Pawel Waszkiewicz

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This paper presents an architecture for a Personal Travel Assistant (PTA) which can elaborate on a users travel request and evaluate travel offers. Information on user behaviour is stored in a case base in the form of a Case Retrieval Net. This lazy approach has the advantages that it is incremental, extendible and allows flexible reuse of the information.(More)
We generalize the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann to obtain computational models for separated Q-categories. We fully describe (a) Yoneda complete and (b) continuous Yoneda complete Q-categories via their formal ball models. Our results yield solutions to two open problems in the theory of(More)
We prove that the category of I-cocomplete separated Q-categories has bilimits of expanding sequences. This result generalises on various levels the well-known theorem of domain theory that guarantees existence of bilimits in the category of directed-complete posets and Scott-continuous maps. In 1973 William Lawvere published a paper (reprinted as (Lawvere(More)
We provide a method for checking if a given auxiliary relation on a poset is the approximation relation on a domain. 1 Motivation If (P, ⊑) is a partial order, then the approximation (called also the way-below relation) is defined for x, y ∈ P as x ≪ y if and only of for any directed subset D of P , if y ⊑ ↑ D, then x ⊑ d for some d ∈ D (↑ D denotes the(More)
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