In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...

Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of additional structures on the objects of a monoidal Kleisli category. It is proposed to consider any uniform class of information transformers (ITs) as a fami...

Certain definitions of information can be seen to be compatible with each other if their relationships are properly understood as referring to different levels of organization in a subsumptive hierarchy. The resulting hierarchy, with thermodynamics subsuming information theory, and that in turn subsuming semiotics, amounts to a naturalizing of the information concept.

Category theory has tong been widely recognised as being conveniently formalisable In constructive mathematics. We describe a computer implementation of its basic concepts, as an extension of the Goteborg implementation of Martin-Lofs theory of types; we discuss some alternative formulations of the theory (and our reasons for rejecting them) and briefly comment on the problems of automating the...

In order to develop a formal framework for data fusion field main data fusion models are observed and a logical model of data fusion is suggested. It is shown that considered data fusion models are representable in the logical model. The logical model being insufficiently general to compare different methods of data fusion is reformulated on category theory language. After that a number of info...

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to infinitely many axioms, and countable model the Löwenheim–Skolem theorem. This paper presents axioms one accept get rid of these features. For matter, some twenty are formulated in non-classical first-orde...

kinds of structured systems in terms of schematic types, as opposed to answering ‘What is (or where is!) a structure?’, then why should we be troubled by the fact that ‘[b]y themselves they [the category-theoretic axioms] assert nothing’ that ‘They merely tell us what it is to be a structure of a certain kind’ and thus are ‘unlike the axioms of set theory, [in that] its axioms are not assertory...

Model theoretic semantics (MTS) has a special attitude to describe semantics, to characterize both artificial and natural languages by pure mathematical tools and some of the basic properties of this attitude are disscussed. The arsenal of MTS equipped here with such tools allowing the investigation at such a level of complexity that approximates the real situations. These tools are developed w...

Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis? We propose to use the language of category theory, in particular diagrams and their colimits, for answering this question. We outline a general approach for representing combinations of logical theories, or ontologies, through interfaces of various kinds, based on diagrams and ...