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**1 - 3**of**3**### Translating Mathematical Vernacular into Knowledge Repositories

"... Abstract. Defining functions is a major topic when building mathematical repositories. Though relatively easy in mathematical vernacular, function definitions rise a number of questions and problems in fully formal languages (see [Dav03]). This becomes even more important for repositories in which p ..."

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Abstract. Defining functions is a major topic when building mathematical repositories. Though relatively easy in mathematical vernacular, function definitions rise a number of questions and problems in fully formal languages (see [Dav03]). This becomes even more important for repositories in which properties of the defined functions are not only stated, but also proved correct. In this paper we investigate function definitions in the Mizar system. Though most of them are straightforward and follow the intuition, we also found a number of examples differing from mathematical vernacular or where different solutions seem equally reasonable. Sometimes there even do not seem to exist solutions not somehow “ignoring mathematical vernacular”. So the question is: Should we seek for some kind of standard, that is a “formal mathematical vernacular”, or should we accept that different authors prefer different styles? 1

### Computer-Driven Searching for Axiomatization of Rough Sets

"... Abstract. The formalization of rough sets in a way understable by machines seems to be far beyond the test phase. For further research, we try to encode some problems within RST and as the testbed of already developed foundations – and in the same time as a payoff of the established framework, we sh ..."

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Abstract. The formalization of rough sets in a way understable by machines seems to be far beyond the test phase. For further research, we try to encode some problems within RST and as the testbed of already developed foundations – and in the same time as a payoff of the established framework, we shed some new light on the well-known question of generalization of rough sets and the axiomatization of approximation operators in terms of (various types of) relations. 1

### Revisions as an Essential Tool to Maintain Mathematical Repositories

"... Abstract. One major goal of Mathematical Knowledge Management is building extensive repositories, in which the mathematical knowledge has been verified. It appears, however, that maintaining such a repository is as hard as building it – especially for an open collection with a large number of contri ..."

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Abstract. One major goal of Mathematical Knowledge Management is building extensive repositories, in which the mathematical knowledge has been verified. It appears, however, that maintaining such a repository is as hard as building it – especially for an open collection with a large number of contributors. In this paper we argue that even careful reviewing of contributions cannot cope with the task of keeping a mathematical repository efficient and clearly arranged in the long term. We discuss reasons for revisions of mathematical repositories accomplished by the “core implementors ” and illustrate our experiences with revisions of MML, the Mizar Mathematical Library. 1