A quick glance at the opening paragraphs in many of the classic logic textbooks reveals a common view: logical methods highlight the reasoning patterns of a single (idealized) agent engaged in some form of mathematical thinking (for example: A (biased) sampling from my bookshelf: Shoenfield's Mathematical Logic: ``Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians"; Enderton's A Mathematical Introduction of Logic: ``Symbolic logic is a mathematical model of deductive thought"; and Chiswell and Hodges Mathematical Logic: ``In this course we shall study some ways of proving statements."). However, this traditional view of the ``subject matter" of logic is expanding. A growing literature is using phrases such as ``rational interaction" or ``information flow" to describe its subject matter while still employing traditional logical methods. The clearest example can be found in the work of Johan van Benthem and others on logical dynamics, Rohit Parikh and others on social software, and Samson Abramsky and others on game semantics.

This project critically examines and develops logical systems for reasoning about communities of (rational and not-so rational) agents engaged in some form of social interaction. Much of this work builds upon existing logical frameworks developed by philosophers and computer scientists incorporating insights and ideas from philosophy (especially epistemology and action theory), game theory, decision theory and social choice theory. The result is a web of logical systems each addressing different aspects of rational agency and social interaction. This project focuses on the central conceptual and technical issues that drive these logical analyses. The main objective is to see the various logical systems as a coherent account of rational agency and social interaction suggesting the following three questions:

1. How can we compare different logical frameworks addressing similar aspects of rational agency and social interaction (eg., how information evolves through social interaction)?
2. How should we combine logical systems which address {\em different} aspects of social interaction towards the goal of a comprehensive (formal) theory of rational agency?
3. How does a logical analysis contribute to the broader discussion of rational agency and social interaction within philosophy and the social sciences?

The typical game playing situation involves a group of self-interested agents, or players, engaged in some " interdependent decision problem". Each person in the group privately chooses a course of action under the assumption that the final outcome depends on the decision of everyone in the group. Agents are self-interested in the sense that they are free to solve their individual decision problems however they see fit. They are not constrained or committed to any team or group point of view but this does not mean that the agents are completely selfish. For some of them, altruistic considerations may play a crucial role in their final decision. Much of the traditional work in game theory has centered around the questions: What should Ann (Bob) do? or what is rational for Ann (Bob) to do? Game theorists have proposed various "solution concepts: as answers to these two questions (the most well known examples being the Nash equilibrium and dominance reasoning).

However, in recent years a number of game-theorists, philosophers and logicians have moved away from directly asking ``what is rational for Ann (Bob) to do?" and tried to understand what does it mean for Ann (Bob) to act rationally in a given interactive situation. These two questions are quite different. In the first case, one looks at social or interactive situations in abstraction from their specific context, and tries to circumscribe, in a (quasi-)axiomatic fashion, criteria of rational decision making. In the other case, one looks at specific game playing situations, here at specific informational contexts, and tries to understand how this context will or should bear on the agents' decisions.

These interrelated expectations do not need to affect the underlying view about what constitutes a rational choice for the players, namely choosing the best option given her (his) current information. Yet, they crucially change the informational background and this takes us beyond this basic view of instrumental rationality. In a joint book project with Olivier Roy, we are developing a theory of interactive rationality based on a theory of mutual and higher-order expectations. Of course, there are many issues that may be relevant for a player as she decides what to do in a game situation. One issue that we take to be particularly salient for the players is the fact that they are in a game situation with other (rational) agents. This is in line with a increasingly popular, but of course not uncontroversial point of view, in epistemic logic and game theory that ``the fundamental insight of game theory [is] that a rational player must take into account that the players reason about each other in deciding how to play." Exactly how the players incorporate the fact that they are interacting with other (actively reasoning) agents into their own decision making process is the subject of much debate. As we will show, subtle differences in assumptions about the players' informational attitudes will lead to alternative accounts of what constitutes rational play.

This project investigages social procedures as executed by rational and not-so rational agents. This is an area where many disciplines meet and have already made important contributions. The problem we focus on is how to understand the complex phenomena that arise when people taking part in a social procedure interact. A careful analysis of these phenomena relies on results and techniques from a variety disciplines, including Logic, Social Philosophy, Game Theory, Social Choice Theory, and Artificial Intelligence. In fact, many social procedures, such as fair division algorithms and voting procedures, have been analyzed in detail by mathematicians and political scientists. These analyses typically focus on comparing the mathematical properties of the various procedures. This is an important step towards understanding how social procedures work, but the main goal of this project is to place these issues in the context of a larger discussion on "designing a good social procedure”. The main theme of this project is that logical methods can facilitate such a discussion. The primary goal is to develop logical frameworks for studying social procedures and surrounding issues. More specifically, this project will investigate logical frameworks that will analyze:

1. The structure of social procedures,
2. The nature of (rational) agents (focusing on informational and preferential dynamics, see the above project on logics of rational agency), and
3. The nature of social interaction.

The result will be a comprehensive study of social procedure integrating important insights from the different disciplines mentioned above.

• NWO Vidi Project on A formal analysis of social procedures (2009-2014)
  People: Eric Pacuit (PI), PhD student
  Value: ~720kEUR (incl. Tilburg University matching funds)
• National Science Foundation International Research Fellowship (2005-2007)
  People: Eric Pacuit (PI)
  Value: $90.350