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Informalising Formal Mathematics: Searching the Mizar Library with Latent Semantics
 In Proceeding of the Third International Conference on Mathematical Knowledge Management, MKM 2004. Bialowieza, Poland. LNCS 3119
"... Abstract. Finding required information in a library of mathematics can be problematic, just as in any other library. However, so far, there are no strong search methods based on the semantics of formal mathematics. This paper describes a new approach based on latent semantic indexing (LSI). Using th ..."
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Abstract. Finding required information in a library of mathematics can be problematic, just as in any other library. However, so far, there are no strong search methods based on the semantics of formal mathematics. This paper describes a new approach based on latent semantic indexing (LSI). Using this, the semantics of terms need not be explicitly defined but is indirectly inferred from a body of documents in which the terms occur. The Mizar library is used as it is a substantial resource of formal mathematics. The system described in the paper adapts Mizar articles to produce an appropriate body of documents that can be used by LSI. Preliminary tests suggest that this approach is able to provide a useful mechanism for the search and retrieval of formal mathematics. 1 Searching for Mathematics Mathematical knowledge management, since its inception, has had two key themes: the organisation of mathematical knowledge; and the successful retrieval of mathematical knowledge. In this paper, we consider the retrieval task when the
The Sylow Theorems
"... Summary. The goal of this article is to formalize the Sylow theorems closely following the book [4]. Accordingly, the article introduces the group operating on a set, the stabilizer, the orbits, the pgroups and the Sylow subgroups. ..."
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Summary. The goal of this article is to formalize the Sylow theorems closely following the book [4]. Accordingly, the article introduces the group operating on a set, the stabilizer, the orbits, the pgroups and the Sylow subgroups.
Deliverable 2.6:
, 2002
"... During the period of the MKM project, Michiel Hazewinkel (the person responsible for WP2) realized that much more work is required on the identification clouds technology before it can be applied in the ways originally foreseen in the MKM proposal and that the original objectives were too ambitious. ..."
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During the period of the MKM project, Michiel Hazewinkel (the person responsible for WP2) realized that much more work is required on the identification clouds technology before it can be applied in the ways originally foreseen in the MKM proposal and that the original objectives were too ambitious. These points were amplified in his (email) responses to the points raised by the project reviewers, which for context, we here quote: • Point 7 (P7) The Work Package 2 (WP2) had as one of its main objectives the “development of stochastic models and corresponding estimators for identification clouds of both formulas and key phrases ” (deliverable D2.2). D2.2 presents a model for the growth of indexes, then proceeds with the introduction of the concept of identification clouds and its possible applications, ending with “Probably the most crucial issue to be addressed at this stage is the formulation of a good probabilistic model of ID clouds complete with statistical estimators”. So, adequate modelling of identification clouds for formulas and key phrases could be an issue here (incidentally, D2.2 contains at the end of Section 13 the sentence “Some preliminary work on formula recognition using identification clouds is planned in the EC project [8].” where ref. [8] is the MKMNET project itself:
Mizar Analysis of Algorithms: Preliminaries
"... V!W X+S6Y)Z\[^]`_aScb/de6Z XY+ [ f ..."
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