Pedersen unifying some key ``mainstream''epistemological concerns with the ``formal'' epistemologicalapparatus.

According to a popular family of theories, assertions and other communicative acts should be understood as attempts to change the context of a conversation. Contexts, on this view, are publicly shared bodies of information that evolve over the course of a conversation and that play a range of semantic and pragmatic roles. I argue that this view is mistaken: performing a communicative act requires aiming to change the mind of one’s addressee, but not necessarily the context. Although changing the context (...) may sometimes be among a speaker’s aims, this should be seen as an extra-communicative aim, rather than one that is necessary for the performance of a communicative act. Along the way, I also argue that contexts needn’t play a role in linking anaphora to their antecedents. On the view that I defend, theories that take publicly shared contexts to play an essential role in the nature of communicative acts or anaphoric dependence conflate an artifact introduced by idealized models of conversation with a feature of the phenomenon being modeled. (shrink)

Common knowledge is usually defined as a state in which everyone knows that p, everyone knows that everyone knows that p, and so on, ad infinitum. This definition is usually attributed to David Lewis, despite the fact that his own formulation bears no resemblance to common knowledge as it is usually understood. In this paper, I argue that this concept of common knowledge requires revision. Contrary to usual practice, it turns out to be difficult to model formally because existing models (...) fail to distinguish between full-blown common knowledge and merely finite levels of interactive knowledge. Conceptually, the concept is incompatible with Lewis's intended purpose and obscures the explanatory role played by rational choice models. I propose that the concept of common knowledge be brought better into alignment with Lewis's actual formulation. This reconceptualization of common knowledge suggests a greater focus on explanations that make recourse to the cognitive constraints of real-world agents. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

We argue that common knowledge, of the kind used in reasoning in law and computing is best analyzed using a dialogue model of argumentation (Walton & Krabbe 1995). In this model, implicit premises resting on common knowledge are analyzed as endoxa or widely accepted opinions and generalizations (Tardini 2005). We argue that, in this sense, common knowledge is not really knowledge of the kind represent by belief and/or knowledge of the epistemic kind studied in current epistemology. This paper takes a (...) different approach, defining it in relation to a common commitment store of two participants in a rule-governed dialogue in which two parties engage in rational argumentation (Jackson & Jacobs 1980; van Eemeren & Grootendorst 2004). A theme of the paper is how arguments containing common knowledge premises can be studied with the help of argumentation schemes for arguments from generally accepted opinion and expert opinion. It is argued that common knowledge is a species of provi- sional acceptance of a premise that is not in dispute at a given point in a dia- logue, but may later be defeated as the discussion proceeds . (shrink)

This thesis is on information dynamics modeled using *dynamic epistemic logic*. It takes the simple perspective of identifying models with maps, which under a suitable topology may be analyzed as *topological dynamical systems*. It is composed of an introduction and six papers. The introduction situates DEL in the field of formal epistemology, exemplifies its use and summarizes the main contributions of the papers.Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how augmenting the standard (...) machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamical systems still falls a collection rich enough to be of interest. Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamical systems, it shows that extensional protocols designed to mimic simple, DEL dynamical systems require infinite representations. Paper IV focuses on *topological dynamical systems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology. Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems. (shrink)