Local Semantics as a Lattice Based on the Partial-all Quantifier

The main problem of system theory is summarized by ; how one can express the growing universe in a universe ? In a set theory, the universe appeared in the diagonal argument is a candidate of the expression of the growing universe, however it is not in a universe. To resolve this problem, we propose the dynamic quantifier and partial-all quantifier that mimic infant's eyes. A universe is defined as a concept lattice that is obtained from a binary relation between two sets. Because a formal concept is defined through a particular operator with all-quantifier, ∀, a concept lattice is complete and the relationship between a relation and a lattice is unique. By contrast, partial-all quantifier, ∀_p, no longer surveys all elements in a given set, and then an obtained lattice is different from a normal concept lattice. In this scheme, a lattice is perpetually changed. If a lattice polynomial is used as syntax,a lattice is used as semantics. Due to partial-all quantifier, a lattice is destined to be local semantics. Especially, lattices that are derived through partial-all quantifier can constitute the hierarchy of distributive law, and then the domain in which perturbation is applied is perpetually changed in the model that a lattice polynomial keeps on transform binary sequences.