Abstract. Theories play an important role in building mathematical knowledge repositories. Organizing knowledge in theories is an obvious approach to cope with the growing number of definitions, theorems, and proofs. However, they are also a matter of subject on their own: developing a new piece of mathematics often relies on extending or combining already developed theories in this way reusing definitions as well as theorems. We believe that this aspect of theory development is crucial for mathematical knowledge management. In this paper we investigate the facilities of the Mizar system concerning extending and combing theories based on structure and attribute definitions. As an example we consider the formation of rough concept analysis out of formal concept analysis and rough sets. 1

Abstract. At first glance Mizar attributes look like unary predicates over mathematical objects enabling a more natural writing and reading. Attributes in Mizar, however, serve additional, more important purposes concerning typing of mathematical objects: Using attributes not only new (sub)types can be introduced, but also the user can characterize further relations between types and in this way make available existing notations for new objects. Thereby it should be stressed that these type relations can stand for elaborated mathematical theorems. This paper describes the properties and benefits of Mizar attributes from a user’s perspective. We comprehend the development of Mizar attributes, and give examples highlighting their use — essentially in the area of algebra. Concluding we discuss their impact on building mathematical repositories. 1

Abstract. Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higher-order predicate logic together with a few constructs for structuring knowledge: attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces and specifying the domains of categories and functors as namespaces with variable operations. All these constructs are logic-internal in the sense that they have a natural translation to higher-order logic so that certain aspects of Mathematical Knowledge Management can be realized in the object logic itself. There are a variety of operations on archives, though in this paper we can only sketch a few of them: knowledge retrieval and theory exploration, merging and splitting, insertion and translation to predicate logic.