We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonic mappings. The second is a contraction principle for monotone maps that guarantees the existence of unique fixed points. 1

We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same

We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B,... ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for non-commutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, � , •) acts on an underlying Q-right module (M, � ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A: M → M and f Q A: Q → Q of (lax) morphisms for each agent A ∈ A. By adjunction, they give rise to epistemic modalities [12], capturing the agents ’ knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [20] — cf. weakest preconditions. This model subsumes the crucial fragment of Baltag, Moss and Solecki’s [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resource-sensitive structure on the epistemic actions. Keywords: Multi-agent communication, knowledge update, resource-sensitivity, quantale, Galois adjoints, dynamic epistemic logic, sequent calculus, Lambek calculus, Linear Logic.

After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem.

The regular spaces which may be realized as the set of maximal elements in an !-continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces.

We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multiple-viewpoint checking, where checks are delegated to single-viewpoint models — efficiently driven by the order structure. Instrumentations of this algorithm enable the detection and location of inconsistencies across viewpoint boundaries. To validate the approach, we investigate multiple-valued models and their compositional property semantics over a finite distributive AC lattice. We prove that this semantics is computed by our algorithm above whenever the primes of the AC lattice determine ‘projected’ single viewpoints and the order between primes is preserved as refinements of single-viewpoint models. As a case study, we discuss a multiple-valued notion of state-machines with first-order logic plus transitive closure. 1

In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cech-complete. An important consequence is that any metric space homeomorphic to the maximal elements of a Scott domain must be completely metrizable. 1

: Wearable computing will change the current paradigms of human-computer interaction. With heads-up displays, unobtrusive input devices, personal wireless local area networks, and a host of other context sensing and communication tools, wearable computing can provide the user with a portable augmented reality where many aspects of everyday life can be electronically assisted. This paper focuses on several such situations, such as an academic or business conference, classroom note-taking, office communication, maintenance, or a visit to a museum. 1 Introduction The recent push for smaller and faster notebook computers is indicative of a major trend in computing. Users want computers that are as portable and convenient as possible to help them with daily activities. In order to accommodate this trend, keyboard-less Personal Digital Assistants (PDA's) were introduced. Current attempts at a PDA revolve around pen computing. While handwriting recognition will improve, these systems will a...

Dcpos can be presented by a preorder of generators and inequational relations expressed as covers. Algebraic operations on the generators (possibly with their results being ideals of generators) can be extended to the dcpo presented, provided the covers are “stable ” for the operations. The resulting dcpo algebra has a natural universal characterization and satisfies all the inequational laws satisfied by the generating algebra. Applications include known “coverage theorems ” from locale theory. 1

1. A finitary probability space (=all probability measures on a fixed finite support) can be faithfully represented by a partial order equipped with a measure of content (e.g. Shannon entropy). 2. This partial order can be obtained via a purely order-theoretic systematic procedure starting from an algebra of properties. This procedure applies to any poset envisioned as an algebra of properties. 1