An analysis of the equational properties of the well-founded fixed point

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study the logical properties of the (parametric) well-founded fixed point operation. We show that the operation satisfies several, but not all of the equational properties of fixed point operations described by the axioms of iteration theories

some economic applications of scott domains

The present paper is structured around two main constructions, fixed points of functors and fibrations and sections of functors. Fixed points of functors are utilized to resolve problems of infinite regress that have recently appeared in economics. Fibrations and sections are utilized to model solution concepts abstractly, so that we can solve equations whose arguments are solution concepts. Most of the objects (games, solution concepts) that we consider can be obtained as some kind of limit of their finite subobjects. Some of the constructions preserve computability. The paper relies heavily on recent work on the semantics of program- ming languages.scott domains,infinite regress,game theory

A Formal Model for Trust in Dynamic Networks

We propose a formal model of trust informed by the Global Computing scenario and focusing on the aspects of trust formation, evolution, and propagation. The model is based on a novel notion of trust structures which, building on concepts from trust management and domain theory, feature at the same time a trust and an information partial order

Approximation in quantale-enriched categories

Our work is a fundamental study of the notion of approximation in V-categories and in (U,V)-categories, for a quantale V and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of V- and (U,V)-categories. We fully characterize continuous V-categories (resp. (U,V)-categories) among all cocomplete V-categories (resp. (U,V)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale V and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory.Comment: 17 page