Rineke Verbrugge

Agent Theory for Team Formation by Dialogue

The process of cooperative problem solving can be divided into four stages. First, finding potential team members, then forming a team followed by constructing a plan for that team. Finally, the plan is executed by the team. Traditionally, protocols like the Contract Net protocol are used for performing the first two stages of the process. In an open environment however, there can be discussion among the agents in order to form a team that can achieve the collective intention of solving the problem. For these cases fixed protocols like contract net do not suffice. In this paper we present a theory for agents that are able to discuss the team formation and subsequently work as a team member until the collective goal has been fulfilled.We also present a solution, using structured dialogues, with an emphasis on persuasion, that can be shown to lead to the required team formation. The dialogues are described formally using modal logics and speech acts.

Creating collective intention through dialogue.

The process of Cooperative Problem Solving can be divided into four stages. First, finding potential team members, then forming a team followed by constructing a plan for that team. Finally, the plan is executed by the team. Traditionally, protocols like the Contract Net protocol are used for performing the first two stages of the process. In an open environment however, there can be discussion among the agents in order to form a team that can achieve the collective intention of solving the problem. For these cases fixed protocols like contract net do not suffice. In this paper we present a solution, using structured dialogues, with an emphasis on persuasion, that can be shown to lead to the required team formation. The dialogues are described formally using modal logics and speech

Logic and Social Cognition: The facts matter, and so do computational models

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models.

Learning to Apply Theory of Mind

In everyday life it is often important to have a mental model of the knowledge, beliefs, desires, and intentions of other people. Sometimes it is even useful to to have a correct model of their model of our own mental states: a second-order Theory of Mind. In order to investigate to what extent adults use and acquire complex skills and strategies in the domains of Theory of Mind and the related skill of natural language use, we conducted an experiment. It was based on a strategic game of imperfect information, in which it was beneficial for participants to have a good mental model of their opponent, and more specifically, to use second-order Theory of Mind. It was also beneficial for them to be aware of pragmatic inferences and of the possibility to choose between logical and pragmatic language use. We found that most participants did not seem to acquire these complex skills during the experiment when being exposed to the game for a number of different trials. Nevertheless, some participants did make use of advanced cognitive skills such as second-order Theory of Mind and appropriate choices between logical and pragmatic language use from the beginning. Thus, the results differ markedly from previous research.

What Eye Movements Can Tell about Theory of Mind in a Strategic Game

This study investigates strategies in reasoning about mental states of others, a process that requires theory of mind. It is a first step in studying the cognitive basis of such reasoning, as strategies affect tradeoffs between cognitive resources. Participants were presented with a two-player game that required reasoning about the mental states of the opponent. Game theory literature discerns two candidate strategies that participants could use in this game: either forward reasoning or backward reasoning. Forward reasoning proceeds from the first decision point to the last, whereas backward reasoning proceeds in the opposite direction. Backward reasoning is the only optimal strategy, because the optimal outcome is known at each decision point. Nevertheless, we argue that participants prefer forward reasoning because it is similar to causal reasoning. Causal reasoning, in turn, is prevalent in human reasoning. Eye movements were measured to discern between forward and backward progressions of fixations. The observed fixation sequences corresponded best with forward reasoning. Early in games, the probability of observing a forward progression of fixations is higher than the probability of observing a backward progression. Later in games, the probabilities of forward and backward progressions are similar, which seems to imply that participants were either applying backward reasoning or jumping back to previous decision points while applying forward reasoning. Thus, the game-theoretical favorite strategy, backward reasoning, does seem to exist in human reasoning. However, participants preferred the more familiar, practiced, and prevalent strategy: forward reasoning.

Sum and Product in Dynamic Epistemic Logic

The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown. We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. We analyse one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that becomes false because it is announced. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking and the complexity is experimentally investigated for several representations and parameter settings.

How much does it help to know what she knows you know? an agent-based simulation study

In everyday life, people make use of theory of mind by explicitly attributing unobservable mental content such as beliefs, desires, and intentions to others. Humans are known to be able to use this ability recursively. That is, they engage in higher-order theory of mind, and consider what others believe about their own beliefs. In this paper, we use agent-based computational models to investigate the evolution of higher-order theory of mind. We consider higher-order theory of mind across four different competitive games, including repeated single-shot and repeated extensive form games, and determine the advantage of higher-order theory of mind agents over their lower-order theory of mind opponents. Across these four games, we find a common pattern in which first-order and second-order theory of mind agents clearly outperform opponents that are more limited in their ability to make use of theory of mind, while the advantage for deeper recursion to third-order theory of mind is limited in comparison.

Logic and Complexity in Cognitive Science

This chapter surveys the use of logic and computational complexity theory in cognitive science. We emphasize in particular the role played by logic in bridging the gaps between Marr’s three levels: representation theorems for non-monotonic logics resolve algorithmic/implementation debates, while complexity theory probes the relationship between computational task analysis and algorithms. We argue that the computational perspective allows feedback from empirical results to guide the development of increasingly subtle computational models. We defend this perspective via a survey of the role of logic in several classic problems in cognitive science (the Wason selection task, the frame problem, the connectionism/symbolic systems debate) before looking in more detail at case studies involving quantifier processing and social cognition. In these examples, models developed by Johan van Benthem have been supplemented with complexity analysis to drive successful programs of empirical research.

Evolution of altruistic punishment in heterogeneous populations.

Evolutionary models for altruistic behavior typically make the assumption of homogeneity: each individual has the same costs and benefits associated with cooperating with each other and punishing for selfish behavior. In this paper, we relax this assumption by separating the population into heterogeneous classes, such that individuals from different classes differ in their ability to punish for selfishness. We compare the effects of introducing heterogeneity this way across two population models, that each represents a different type of population: the infinite and well-mixed population describes the way workers of social insects such as ants are organized, while a spatially structured population is more related to the way social norms evolve and are maintained in a social network. We find that heterogeneity in the effectiveness of punishment by itself has little to no effect on whether or not altruistic behavior will stabilize in a population. In contrast, heterogeneity in the cost that individuals pay to punish for selfish behavior allows altruistic behavior to be maintained more easily. Fewer punishers are needed to deter selfish behavior, and the individuals that punish will mostly belong to the class that pays a lower cost to do so. This effect is amplified when individuals that pay a lower cost for punishing inflict a higher punishment. The two population models differ when individuals that pay a low cost for punishing also inflict a lower punishment. In this situation, altruistic behavior becomes harder to maintain in an infinite and well-mixed population. However, this effect does not occur when the population is spatially structured.

On the provability logic of bounded arithmetic

In this paper we develop techniques to build various sets of highly undecidable sentences in Ido + i2,. Our results stem from an attempt to prove that the modal logic of provability in Ido + Ql, here called PLSZ, is the same as the modal logic L of provability in PA. It is already known that L s PLSZ. We prove here some strict containments of the form PLSZ c T/z(%) where %’ is a class of Kripke frames. Stated informally the problem is whether the provability predicates of Ido + Q2, and PA share the same modal properties. It turns out that while Ido + !Sl certainly satisfies all the properties needed to carry out the proof of Godel’s second incompleteness theorem (namely L E PLQ), the question whether L = PLQ might depend on difficult issues of computational complexity. In fact if