Translating Mathematical Vernacular into Knowledge Repositories

Grabowski, Adam; Schwarzweller, Christoph

doi:10.1007/11618027_4

Cited by 17 publications

(11 citation statements)

References 8 publications

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“…Even if we claim the Mizar Mathematical Library to be really exhaustive repository of formalized elementary mathematical facts [6], in our work we had to fill some unexpected gaps, as mediate or serial relations;…”

Section: A Grabowski / Automated Discovery Of Properties Of Rough Setsmentioning

confidence: 99%

Automated Discovery of Properties of Rough Sets

Grabowski

2013

Fundamenta Informaticae

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The computer certification of rough sets (the translation in a way understandable by machines) seems to be far beyond the test phase. To assure the feasibility of the approach, we try to encode selected problems within rough set theory 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) binary relations. We show how much the human work can be enhanced with the use of automatic tools, without loosing too much time for the translation. Although the syntax is understandable by the computer, it offers relative flexibility and expressive power of the formal language. A. Grabowski / Automated Discovery of Properties of Rough Setsbe reduced to the first order logic, but the application of existing provers to the questions which arose in rough set theory is not that straightforward as one can expect to be.We deal with the Zhu's paper [16] on the axiomatization of various generalizations of rough sets with respect to ordinary binary relation properties. It was not surprising that the original Pawlak's approach [9] would soon be generalized, and so did Skowron and Stepaniuk [10], Yao [14], and Zhu [16], among others. But similar work, although precious and carefully driven by human hand, can be done by computers.Rough sets deliver important tools to discover knowledge from databases, it is now especially valuable taking into account the amount of stored information and the form of the records. Digitization of mathematical journals gets more and more popular, and it is often the case of:• new material, when papers can be published faster, so information exchange, and hence research is more efficient and accessible -here the well-known example could be Springer's Online First;

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Section: A Grabowski / Automated Discovery Of Properties Of Rough Setsmentioning

confidence: 99%

Automated Discovery of Properties of Rough Sets

Grabowski

2013

Fundamenta Informaticae

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“…Computerized proofs can be further improved in order to make their presentation more legible and accessible for human mathematicians [8]. Proof graphs measuring information flow available in the MML can be useful for that purpose as well [7,19].…”

Section: Current Mizarmentioning

confidence: 99%

Four Decades of Mizar

2015

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“…Now the system consist of three main parts: (1) a special formal language, in which mathematics can be expressed. This language is close to the vernacular used by human mathematician [14]. When used, the language expressions can be automatically checked for grammatical correctness; (2) the software, which verifies the correctness of formalized knowledge, in the classical logical framework; and last, but not least, (3) a huge collection of certified mathematical knowledge -the MML.…”

Section: The Mizar Systemmentioning

confidence: 99%

Equality in computer proof-assistants

Grabowski¹,

Korniłowicz²,

Schwarzweller³

2015

Annals of Computer Science and Information Systems

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Abstract-Equality is fundamental notion of logic and mathematics as a whole. If computer-supported formalization of knowledge is taken into account, sooner or later one should precisely declare the intended meaning/interpretation of the primitive predicate symbol of equality. In the paper we draw some issues how computerized proof-assistants can deal with this notion, and at the same time, we propose solutions, which are not contradictory with mathematical tradition and readability of source code. Our discussion is illustrated with examples taken from the implementation of the MIZAR system.

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Translating Mathematical Vernacular into Knowledge Repositories

Cited by 17 publications

References 8 publications

Automated Discovery of Properties of Rough Sets

Automated Discovery of Properties of Rough Sets

Four Decades of Mizar

Equality in computer proof-assistants

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