Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d ×m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...

Most standard solution concepts of extensive games are history-insensitive in the sense that no matter at which information set one is, it is assumed that each player believes that everybody else is rational. In reality, each history of moves reveals certain traits of the players to one another. It is argued in this paper that solution concepts ought to make use of this fact. An example of such...

In this paper we approach both procedural and substantive irrationality of artificial agent cognitive systems and consider that when it is not possible for an agent to make a logical inference (too expensive cognitive effort or not enough knowledge) she might replace certain parts of the logical reasoning with mere associations.