Sammanfattning
This thesis is on information dynamics modeled using *dynamic epistemic logic* (DEL). 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 selfcontained 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 longterm 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 metricbased 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 noncompact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems.
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 selfcontained 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 longterm 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 metricbased 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 noncompact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems.
Originalspråk  engelska 

Kvalifikation  Doktor 
Handledare 

Förlag  
ISBN (tryckt)  9789188473707 
ISBN (elektroniskt)  9789188473714 
Status  Published  2018 feb. 
Bibliografisk information
Defence detailsDate: 20180316
Time: 13:15
Place: C121, LUX, Helgonavägen 3, Lund
External reviewer(s)
Name: van Benthem, Johan
Title: professor
Affiliation: Stanford University, USA
