Section: New Results
Foundations of Process Calculi
Group Distributed Knowledge.
We introduced spatial constraint systems (scs) as semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social networks. They have also been used for proving new results about modal logics and giving semantics to process calculi. In [19] we developed the theory of scs to reason about the distributed information of potentially infinite groups. We characterized the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provided an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. We showed compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provided algorithms that compute the distributive group information of finite groups. Furthermore, in [14] we summarized all the main results we have obtained about scs.
Group Polarization.
Social networks can make their users become more radical and isolated in their own ideological circle causing dangerous splits in society in a phenomenon known as group polarization. In [22] we developed a preliminary model for social networks, and a measure of the level of polarization in these social networks, based on Esteban and Ray's classic measure of polarization for economic situations. Our model includes information about each agent's quantitative strength of belief in a proposition of interest and a representation of the strength of each agent's influence on every other agent. We considered how the model changes over time as agents interact and communicate, and included several different options for belief update, including rational belief update and update taking into account irrational responses such as confirmation bias and the backfire effect. Under various scenarios, we considered the evolution of polarization over time, and the implications of these results for real world social networks.
Lattice Theory.
Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. In [28] we studied the cardinality of the set
Festschrift Contribution.
In a Festschrift dedicated to Catuscia Palamidessi [26], we presented an article with original solutions to four challenging mathematical puzzles [23]. The first two are concerned with random processes. The first problem can be reduced to computing, for arbitrary large values of