In this article, we present a modal logic that extends the basic modal logic ML with two dynamic operators: copy, which replicates the current model, labelling each copy with a different prop...

Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

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)

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)

Guarded actions are changes with preconditions acting as a guard. Guarded action models are multimodal Kripke models with the valuations replaced by guarded actions. Call guarded action logic the result of adding product updates with guarded action models to PDL (propositional dynamic logic). We show that guarded action logic reduces to PDL.

This paper introduces DEMO, a Dynamic Epistemic Modelling tool. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, translation of dynamic epistemic formulas to PDL formulas, and so on. The paper implements the reduction of dynamic epistemic logic [16, 2, 3, 1] to PDL given in [12]. The reduction of dynamic epistemic logic to automata PDL from [24] is also discussed and implemented. Epistemic models are minimized under bisimulation, and (...) update action models are minimized under action emulation (the appropriate structural notion for having the same update effect, cf. [13]). The paper is an exemplar of tool building for epistemic update logic. It contains the full code of an implementation in Haskell [22], in ‘literate programming’ style [23], of DEMO. (shrink)