AGM-Style Revision of Beliefs and Intentions from a Database Perspective (Preliminary Version)

We introduce a logic for temporal beliefs and intentions based on Shoham's database perspective. We separate strong beliefs from weak beliefs. Strong beliefs are independent from intentions, while weak beliefs are obtained by adding intentions to strong beliefs and everything that follows from that. We formalize coherence conditions on strong beliefs and intentions. We provide AGM-style postulates for the revision of strong beliefs and intentions. We show in a representation theorem that a revision operator satisfying our postulates can be represented by a pre-order on interpretations of the beliefs, together with a selection function for the intentions

Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries

We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurences of this or closely related Hopf algebras in other mathematical domains, such as foliations, Runge Kutta methods, iterated integrals and multiple zeta values. We emphasize the unifying role which the Butcher group, discovered in the study of numerical integration of ordinary differential equations, plays in QFT.Comment: Survey paper, 12 pages, epsf for figures, dedicated to Mosh\'e Flato, minor corrections, to appear in Lett.Math.Phys.4

Using the Hopf Algebra Structure of QFT in Calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions.Comment: 28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.

A betting interpretation for probabilities and Dempster-Shafer degrees of belief

There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting offers will not multiply the capital it risks by a large factor. Both interpretations can be applied to ordinary additive probabilities and used to justify updating by conditioning. Only the second can be applied to Dempster-Shafer degrees of belief and used to justify Dempster's rule of combination.Comment: 20 page

The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors