We show how two general notions of domain theory, the logic induced from the Scott topology on a domain, together with the Smyth powerdomain, interact with the theory of default reasoning introduced by Reiter 19]. We deene extensions, which are xed points of a certain non-monotonic operator on a Scott domain induced by a normal default set over that domain. We specialize this deenition to the S...

We prove the convergence of density on scale Z -1 to Bohr atom with infinitely many electrons (strong Scott conjecture) for a model that is known describe heavy atoms accurately.

We show there exists a continuous compactly supported function ' de ned on the reals satsifying '(x) = c0'(2x) + c1'(2x 1) + c2'(2x 2) if and only if c1 = 1, c0 + c2 = 1, and jc0j; jc2j < 1. The functions ' are examples of scaling functions from the theory of wavelets. x

Stable bistructures are a generalisation of event structures to represent spaces of functions at higher types; the partial order of causal dependency is replaced by two orders, one associated with input and the other output in the behaviour of functions. They represent Berry’s bidomains. The representation can proceed in two stages. Bistructures form a categorical model of Girard’s linear logic...

The paper introduces a new generalized closed set via semi local function. Its relationship with other existing generalized closed sets are established. It’s basic properties are discussed. A new decomposition of continuity is derived. General Terms Ideal topological space, local function and semi-local function.

In higher-type computation, established by Kleene and Kreisel in the late 1950’s (independently), one works with the data types obtained from the discrete natural numbers by closing under finite products and function spaces. For the theory of higher-type programming languages, it is natural to work with a corresponding hierarchy, or type structure, of domains, identified by Ershov and Scott in ...

The Scott rank of a countable structure is a measure, coming from the proof of Scott’s isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of Lω1ω) is the set of Scott ranks of countable models of that theory. In ZFC + PD we give a descriptive-set-theoretic classification of the sets of ordinals which are the Scott spectrum of a ...

Scott discovered his domain-theoretic models of the λ-calculus, isomorphic to their function space, in 1969. A natural completeness problem then arises: whether any two terms equal in all Scott models are convertible. There is also an analogous consistency problem: whether every equation between two terms, consistent with the λ-calculus, has a Scott model. We consider such questions for wider s...

In this paper, the definition of meet-continuity on $L$-directedcomplete posets (for short, $L$-dcpos) is introduced. As ageneralization of meet-continuity on crisp dcpos, meet-continuity on$L$-dcpos, based on the generalized Scott topology, ischaracterized. In particular, it is shown that every continuous$L$-dcpo is meet-continuous and $L$-continuous retracts ofmeet-continuous $L$-dcpos are al...