Please send your submission in PDF format, at most 10 pages in LNCS style, 10 pts, bibliography included (see http://www.springer.com/computer/lncs?SGWID=0-164-6-793341-0 ). If needed due to space reasons, technical material such as proofs may be added in an appendix of at most 5 pages. The PDF files have to be uploaded online via the workshop’s submission website:

http://www.easychair.org/conferences/?conf=logiccognition2012

The author notification date is May 7, 2012. Prior to the workshop, speakers will have the opportunity to submit an extended abstract for inclusion in the ESSLLI proceedings and/or CEUR Workshop Proceedings (deadline July 15, 2012). We intend to make online proceedings available, and we ask you to format your final version in the same LNCS style. Maximum length is 12 pages. A technical appendix of up to 5 pages is allowed. All participants must register for ESSLLI.

After the workshop, selected authors will be invited to submit a revised and extended version of their paper for a special issue of the Journal of Logic, Language and Information (JoLLI), devoted to Logic and Cognition.

Iris van Rooij

Call for Papers
Extended Deadline: March 14, 2012

Workshop Description:

The roots of logic go back to antiquity, where it was mostly used as a tool for analyzing human argumentation. In the 19th century Gottlob Frege, one of the founders of modern logic and analytic philosophy, introduced anti-psychologism in the philosophy of mathematics. In the following years anti-psychologism, the view that the nature of mathematical truth is independent of human ideas, was one of the philosophical driving forces behind the success of mathematical logic. During the same period in the 19th century, also modern psychology (Helmholtz, Wundt) was born. However, the notion of anti-psychologism often stood in the way of a potential merge of the disciplines and led to a significant separation between logic and psychology research agendas and methods. Only since the 1960s, together with the growth of cognitive science inspired by the ‘mind as computer’ metaphor, the two disciplines have started to interact more and more. Today, we finally observe an increase in the collaborative effort between logicians, computer scientists, linguists, cognitive scientists, philosophers, and psychologists.

We plan to discuss the empirical research motivated by logical theories as well as logics inspired by experimental studies. As a result, we hope to contribute towards an increase in collaboration between logicians and cognitive scientists.

The meeting is partially sponsored by a Vici grant NWO-277-80-001

Invited speakers:
Paul Egré
Iris van Rooij

The workshop will take place as part of the 24th European Summer School in Logic, Language and Information (ESSLLI 2012): http://www.esslli2012.pl/

Submissions Details:

Please send your submission in PDF format, at most 10 pages in LNCS style, 10 pts, bibliography included (see http://www.springer.com/computer/lncs?SGWID=0-164-6-793341-0 ). If needed due to space reasons, technical material such as proofs may be added in an appendix of at most 5 pages. The PDF files have to be uploaded online via the workshop’s submission website:

http://www.easychair.org/conferences/?conf=logiccognition2012

The author notification date is May 7, 2012. Prior to the workshop, speakers will have the opportunity to submit an extended abstract for inclusion in the ESSLLI or/and CEUR Workshop Proceedings proceedings (deadline July 15, 2012). All participants must register for ESSLLI. However, we will be able to partially refund ESSLLI fees for selected speakers.

After the workshop, selected authors will be invited to submit a revised and extended version of their paper for a special issue of the Journal of Logic, Language and Information (JoLLI), devoted to Logic and Cognition.

Program Committee:
Jakub Szymanik (co-chair)
Rineke Verbrugge (co-chair)
Leon de Bruin
Eve Clark
Robin Clark
Paul Egré
Fritz Hamm
Alice ter Meulen
Marcin Mostowski
Maartje Raijmakers
Iris van Rooij
Keith Stenning
Marcin Zajenkowski

Important Dates:
Extended submission deadline:   March 14, 2012
Notifications:   May 7, 2012
Camera-ready copy:  July 15, 2012
Workshop:  August 13-17, 2012

Program chairs: Jakub Szymanik, Rineke Verbrugge
Contact: logic.cognition@gmail.com

The applet above shows an implementation of simulated agents playing the game of limited bidding. These agents are constrained in their ability to model the mental content of others.

Game outline

Limited bidding is a simplified version of a game described in “Edward de Bono’s super mind pack”. At the beginning of the game, both players receive five numbered tokens. The number corresponds to the value of the token. Over the course of five rounds, players simultaneously choose one of their own tokens to play. Whoever picks the highest value token wins the round. If both players pick the same value token, there is no winner. Since each token can only be used once per game, players are forced to play strategically.

Game-theoretically, the optimal way to play limited bidding is by randomizing every choice. That is, under the assumption of common knowledge of rationality, a players should randomly pick one of the tokens still available to them. However, the agents in this applet suspect that their opponent may not be fully rational. Moreover, they are limited in their ability to make decisions themselves. By playing the game repeatedly against the same opponent, agents try to learn to predict what their opponent will do, and change their strategy accordingly.

Theory of mind

Theory of mind refers to the individual’s ability to model mental content of others, such as beliefs, desires or intentions. The agents modeled in the applet are constrained in their theory of mind. At the most basic level, a zeroth-order theory of mind agent tries to model his opponent through patterns of behaviour. For example, a zeroth-order theory of mind agent might find out that his opponent always plays token 5 at the start of the game, or tends to save token 3 for last. However, he is unable to realize that his opponent might be doing the same. In fact, a zeroth-order theory of mind agent does not realize that his opponent has goals that are opposite to the ones he has himself. The agent’s zeroth-order beliefs are represented by red bars in the applet, which indicate how likely the agent believes it to be that his opponent is going to play a certain token.

A first-order theory of mind agent realizes that his opponent might be a zeroth-order theory of mind agent, and tries to predict what she is going to do by putting himself in her position. He looks at the game from the point of view of his opponent to determine what he would believe if the situation were reversed, and uses this as a prediction for his opponent’s actions. For example, a first-order theory of mind agent might realize that he has started the game by using token 3 a few times in a row, and suspect that his opponent is going to try and take advantage of that. First-order beliefs show how likely the agent thinks his opponent to believe that he is going to play a certain token. In the applet, this is indicated by the height of the green bars.

A second-order theory of mind agent takes this reasoning one step further. He puts himself into the position of his opponent, but also believes that she might be putting herself into his position. In the applet, the height of the blue bars indicate the agent’s second-order beliefs.

Based on zeroth-, first- and second-order beliefs, an agent makes different predictions about what his opponent is going to do. The agent must therefore also form beliefs about which of these predictions will yield the best results. An agent’s combined beliefs represent how the different order of theory of mind are combined into a single prediction of his opponent’s actions.

Although the agents in the applet make use of theory of mind, they do not remember the choices of their opponent. Instead, when they see the outcome of a game, they form beliefs about what the opponent is going to do next time and forget what they saw. As an alternative type of agent, a high memory agent is a zeroth-order theory of mind agent that remembers what his last choice was. That is, the high memory agent forms beliefs about what his opponent is going to do in reaction to him playing each of the possible tokens.
In terms of memory, a high memory agent uses about the same amount of space as a second-order theory of mind agent, although this space is used differently.

Controls

The applet has a number of controls to allow users to judge the effect of using a higher order of theory of mind on the performance of agents in the limited bidding game.

• Player one, player two: Determines the type of player. Both players can be either zeroth-, first- or second-order theory of mind agents. Additionally, player one may also be a high memory agent, while player two can be controlled by a human user.
• Learning speed: Determines how strongly an agent changes his beliefs based on new information. A learning speed of 0.0 means that an agent doesn’t learn at all, while an agent with learning speed 1.0 learns so quickly that he cannot remember anything more than the last game.
• Reset: Resets the game to the start situation.
• Play round: Plays one round of the game, and pauses afterwards. This action is not possible if player two is a human player.
• Play game: Repeatedly plays rounds of the game until no tokens are left. This action is not possible if player two is a human player.
• Tokens: When player two is a human player, the game only continues once player two has revealed his choice by clicking on one of the tokens that are still available to player two. In other cases, selecting the tokens has no effect.

The applet can also be downloaded to be used as an offline version.

To show the effects of heterogeneity, the population is divided into two classes that can differ in the cost they pay to punish others for their selfish behaviour, as well as the effectiveness of their punishment (i.e. the cost selfish individuals pay for being punished).

Infinite and well-mixed population

In the infinite and well-mixed population, individuals play the game with randomly selected co-players, and are assumed never to meet the same co-players twice. In this scenario, bright dots indicate that eventually, the entire population is altruistic. That is, the entire population contributes to the public good. Light gray dots indicate the same, but also that individuals that have to pay a high cost to punish never actually punish. Dark gray dots, on the other hand, indicate that selfish behaviour persists in the population.

Lattice-based population

In the lattice-based population, individuals only play the game in specific groups. Each individual is part of five different groups, and only plays the game with the members of those groups. In this scenario, the brightness of the dots indicates how much of the population eventually becomes altruistic: bright white dots show that the entire population contributes to the public good, while black dots indicate that everybody refuses to play the game.

The color of a dot indicates how punishers are distributed across the classes. When a dot is red, this means that punishers are mostly those individuals that pay the least for punishing. Blue dots, on the other hand, show that punishment is done mostly by the individuals that are more effective punishers. The brighter the color of a dot, the higher the difference: a gray dot shows that on average, punishers are uniformly distributed across classes.

Controls

Since the results are shown in a three-dimensional figure, the full extent of the results are not immediately visible. Also, the combination of brightness and color may make some of the results harder to determine. The following controls are available:

• Up arrow or left arrow: Move the slice plane backwards.
• Down arrow or right arrow: Move the slice plane forwards.
• Page up: Move the slice plane backwards ten steps.
• Page down: Move the slice plane forwards ten steps.
• C or S: Toggle the display of color.
• B or V: Toggle the display of brightness.

The applet can also be downloaded to be used as an offline version.