## Speaker:

Paul Harrenstein, PhD Student, University of Utrecht, The Netherlands

## Title:

Towards a Notion of Game-theoretical Consequence

## Location:

1:00pm, Friday 14 May 2004

## Abstract:

Von Neumann and Morgenstern presented game-theory as a branch of
mathematics that deals with problems that had nowhere been dealt with
before. From a mathematical point of view, the participants in a
situation of conflict can be seen as each trying to maximize the same
function (the outcome of the game) according to an idiosyncratic
principle (their preferences).
Moreover, none of the players have control over all variables of the
function. The also argued that the usual notion of optimality is no
longer available and new solution concepts had to be developed to
take its place. Most notably among these game-theoretical solution
concepts is still that of a Nash-equilibirum.
Logical notions of consequence have frequently been related to
game-theoretical solution concepts. The correspondence between a
formula being classically valid and the existence of a winning
strategy for a player in a related two-person game, has been most
prominent in this context.
We, however, propose a conservative extension of the classical notion of logical
consequence for propositional logic based on a generalization of
Nash-equilibrium.
We construe propositional variables as decision variables that are
possibly in the control of various volitional agents an we pursue the logical
consequences of this idea. The game-theoretical concept of
consequence that results opens up a line of theoretical research
in which logic, game theory and social choice theory interact at
the same level.