The aim of this paper is to develop a formal theory of Mizar linguistic concepts following the ideas from [14] and [13]. The theory here presented is an abstract of the existing implementation of the Mizar system and is devoted to the formalization of Mizar expressions. The base idea behind the formalization is dependence on variables which is determined by variable-dependence (variables may depend on other variables). The dependence constitutes a Galois connection between opposite poset of dependence-closed set of variables and the sup-semilattice of widening of Mizar types (smooth type widening).
In the paper the concepts strictly connected with Mizar expressions are formalized. Among them are quasi-loci, quasi-terms, quasi-adjectives, and quasi-types. The structural induction and operation of substitution are also introduced. The prefix
MML identifier: ABCMIZ 1, version: 7.9.01 4.101.1015