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1

TWO FORMAL APPROACHES TO ROUGH SETS

100%
Grabowski A., Jastrzebska M.
Studies in Logic, Grammar and Rhetoric
|
2009
|
issue 18(31)
25-34
EN
The formalization of rough sets in a way understable to machines seems to be far beyond the test phase. For further research, we try to encode the bunch of classical papers within RST and as the testbed of already developed foundations of the theory we try to adopt the interval set model to put it within the existing set-theory machinery in the Mizar computer-checked repository.
2

FORMALIZATION OF PROPOSITIONAL LINEAR TEMPORAL LOGIC IN THE MIZAR SYSTEM

80%
Giero M.
Studies in Logic, Grammar and Rhetoric
|
2010
|
issue 22(35)
7-21
EN
The paper describes formalization of some issues of propositional linear temporal logic (PLTL). We discuss encountered problems and applied solutions. The formalization was carried out in the Mizar system. In comparison with other systems, Mizar is famous for its large repository of computer checked mathematical knowledge and also for its user-friendly knowledge representation and proof language.
3

A LANGUAGE FOR MATHEMATICAL KNOWLEDGE MANAGEMENT

80%
Kieffer S., Avigad J., Friedman H.
Studies in Logic, Grammar and Rhetoric
|
2009
|
issue 18(31)
51-66
EN
We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under various complexity measures.
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