in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

The content of a membrane in a configuration of an ‘exact’ P system is described by a multiset. Recall that a (crisp) multiset over a set of types X is simply a mapping d : X → N. The usual interpretation of a multiset d : X → N is that it describes a set consisting of d(x) “exact” copies of each type x ∈ X. In particular, it is assumed that the set described by the multiset does not contain an...

We compare the expressive power of a class of well-structured transition systems that includes relational automata, Petri nets, lossy channel systems, constrained multiset rewriting systems, and data nets. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverabil...

Here and in what follows we assume S is a finite multiset in R d. This means tha t the points in S have "multiplicity". Strict ly speaking, a multiset is a map S : F --, R d and in our case F is finite. Then corekS = M{convS(E) : E C_ F, IF \ El _< k}. From now on we do not say explicitly tha t the sets in question are multisets. This will make the no ta t ion simpler and will not cause confusi...

The Möbius function of a partially ordered set is a very convenient formalism for counting by inclusion-exclusion. An example of central importance is the partition lattice, namely the partial order by refinement on partitions of a set {1, . . . , n}. It seems quite natural to generalize this to partitions of a multiset, i.e. to allow repetition of the letters. However, the Möbius function is n...

We introduce an evolution-communication model for tissue P systems where communication rules are inspired by the general mechanism of cell communication based on signals and receptors: a multiset can enter a cell only in the presence of another multiset. Some basic variants of this model are also considered where communication is restricted either to be unidirectional or to use special multiset...

This paper presents a mechanism called LERS-M for learning production rules from very large databases. It can be implemented using objectrelational database systems, it can be used for distributed data mining, and it has a structure that matches well with parallel processing. LERS-M is based on rough multisets and it is formulated using relational operations with the objective to be tightly cou...

In this work we consider modeling of services with workflow modules, which form a Petri net subclass. The service compatibility problem is to answer the question, whether two services fit together, i.e. whether the composed system is correct. We study complementarity of resources, produced/consumed by two services — a necessary condition for the service compatibility. Resources, which are produ...