Combining Uncertain Evidence

In this talk I will give an overview of my dissertation Combining Uncertain Evidence: Logic and Complexity. I will focus on my joint work with Ronald de Haan and Aybüke Özgün on a new model for measuring degrees of belief based on uncertain, partial, and possibly contradictory evidence [1]. This kind of evidence is present in many data-driven scenarios, such as the performance of autonomous agents. In order to compute degrees of belief based on evidence, it is necessary to combine it and define what justifies believing a certain proposition. We study how to address these challenges by combining tools from two different established approaches for combining evidence: Dempster-Shafer theory and topological models of evidence. As a result, we obtain a belief model that can reproduce both approaches when appropriate constraints are imposed and, in particular, is flexible enough to compute beliefs according to different standards that represent agents' evidential demands. The latter novelty allows users of our model to use it to compute an agent's (possibly) different degrees of belief, based on the same evidence, in situations where, e.g., the agent prioritizes avoiding false negatives and when it prioritizes avoiding false positives.  I will conclude the talk by presenting the key points of the other main results of my thesis.

[1] Pinto Prieto, Daira, de Haan, Ronald, and Özgün, Aybüke. "A Belief Model for Conflicting and Uncertain Evidence: connecting Dempster-Shafer Theory and the Topology of Evidence." In Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning, 552-561. August 2023. https://doi.org/10.24963/kr.2023/54.

To be effective artificial agents need to reason with norms and align with values. Norms are not constrains, in the sense that an agent may choose to disobey them. Values are underspecified, context dependent and possibly mutually contradictory in a possible choice an agent is considering to take. Both these task are hard challenges to execute by computation even when it is clear what the desires and goals of the agent are. Artificial agents are not individuals. They are not fully autonomous because people determine their desires. They are also not unique: a type of agent serves or operates on behalf of many people. Thus we face the problem of who decides the morals and norms of an artificial agent? This talk reflects on the possibility or challenge of using social choice, elections if you will, to decide the desires, values, goals of an artificial agent. What can be accomplished by social choice what can possibly go wrong by using it?

In this talk, we will give a brief account of some of our recent research trying to combine possibilistic approaches with preference learning or estimation methods. In particular, we will highlight why the fact that possibility distributions and measures extend set-valued representation can be beneficial, compared to a purely set-based or probabilistic-based approaches. We will first speak about incremental learning of preferences under a version space approach where sets of possible models are maintained after each observation of preferential information, and how the use of possibilities can help in relaxing strong assumptions such as having an oracle decision maker and a perfect model assumption. We will then briefly present how the use of set-theoretic or logical operations can help in fusing possibilistic information and analyse preferential information. 

In this presentation I focus on a philosophical analysis of comparative epistemic assertions that capture the epistemic superiority of an individual or a group of agents over other agent(s).  Such assertions can express that a group of agents collectively knows everything that another group of agents knows. I present examples of epistemic superiority and analyze them in the context of different epistemic conditions. Next I focus on what agents (collectively/individually) know about their own epistemic superiority or that of others. On the dynamic side, I will discuss the type of actions by which epistemic superiority can be acquired. Such informational events subsume actions such as ‘sharing all you know’ with a group or an individual, giving someone access to a folder or database, hacking a database without the owner’s knowledge, etc. In this setting I will reason about epistemic group attitudes and ask when agents in a group can achieve common knowledge by means of specific information-sharing actions only within their subgroups. This leads to the introduction of a new collective attitude called common distributed knowledge. In the presentation I will show how common distributed knowledge combines features of both common knowledge and distributed knowledge. This presentation is based on joint work with A. Baltag on a philosophical discussion of the results in [1,2].

[1] A. Baltag and S. Smets, Learning what Others Know, in: Kovacs, L. and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming AI and Reasoning, EPiC Series in Computing, (2020), Volume 73, pp. 90-110.

[2] A. Baltag and S. Smets, Logics for Data Exchange and Communication, (2024), Proceedings of Advances in Modal Logic, College Publications.