We introduce a version of operational set theory, OST, without a choice operation, which has a machinery for ∆0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke-Platek set theory KP with infinity are pairwise Π1 equivalent. We al...

We consider evaluation strategies for database queries expressed in three functional query languages: the complex value algebra, the simply typed lambda calculus, and method schemas. Each of these query languages derives its expressive power from a diierent primitive: the complex value algebra from the powerset operator, the simply typed lambda calculus from list iteration, and method schemas f...

This paper explores the relationship between simulation and the emerging topics of Lean Thinking and lean construction. The ideas which have motivated the evolution of lean construction concepts are presented. The use of simulation as a means of evaluating the benefit of using lean construction techniques is discussed. Two examples of lean thinking based re-design of common construction process...

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

This paper introduces formative processes, composed by transitive partitions. Given a family F of sets, a formative process ending in the Venn partition of F is shown to exist. Sufficient criteria are also singled out for a transitive partition to model (via a function from set variables to unions of sets in the partition) all set-literals modeled by . On the basis of such criteria a procedure ...

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T , uses a single modal operator ∇T of arity given by the functor T itself, and its semantics is defined in term...

We place ourselves in a so-called meet-closed description context; that is a context consisting of a finite nonempty entity set E whose elements are described in a complete meet-semilattice D, by means of a descriptor δ. Then we consider multiway quasi-ultrametric dissimilarities on E, a class of multiway dissimilarities that, with their relative k-balls, extend the fundamental in classificatio...

This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the ...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...