Four Decades of Mizar

Adam Grabowski, Artur Korniłowicz, Adam Naumowicz
2015 Journal of automated reasoning  
This special issue is dedicated to works related to Mizar, the theorem proving project started by Andrzej Trybulec in the 1970s, and other automated proof checking systems used for formalizing mathematics. A. Grabowski et al. -It would facilitate detection of errors, verification of references, elimination of repeated theorems, etc., -It would open a way to machine assisted education of the art of proving theorems, -It would enable automated generation of input into typesetting systems. Mizar 1
more » ... is the name of both a formal language in which the mathematics is written, and of an entire software system that checks the texts for logical correctness and manages the data base of Mizar articles (formal texts written in the Mizar language [30]). The logical basis of Mizar is a system of natural deduction close to the "composite system of logic" developed by Stanisław Jaśkowski [12] . In the period of over 40 years, a number of different versions of the Mizar system have been investigated. The history of the first 30 years of Mizar development has been described in "Mizar: the first 30 years" by Roman Matuszewski and Piotr Rudnicki [16] . Various linguistic constructions have been introduced that made the Mizar language a more accurate reflection of the natural language of mathematics. Among the most important versions of the system we can distinguish: Mizar PC-processing propositional calculus (around 1975) [26]; Mizar QC-processing quantifier calculus (1977) [27,28]; Mizar FC-supporting functional notation (1979); Mizar-MSE-multi-sorted with equality (1982); Mizar-2,3,4direct predecessors of the current Mizar.
doi:10.1007/s10817-015-9345-1 fatcat:wclwjz6eqzbvbis7w5tdolu5n4