Several approaches of structuring (factorization, decomposition) of Dempster-Shafer joint belief functions from literature are reviewed with special emphasis on their capability to capture independence from the point of view of the claim that belief functions generalize bayes notion of probability. It is demonstrated that Zhu and Lee's {Zhu:93} logical networks and Smets' {Smets:93} directed ac...

Graphical models have become a standard tool for representing complex probability models in statistics and artificial intelligence. In problems arising in artificial intelligence, it is useful to use the belief network formalism to represent uncertain relationships among variables in the domain, but it may not be possible to use a single, fixed belief network to encompass all problem instances....

We characterize belief-free equilibria in infinitely repeated games with incomplete information with an arbitrary number of players and arbitrary information structures. This generalizes Hörner and Lovo (2008), which restrict attention to the two-player case and to information structures that have a product structure. Our characterization requires introducing a new type of individual rational c...

We formalize several ways of accounting, in the context of logically closed theories, for foundationalist intuitions that underlie change operations applying to belief bases. A positive and a negative concept of entrenchment is defined on the basis of the structure of a given, possibly prioritized belief base. Only the latter, more fine-grained concept proves to be appropriate for a successful ...

Compact specification of relationships between variables in a graphical model requires reducing the number of parameters in the valuation (probability potential, belief function, or utility) expressing that relationship. Finding structure (such as logical relationships) among the possible outcomes suggests reduced parameter representations of valuations. The TS-set notation, introduced here, he...

This article presents an alignment model of cultural formation, arguing that belief systems become increasingly constrained from earlier periods life-course to adulthood. I show the pairwise correlations between beliefs increase and structure personal culture becomes relatively more aligned before entering Moreover, rate change slows down with each year age, suggesting process is most prevalent...

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N ≥ 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; ...

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a h...

This paper deals with the problem of uniqueness of reconstruction in Open Logic by introducing the concept of total-ordered partitions, an ordering structure modeling belief degrees of knowledge, and rede ning the reconstruction operation. Based on the resulting de nition, a nontrivial condition for the convergency of cognitive processes is given. It is shown that if new knowledge is not always...