Abstract We give two concrete examples of continuous valuations on dcpo’s to separate minimal valuations, point-continuous and valuations: (1) Let ${\mathcal J}$ be the Johnstone’s non-sober dcpo, μ valuation with ( U )=1 for nonempty Scott opens )=0 $U=\emptyset$ . Then, is a that not minimal. (2) Lebesgue measure extends Sorgenfrey line $\mathbb{R}_\ell$ Its restriction open subsets λ. its im...

Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges-Vita topol...

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of  possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a c...

Cumene Hydroperoxide (CHP) has been used in the production of Dicumyl Hydroperoxide (DCPO) and phenol. In Taiwan, several severe fire or explosion incidents have occurred due to its thermal instability or reactivity. In this research, the exothermic decomposition of CHP in Cumene was characterized by isothermal microcalorimeter, TAM (thermal activity monitor), because isothermal testing offers ...

A signature gives rise to a language L (Var) by extending with variables x 2 Var and binding constructs x and x, corresponding to least and greatest xed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone-algebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results p...

We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we d...

Abstract. A remarkable result due to Kou, Liu & Luo states that the condition of continuity for a dcpo can be split into quasi-continuity and meet-continuity. Their argument contained a gap, however, which is probably why the authors of the monograph Continuous Lattices and Domains used a different (and fairly sophisticated) sequence of lemmas in order to establish the result. In this note we s...

We use a generic notion of flatness in the enriched context to define various completions of metric spaces – enrichments over [0, ∞] – and preorders – enrichments over 2. We characterize the weights of colimits commuting in [0, ∞] with the conical terminal object and cotensors. These weights can be interpreted in metric terms as peculiar filters, the so-called filters of type 1. This generalize...

Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call the complexity approach space, the space of all functions in X = ]0,∞]Y , where Y can be a more dimensional input space. The set X, which is a dcpo for the pointwise order, moreover...

This study aims to assess the trend of domestic crimes reported in Davao City. The followed quantitative research method and utilized secondary domestic/criminal violence data collected by City Police Office (DCPO). Descriptive statistics, analysis, percentage change were used analyze gathered. Results revealed that theft attained highest incidence among crime cases as 2017, 2018, 2019 but was ...