It is known that without synchronization via a global clock one cannot obtain common knowledge by communication. Moreover, it is folklore that without communicating higher-level information one cannot obtain arbitrary higher-order shared knowledge. Here, we make this result precise in the setting of gossip where agents make one-to-one telephone calls to share secrets: we prove that “everyone knows that everyone knows that everyone knows all secrets” is unsatisfiable in a logic of knowledge for gossiping. We also prove that, given n agents, $2n-3$ calls are optimal to reach “someone knows that everyone knows all secrets” and that $n - 2 + \binom{n}{2}$ calls are optimal to reach “everyone knows that everyone knows all secrets.”

Sedlár and Vigiani [18] have developed an approach to propositional epistemic logics wherein (i) an agent’s beliefs are closed under relevant implication and (ii) the agent is located in a classical possible world (i.e., the non-modal fragment is classical). Here I construct first-order extensions of these logics using the non-Tarskian interpretation of the quantifiers introduced by Mares and Goldblatt [12], and later extended to quantified modal relevant logics by Ferenz [6]. Modular soundness and completeness are proved for constant domain semantics, using non-general frames with Mares–Goldblatt truth conditions. I further detail the relation between the demand that classical possible worlds have Tarskian truth conditions and incompleteness results in quantified relevant logics.

In this paper, I develop an algorithmic impossible-worlds model of belief and knowledge that provides a middle ground between models that entail that everyone is logically omniscient and those that are compatible with even the most egregious kinds of logical incompetence. In outline, the model entails that an agent believes (knows) $\phi $ just in case she can easily (and correctly) compute that $\phi $ is true and thus has the capacity to make her actions depend on whether $\phi $. The model thereby captures the standard view that belief and knowledge ground are constitutively connected to dispositions to act. As I explain, the model improves upon standard algorithmic models developed by Parikh, Halpern, Moses, Vardi, and Duc, among other ways, by integrating them into an impossible-worlds framework. The model also avoids some important disadvantages of recent candidate middle-ground models based on dynamic epistemic logic or step logic, and it can subsume their most important advantages.

Williamson (2000) argues that the KK principle is inconsistent with knowledge of margin for error in cases of inexact perceptual observations. This paper argues, primarily by analogy to a different scenario, that Williamson's argument is fallacious. Margin for error principles describe the agent's knowledge as a result of an inexact perceptual event, not the agent's knowledge state in general. Therefore, epistemic agents can use their knowledge of margin for error at most once after a perceptual event, but not more. This insight blocks a crucial step in Williamson's original argument. Along the way, the value of standard epistemic logic for analyzing margin for error reasoning is challenged.

As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of these logics.

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for priority merge for which we also provide a complete set of reduction axioms.

This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.

We define a Public Announcement Separation Logic (PASL) that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying its semantics and illustrating its interest for modelling systems, we provide a sound and complete tableau calculus that deals with resource, agent and announcement constraints and give also a countermodel extraction method.

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

The logic of Conditional Beliefs (CDL) has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics for CDL is defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization of CDL is sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus for CDL is obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions.