Formal Mathematics for Mathematicians

Abstract

The collection of works for this special issue was inspired by the presentations given at the 2011 AMS Special Session on Formal Mathematics for Mathematicians: Developing Large Repositories of Advanced Mathematics. The issue features a collection of articles by practitioners of formalizing proofs who share a deep interest in making computerized mathematics widely available.

Topological structures as a tool for formal modelling of rough sets

“…The Mizar Mathematical Library (MML) [27] is based on Tarski-Grothendieck set theory, which is very close to the one used by the majority of mathematicians [30]. Hence it is not very strange that general topology is one of the widely represented parts of mathematics within this repository of knowledge (see Table I for details, general topology holds fifth position w.r.t.…”

Four Decades of Mizar

“…In the MML there are also systematically developed branches of mathematics [33], e.g., set theory [21], topology, functional analysis, abstract algebra [20], category theory, and lattice theory. Some of the results proven for lattices were obtained with the help of equational provers-like EQP/Otter (now Prover9).…”

Definitional Expansions in Mizar

“…Expanding everything to primitives introduces much knowledge to the reasoning, which can help to draw more conclusions. But clearly, in proof assistants used in practice [26,29], where their efficiency is one of the crucial points (users should wait for answers from systems for reasonable amount of time), the fast growing size of fully expanded theories is an important factor in slowing down the processing [18].…”