From Shared Evidence to Group Attitudes -- SEGA
Complex, coordinated efforts such as organizing national intelligence, rescuing flood victims, or conducting large-scale scientific research require both pooling and sharing information. These two processes are related but different. A commanding officer may pool intelligence and be able to locate a target while an agent in the field is unable to do so. The fact that the intelligence is not shared, or “out in the open” for all field officers, might even be crucial to the success of the operation. What is, then, the precise relationship between pooling and sharing information? Is shared information always pooled? How can individuals with limited time and resources effectively share and/or pool the information they have?
These questions have attracted a lot of attention in philosophical logic, but up to now the answers rest heavily on idealizations. Agents in these models are “logically omniscient”, i.e, they know all the logical consequences of their information. So in these models pooling is just a matter of putting together all the information of each agent. But in general reaching the right conclusions from pooling might not be trivial at all. Standard logical models also assume that the agents can store highly complicated notions, for instance an unbounded number of iterations of “everybody knows that everybody knows that…”, which are at the heart of the definition of so-called “common knowledge.”
This project will lift these idealizations and study sharing and pooling for agents with limited cognitive and inferential capacities. We will develop notions of shared information, e.g. common knowledge, for agents who do not have the full deductive power of classical models, and will use tools from the theory of judgment aggregation and belief merging to develop new logical models of information pooling for non-ideal agents. Finally, we will study how information dynamics in groups, and in particular the dialectics of questions and answers, can foster or prevent both pooling and sharing.
Sub-project 1: Varieties of pooling and belief merging
Research Team: Ondrej Majer, Vít Punčochář, Olivier Roy, Igor Sedlár and (collaboration partners) Thomas Agotnes, Umberto Grandi and Gabriella Pigozzi.
The goal of this sub-project is to extend current models of information pooling in epistemic logic in order to cover more realistic cases. We look at pooling with possibly inconsistent inputs and logically incomplete outputs, and distinguish between pooling of reasons and pooling of conclusions. To do this we draw from theories of belief merge, previous work by the participants, and formal argumentation theory. This will provide new insights for the logical models of knowledge and beliefs, and may have a significant impact on our understanding of group agency.
Distributed knowledge only applies to a very restricted, and highly idealized set of circumstances. It only operates on jointly consistent inputs, and its output, i.e. the pooled information, is always closed under logical consequence. In realistic scenarios these assumptions obviously fail. An intelligence officer might receive evidence from field agent 1 that the target is in location A, and another piece of evidence from agent 2 that the target is in location B, with neither piece of evidence overriding the other. Or the coordinator of a rescue mission might not be able to draw all the relevant logical consequences of the scattered data (visual cues, witness reports, satellite data, etc) she receives on the fly, even if this data is not inconsistent. It might just be too complicated. Distributed knowledge was not designed to study pooling in such cases, i.e. potentially inconsistent data, or for agents with limited computational capacities.
The project will overcome these limitations by drawing from the theory of belief merging. The first step of this project will be to identify to which belief merge operation(s) distributed knowledge corresponds to. The main challenge here will be to take into account the capacity to represent higher-order attitudes in epistemic logic, a feature which is not standardly taken into account in the belief merging literature. The primary contribution of this project is in epistemic and doxastic logic. The project will explore a much richer landscape of pooling methods than that which has been studied up to now, and will situate the logical view on pooling within the larger belief merging literature. But as the examples above suggest, how (and how much) information is pooled can have a large impact on what collectives such as a rescue team or the secret services can achieve. This pertains to the theory of group agency, where findings in logic and social epistemology have also been quite influential.
Sub-project 2: Sharing and fixed-points for non-classical reasoners
Research Team: Marta Bílková, Norbert Gratzl, Adam Přenosil, Olivier Roy, Igor Sedlár
This sub-project will concentrate on the properties of shared attitudes, such as common knowledge and common belief, without certain idealising assumptions concerning the agents’ reasoning capacities.
Formally, this boils down to the investigation of epistemic logics for group-attitudes where the underlying propositional logic is non-classical, to allow for a more realistic representation of shared attitudes in the presence of incomplete and inconsistent information. The basic idea of our approach is to explore explicit representations of information states instead of relying merely on the standard representations using epistemic alternatives or full-fledged possible worlds. This leads to non-classical logics of explicit information states. We shall concentrate on logics based on lattices, and on substructural logics in particular.
The project will consider different approaches to modelling such common attitudes, the shared environment and fixed-point approach in particular. The investigation of the latter will draw on results concerning fixed-points in lattice theory, and general results on substructural logics, using both model- and proof-theoretic methods. The main contribution of this project is at the intersection of epistemic logic, substructural logic and modal fixed-point logic.
Sub-project 3: From sharing to pooling and back: the dynamics of questions and answers
Research Team: Marta Bílková, Norbert Gratzl, Ondrej Majer, Michal Peliš.
This project will study how pooling and sharing can be fostered, elicited or prevented through questions and answers. We will do so by drawing from recent work and methods in the logical modeling of questions. This will augment and generalize known results in epistemic logic on the possibility of “turning” distributed knowledge into common knowledge, and will provide a natural testing ground for and an opportunity to integrate the results obtained in the other two projects.
Asking and answering questions in a group is a kind of communication where an open problem (individual or group question) encourages pooling of scattered information (distributed knowledge) together so as to find a shared solution (common knowledge). This is a “general task” for a dynamic version of erotetic epistemic logic (EEL).
The first goal of this project is to develop a more plausible version of EEL. This model gives satisfactory analysis for some kinds of questions, while for another it gives unintuitive results. To correct that we need to replace the background epistemic (doxastic) logic S5 (KD45) by a weaker framework. In this project we will look at substructural logics based on information states semantics. We are going to develop new definitions of askability, both for individuals and for groups with limited inferential capacities, and study the relationship between the presuppositions of questions and the informational context, i.e. what is commonly known in the community of speakers. This will of course require taking into account both the theories for shared knowledge developed in Project 2, as well as the new notions of pooled information developed in Project 1.
In the second step we will move to the dynamics of questions and answers. Questions can indeed be seen as issues raised by group of agents: they want to solve an initial problem, i.e. answer the question, based on both what is commonly known and the information that could be obtained by pooling. But resolving an issue doesn’t mean making the pooled information public. Think of the case of coordinating intelligence operations. Answers to questions sometimes need to be private or only available to sub-groups, and might even be meant to deceive non-group members. To handle such cases we need to go beyond communication viewed as public announcements, and look at a more general class of learning events. Technically, this will mean developing the logical theory of action models for EEL: axiomatization, expressive power, decidability. With this in hand we will study in more detail the effects of this dynamics on the pooled and shared information of agents in groups, and identify conditions under which asking the right sort of question can foster or prevent pooled information from becoming common knowledge.