In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

The work investigates the powerlocales (lower, upper, Vietoris) of localic completions of generalized metric spaces. The main result is that all three are localic completions of generalized metric powerspaces, on the Kuratowski finite powerset. Applications: (1) A localic completion is always open, and is compact iff its generalized metric space is totally bounded. (2) The Heine-Borel Theorem i...

We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical a...

This report is based on the article [1] by Koetter and Kschischang. The authors introduced a novel approach for constructing codes by selecting a subset of a powerset of a vector space. With the code construction, they also defined an operator channel for code transmission. The codewords are vector subspaces. The data is transmitted by using one of the bases of such a subspace. The properties o...

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable...

Composing various powerset functors with the term monad gives rise to the concept of generalised terms. This in turn provides a technique for handling many-valued sets of terms in a framework of variable substitutions, thus being the prerequisite for categorical unification in many-valued logic programming using an extended notion of terms. As constructions of monads involve complicated calcula...

In an earlier paper, the author used derivatives to construct a deterministic automaton recognizing the language defined by an ω-regular expression. The construction was related to a determinization method invented by Safra. This paper describes a new construction, inspired by Piterman’s improvement to Safra’s method. It produces an automaton with fewer states. In addition, the presentation and...

A coalgebraic definition of finite and infinite trace semantics for probabilistic transition systems has recently been given using a certain Kleisli category. In this paper this semantics is developed using a coalgebraic method which is an instance of general determinization. Once applied to discrete systems, this point of view allows the exploitation of the determinized structure by up-to tech...

With the ongoing global financial crisis – which began with the collapse of the US sub-prime market in 2007 – the Barbadian economy is expected to contract in 2009. As a means of stimulating economic activity and providing job opportunities, the government has committed itself to completing 572 houses during the 2009/10 financial year. However, the arguments in favour of allocating more resourc...

For an r-graph H, let C(H) = minS d(S), where the minimum is taken over all (r− 1)-sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of H. Given a family F of r-graphs, the co-degree Turán number co-ex(n,F) is the maximum of C(H) among all r-graphs H which contain no member of F as a subhypergraph. Define the co-degree density of a family F to be γ(F) = li...