NONDETERMINACY AND RECURSION VIA STACKS AND GAMES

The weakest-precondition interpretation of recursive procedures is developed for a language with a combination of unbounded demonic choice and unbounded angelic choice. This compositional formal semantics is proved to be equal to a game-theoretic operational semantics. Two intermediate stages are exploited. One step consists of unfolding the declaration of the recursive procedures. Fixpoint induction is used to prove the validity of this step. The compositional semantics of the unfolded declaration is proved to be equal to a formal semantics of a stack implementation of the recursive procedures. After an introduction to boolean two-person games, this stack semantics is shown to correspond to a game-theoretic operational semantics

Inductive Definition and Domain Theoretic Properties of Fully Abstract

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF + "parallel conditional function"), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is new, in that it is given level-by-level in the finite type hierarchy. To prove full abstraction and non-dcpo domain theoretic properties of these models, a theory of computational strategies is developed. This is also an alternative and, in a sense, an analogue to the later game strategy semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong; and Nickau. In both cases of PCF and PCF^+ there are definable universal (surjective) functionals from numerical functions to any given type, respectively, which also makes each of these models unique up to isomorphism. Although such models are non-omega-complete and therefore not continuous in the traditional terminology, they are also proved to be sequentially complete (a weakened form of omega-completeness), "naturally" continuous (with respect to existing directed "pointwise", or "natural" lubs) and also "naturally" omega-algebraic and "naturally" bounded complete -- appropriate generalisation of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page

On the emergent Semantic Web and overlooked issues

The emergent Semantic Web, despite being in its infancy, has already received a lotof attention from academia and industry. This resulted in an abundance of prototype systems and discussion most of which are centred around the underlying infrastructure. However, when we critically review the work done to date we realise that there is little discussion with respect to the vision of the Semantic Web. In particular, there is an observed dearth of discussion on how to deliver knowledge sharing in an environment such as the Semantic Web in effective and efficient manners. There are a lot of overlooked issues, associated with agents and trust to hidden assumptions made with respect to knowledge representation and robust reasoning in a distributed environment. These issues could potentially hinder further development if not considered at the early stages of designing Semantic Web systems. In this perspectives paper, we aim to help engineers and practitioners of the Semantic Web by raising awareness of these issues