Aggregation of information from different sources is one of the key problems in modern computer science and artificial intelligence. An expert system diagnosing cancer or financial risk must be updated in light of new information. Intelligent agents must combine their information in order to coordinate their actions. A biomedical ontology developed by one set of experts might have to be combined with one developed by another team. Large language models combine information from a vast collection of texts. Database tables frequently need to be integrated. A committee must combine the opinions of its members in order to reach a conclusion, and the same is true for any algorithmic decision mechanism. An electric car must combine the inputs of its sensors in order to reach a decision. The whole paradigm of cloud computing is based on combining information stored in different physical locations. In the connected world we live in now, aggregation of information happens everywhere, all the time.

No wonder, then, that information aggregation has been the topic of study in many different sub-areas of computer science and artificial intelligence – and beyond. In epistemic logic [6], various notions of group knowledge and belief [2] are formalised and their logical and computational properties studied, the most well-known being common knowledge and distributed knowledge. These play a fundamental role in studying coordination in distributed systems, as well as in other diverse areas such as game theory [5] and the study of conventions [10]. A fundamental problem with information aggregation is, of course, that information coming from different sources might be inconsistent and must be reconciled. This is the key problem studied in the area of paraconsistent logic [14]. In particular, discussive logic [8, 13] combines points of view from several different participants in a discussion to a logical consistent point of view. In the area of belief revision [7], a belief state – or a database – is represented by a set of sentences, and belief change operations such as the introduction or removal of beliefs. In both these cases, changes affecting other sentences may be needed – for instance in order to retain consistency. Rationality postulates for such operations have been proposed [3], and representation theorems have been obtained that characterise specific types of operations in terms of these postulates. The area of belief merging [9], also called belief fusion, studies the aggregation of symbolic information (expressed in propositional logic) into a consistent base. Applications include combining conflicting sensor information received by the same agent as well as combining multiple databases. It also has applications in the AI sub-field of multi-agent systems. Distributed databases are databases with data stored in different computers at the same location or at different locations in a network of loosely coupled interconnected computers. Distributed queries, distributed transations and distributed query languages such as distributed SQL effectively aggregate these into a single logical database. In the area of semantic technologies such as the semantic web, ontology merging [12] is the important problem of combining two different ontologies (a formal description of categories, properties, relations, etc., in some domain) into one. In the area of recommender systems [1], the collaborative filtering technique aggregate interests of preferences of other users to make recommendations for someone else.

But the study of the principles behind information aggregation also goes far outside of formal logic, computer science and artificial intelligence. For example, the field of judgment aggregation, concerned with the problem of how a group of individuals can make consistent collective judgments on a set of propositions on the basis of the group members’ individual judgments on them, originated in political science and law [11]. The field of preference aggregation [4] is concerned with aggregating individual preferences into group preferences, originated in (indeed, defined the whole field of) social choice theory. Also in the social sciences, in the field of social network analysis [15], concepts such as influence, diffusion and informational cascades explain how an individual in a social network adapts her behaviour as a function of the aggregate behaviour of their connections.

In other words, information aggregation is of interest to computer scientists, logicians, artificial intelligence researchers and practitioners, philosophers, economists and social scientists.

For this Shonan meeting we will bring together researchers from all these disciplines in order to study the logical and computational foundations of information aggregation. While connections between some of the areas mentioned above have been studied, one example being the relationship between belief merging and judgment aggregation, many connections have not been studied or are not well understood, and there is a great potential for a transfer of results and methods between the different areas. In many of these areas computational issues have been largely ignored up to now.

While understanding the logical and computational underpinnings of reasoning about information aggregation is of obvious crucial importance for systems that use logical formalisms explicitly, such as in formal specification and automated verification of coordination properties of multi-agent systems or in rule-based systems in artificial intelligence, it is in fact highly relevant for any implementation that involves aggregation of information. For example, it can give us insight into the fundamental possibilities and limitations of large languagemodels when it comes to aggregating information in a way that is both consistent and computationally tractable at the same time.

Never has understanding the fundamental principles behind information aggregation been more timely and salient than in the age of large language models. Furthermore, as reasoning is rapidly becoming one of the main challenges of LLMs, understanding the fundamental trade-offs between computational tractability and (para-)consistent reasoning about information aggregated from different sources has never been more important.

We plan to invite researchers working on (see also above for how these areas relate to the aggregation problem):

• Reasoning about group knowledge and belief in epistemic and doxastic logic
• The coordination problem in multi-agent systems
• Large language models
• Paraconsistent reasoning
• Belief revision
• Belief merging
• Distributed databases
• Ontology merging
• Recommender systems
• Judgment- and preference aggregation
• Social network analysis

As the problem of information aggregation has been studied from different angles and with sometimes different and sometimes similar models and techniques in each of these areas, it is crucial that as many as possible of them are represented in order to maximize the possibility for new synergies.
Most of these areas are inter-disciplinary, and the list of invitees thus include researchers from:

• Logic-based knowledge representation and reasoning (a sub-field of artificial intelligence)
• Multi-agent systems (a sub-field of artificial intelligence)
• Machine learning (a sub-field of artificial intelligence)
• Formal specification and verification in computer science
• Mathematical and philosphopical logic
• Algorithmic game theory
• Sociology
• Computational social choice

See the list of invitees in the attached spreadsheet for notes about research interests/areas.

The meeting is intended to be exploratory, with the goal of finding new connections, synergies and syntheses. To this end, the meeting will start with researchers in each of the different disciplines presenting:

1. key models, techniques and results, and
2. the most important results

related to reasoning about information aggregation, from their area.

One of the main goals of the meeting is to identify opportunities for transfers of frameworks between the disciplines, e.g., enabling problems on the research frontier of one discipline to be solved using models, techniques and results from another. It is difficult to predict in advance what these opportunities will be, but the following are some examples of potential and promising directions.

• Can open problems on the research frontier of multi-agent formal specification and automated verification, e.g., coordination problems, be approached by using ideas, models, techniques and results from preference aggregation (a prominent sub-field of social choice theory)?

• How can we characterize the trade-off between computational tractability and the ability to reason about properties of aggregated information construed as group belief in the analysis of large language models?
• What can undecidability results from epistemic logic and belief revision tell us about the fundamental computational limits of large language models?
• Is the machinery developed for formal specification and automated verification of multi-agent systems based on epistemic, doxastic and temporal logic suitable for formally verifiying properties of large language models? If not, how can they be adapted?
• How can paraconsistent and discussive logics be used to guide the reasoning process in the face of inconsistent information from different sources in large language models?

• Does information learned through informational cascades in social network always lead to group belief that is consistent with belief revision postulates?

• In preference- and judgment aggregation, a solution to the seemingly fundamental result about the impossibility of consistent aggregation (Arrow’s theorem) is the observation that most “real” preference orderings are socalled single-peaked. Can a similar observation be made for large language models?

  It is important to note that these are merely examples, and that a main outcome of the meeting is the identification and exploration of other potential connections.

[1] Charu C Aggarwal et al. Recommender systems, volume 1. Springer, 2016.

[2] Thomas Agotnes and Yı N Wang. Group belief. Journal of Logic and Computation, 31(8):1959–1978, 2021.

[3] Carlos E Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. The journal of symbolic logic, 50(2):510–530, 1985.

[4] Kenneth J Arrow, Amartya Sen, and Kotaro Suzumura. Handbook of social choice and welfare. Elsevier, 2010.

[5] Robert J Aumann. Agreeing to disagree. The Annals of Statistics, 4(6):1236–1239, 1976.

[6] Ronald Fagin, Joseph Y Halpern, Yoram Moses, and Moshe Vardi. Reasoning about knowledge. MIT press, 2004.

[7] Peter Gardenfors. Belief revision. Number 29. Cambridge University Press, 2003.

[8] Stanis law Jaskowski. Rachunek zdan dla systemow dedukcyjnych sprzecznych. Studia Societatis Scientiarum Torunensis, Sectio A, (5):57–77, 1948.

[9] Sebastien Konieczny and Ramon Pino Perez. Logic based merging. Journal of Philosophical Logic, 40:239–270, 2011.

[10] David Kellogg Lewis. Convention: A philosophical study. 1969.

[11] Christian List. The theory of judgment aggregation: an introductory review. Synthese, 187(1):179–207, 2012.

[12] Natalya Fridman Noy, Mark A Musen, et al. Algorithm and tool for automated ontology merging and alignment. In Proceedings of the 17th National Conference on Artificial Intelligence (AAAI-00). Available as SMI technical report SMI-2000-0831, volume 115. sn, 2000.

[13] Hitoshi Omori and Jesse Alama. Axiomatizing jaskowski’s discussive logic d 2. Studia Logica, 106(6):1163–1180, 2018.

[14] Graham Priest. Paraconsistent logic. In Handbook of philosophical logic, pages 287–393. Springer, 2002.

[15] Stanley Wasserman and Katherine Faust. Social network analysis: Methods and applications. 1994.