We propose a new dynamic hybrid logic to reason about social networks and their dynamics building on the work of “Logic in the Community” by Seligman, Liu and Girard. Our framework distinguishes between the purely private sphere of agents, namely their mental states, and the public sphere of their observable behavior, i.e., what they seem to believe. We then show how such a distinction allows our framework to model many social phenomena, by presenting the case of pluralistic ignorance as an (...) example and discussing some of its dynamic properties. (shrink)

A group is in a state of pluralistic ignorance (PI) if, roughly speaking, every member of the group thinks that his or her belief or desire is different from the beliefs or desires of the other members of the group. PI has been invoked to explain many otherwise puzzling phenomena in social psychology. The main purpose of this article is to shed light on the nature of PI states – their structure, internal consistency and opacity – using the formal apparatus (...) of Dynamic Doxastic Logic, and also to study the sense in which such states are “fragile”, i.e. to identify plausible conditions under which a PI state cascades into a state of shared belief as the result of announcement. (shrink)

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between (...) actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'. (shrink)

Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain (...) kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. (shrink)

The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result. But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action (...) emulation as a notion of equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect. We first concentrate on the general case, and next focus on the important case of action models with propositional preconditions. Our notion of action emulation yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action. (shrink)

Logic is not just about single-agent notions like reasoning, or zero-agent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.

Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also (...) show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), interpreted epistemically. This system is capable of expressing all model-shifting operations with finite action models, while providing a compositional analysis for a wide range of informational events. This makes LCC a serious candidate for a standard in dynamic epistemic logic, as we illustrate by analyzing some complex communication scenarios, including sending successive emails with both ‘cc’ and ‘bcc’ lines, and other private announcements to subgroups. Our proofs involve standard modal techniques, combined with a new application of Kleene’s theorem on finite automata, as well as new Ehrenfeucht games of model comparison. (shrink)

In this paper, we investigate the use of event models for automated planning. Event models are the action defining structures used to define a semantics for dynamic epistemic logic. Using event models, two issues in planning can be addressed: Partial observability of the environment and knowledge. In planning, partial observability gives rise to an uncertainty about the world. For single-agent domains, this uncertainty can come from incomplete knowledge of the starting situation and from the nondeterminism of actions. In multi-agent domains, (...) an additional uncertainty arises from the fact that other agents can act in the world, causing changes that are not instigated by the agent itself. For an agent to successfully construct and execute plans in an uncertain environment, the most widely used formalism in the literature on automated planning is “belief states”: sets of different alternatives for the current state of the world. Epistemic logic is a significantly more expressive and theoretically better founded method for representing knowledge and ignorance about the world. Further, epistemic logic allows for planning according to the knowledge (and iterated knowledge) of other agents, allowing the specification of a more complex class of planning domains, than those simply concerned with simple facts about the world. We show how to model multi-agent planning problems using Kripke-models for representing world states, and event models for representing actions. Our mechanism makes use of slight modifications to these concepts, in order to model the internal view of agents, rather than that of an external observer. We define a type of planning domain called epistemic planning domains, a generalisation of classical planning domains, and show how epistemic planning can successfully deal with partial observability, nondeterminism, knowledge and multiple agents. Finally, we show epistemic planning to be decidable in the single-agent case, but only semi-decidable in the multi-agent case. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

Barteld Kooi and Bryan Renne (2011). Generalized Arrow Update Logic. In K.R. Apt (editor). Theoretical Aspects of Rationality and Knowledge, Proceedings of the Thirteenth Conference (TARK 2011), pp. 205-211.

The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We (...) propose action emulation as a notion of equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect. We first concentrate on the general case, and next focus on the important case of action models with propositional preconditions. Our notion of action emulation yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action. (shrink)

Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [8]), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam [22]), STIT (Belnap et al. [5]), Process Algebra and Game Semantics (Abramsky [1]). This variety is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two systems (...) that both address the dynamics of knowledge and information flow in multi-agent systems. One is IS/ETL (IS and ETL are, from a technical point of view, the same up to model transformations, cf. [20]), which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. These models provide a Grand Stage where histories of some process unfold constrained by a protocol, and a matching epistemic-temporal language describes what happens. The other framework is Dynamic Epistemic Logic (DEL, [10, 4, 34]) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. Temporal evolution is then computed from some initial epistemic model through a process of successive ‘product updates’. It has long been unclear how to best compare IS/ETL and DEL. Various aspects have been investigated in [10, 30, 32], but in this paper, we study the interface in a more systematic way. Often, DEL and ETL are presented as alternative ways of adding dynamics to multi-agent epistemic models. In this paper, we rather focus on how merging the two different modeling choices leads to interesting new questions. Our leading interest here will be a view of informational processes as evolving over time. To see what we mean, consider the simplest version of DEL, viz. the logic of public announcements PAL ([23]) which adds a very specific type of communicative 1 action to epistemic models: a public announcement.. (shrink)

We discuss games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. We propose matching logical languages for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic-epistemic language’ – and we find correspondences between special axioms and particular modes of playing games with their information dynamics. At the ‘outcome level’, we present suitable notions of game equivalence, plus some (...) simple representation results. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula α as the theory defined by the set of all those models of α that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates (...) describe properties of iterated revisions. (shrink)

Hans van Ditmarsch and Barteld Kooi (2008). Semantic results for ontic and epistemic change. In: G. Bonanno, W. van der Hoek and M. Wooldridge (editors). Logic and the Foundations of Game and Decision Theory (LOFT 7). Texts in Logic and Games 3, pp. 87-117, Amsterdam University Press, Amsterdam.

This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229-237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113-118, 1981). The point is to (...) develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection. (shrink)

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of (...) an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. (shrink)

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We (...) also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs. (shrink)

• We study a new composition operation on (epistemic) multiagent models and update actions that takes vocabulary extensions into account.

It has become a truism that we live in so-called information societies where new information technologies have made information abundant. At the same time, information science has made us aware of many phenomena tied to the way we process information. This article explores a series of socio-epistemic information phenomena resulting from processes that track truth imperfectly: pluralistic ignorance, informational cascades, and belief polarization. It then couples these phenomena with the hypothesis that modern information technologies may lead to their amplification so (...) as to give rise to what are called “infostorms.” This points to the need for studying further the exact relations between information technologies and such infostorms, as well as the ways we may design technologies to avoid being misled away from what we have good reasons to believe. (shrink)

We generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single-agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting. Finally, we give an example of revision operator that fulfills one of these new postulates and give (...) an example of revision on a concrete example. (shrink)