We look at multi-agent versions of three different belief contraction operations (severe withdrawal, conservative contraction and moderate contraction), considering them as dynamic operations on plausibility models, meant to represent joint actions of “suspension of belief” by groups of agents (or by individual agents). We provide sound and complete axiomatizations, in the presence of standard static operators such as conditional belief, knowledge and safe belief.

The spread and exchange of information among people has been formally studied in the social sciences since the 1950s. The ways in which we do communicate has changed multiple times since. In particular, since the digitalization of communication methods, the speed of information exchange, the connectivity among people and with artificial agents, the reachability of information contents have all changed. Moreover, we now have an almost permanent record of what knowledge has been communicated, when, by whom. This novel status of information exchange has rapidly become a new field of studies on its own. The understanding of networked communication has thus become ubiquitous in multi-agent systems in AI, in epistemic-social logics and of course in social network analysis. Works that address this challenge are also split across these fields. This special issue is devoted to the theme of the ECAI workshop ‘Netreason: Reasoning About Social Networks’ (organized online on September...

Abstract This paper proposes different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization based on balance theory. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this work, we examine different possibilities for extending this basic language to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms. Furthermore, we define the property of full balance rather than balanced-up-to-a-degree. We look into the complexity of the model checking problem and show a non-compactness result of the extended language. Along the way, we provide axioms for weak balance. We also look at a full hybrid extension and reason about network changes with dynamic modalities. Then, to explore the measures of how far a network is from polarization, we consider variations of measures in relation to balance.

We propose a number of powerful dynamic-epistemic logics for multi-agent information sharing and acts of publicly or privately accessing other agents’ information databases. The static base of our logics is obtained by adding to standard epistemic logic comparative epistemic assertions for groups or individuals, as well as a common distributed knowledge operator (that combines features of both common knowledge and distributed knowledge). On the dynamic side, we introduce actions by which epistemic superiority can be acquired: “sharing all one knows” (by e.g. giving access to one’s information database to all or some of the other agents), as well as more complex informational events, such as hacking. We completely axiomatize several such logics and prove their decidability.

In this paper, we propose a unified logical framework for representing and analyzing various forms of correlated information change. Our main thesis is that "logical dynamics," in the sense of van Benthem (Exploring logical dynamics. CSLI Publications, Stanford, 1996; Logical dynamics of information and interaction. Cambridge University Press, Cambridge, 2011), and in particular dynamic epistemic notions of conditional, as developed in Baltag and Smets (Electron Notes Theor Comput Sci 165:5-21, 2006a; Stud Log 89:185-209, 2008a; Texts in logic and games. Amsterdam University Press, Amsterdam, pp 9-58, 2008b), play a central role in understanding and modeling a wide range of apparently very different information-gathering phenomena which do have one specific feature in common, namely the very act of learning new information may directly change the reality that is being learned. On the one hand, we focus on the way in which an introspective agent changes her beliefs when learning new higher-order information, i.e., information that may refer to her own beliefs. On the other hand, we analyze situations in which an observer learns about a phenomenon by performing observations that may perturb the very phenomenon under study, as in the case of quantum measurements, or observations in social sciences, psychology and medicine. Our formal techniques are based on ideas from dynamic logic and on the modeling of "dynamic conditionals." We offer a semantics based on "test frames," i.e., Kripke frames labeled by propositional formulae which yields a unified setting for the two types of correlated information change under study. We show how this framework can be used to analyze the ontic and epistemic-informational aspects of quantum measurements and to compare them with other types of observation, testing, belief revision, counterfactual conditionals, etc.

We analyze the learning power of iterated belief revision methods, and in particular their universality: whether or not they can learn everything that can be learnt. We look in particular at three popular methods: conditioning, lexicographic revision and minimal revision. Our main result is that conditioning and lexicographic revision are universal on arbitrary epistemic states, provided that the observational setting is sound and complete (only true data are observed, and all true data are eventually observed) and provided that a non-standard (non-well-founded) prior plausibility relation is allowed. We show that a standard (well-founded) belief-revision setting is in general too narrow for this. We also show that minimal revision is not universal. Finally, we consider situations in which observational errors (false observations) may occur. Given a fairness condition (saying that only finitely many errors occur, and that every error is eventually corrected), we show that lexicographic revision is still universal in this setting, while the other two methods are not.

What happens if in the Muddy Children story [22] we drop the assumption that the public announcements (made by the father and by the children) are commonly known to be always true, and instead we simply assume that they are true and commonly believed to be true? More generally, what happens in the long term with a group's beliefs, knowledge and "epistemic states" (fully describable in fact by conditional beliefs), when receiving (or exchanging) a sequence of public announcements of truthful but uncertain information? Do the agents' beliefs (or knowledge, or conditional beliefs, or other doxastic attitudes such as "strong beliefs") reach a fixed point? Or do they exhibit instead a cyclic behavior, oscillating forever?

We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (nonnegatively introspective) type of "knowledge". We develop a probabilistic version of this concept ("degree of safety") and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing "action models" and a notion of probabilistic update product, that comes together with appropriate reduction laws.

The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems. Here we extend that work to a sound (but not necessarily complete) logic for composite systems, which brings together ideas from the quantum logic tradition with concepts from (dynamic) modal logic and from quantum computation. This Logic of Quantum Programs (LQP) is capable of expressing important features of quantum measurements and unitary evolutions of multi-partite states, as well as giving logical characterisations to various forms of entanglement (for example, the Bell states, the GHZ states etc.). We present a finitary syntax, a relational semantics and a sound proof system for this logic. As applications, we use our system to give formal correctness proofs for the Teleportation protocol and for a standard Quantum Secret Sharing protocol; a whole range of other quantum circuits and programs, including other well-known protocols (for example, superdense coding, entanglement swapping, logic-gate teleportation etc.), can be similarly verified using our logic.