Quasilattices and complex concept analysis

Abstract

Quasilattices are algebraic structures that comprise a semilattice-ordered system of lattices. In this paper, certain quasilattices (that are characterized abstractly by a local completeness property) provide an extension of Wille's concept analysis to the study of complex systems that function on a number of distinct levels. In an important special case, a chain semilattice serves to represent a time series governing the evolution of a single system.

Natural set representations of locally complete quasilattices have opposed set inclusions describing order relations within a complete lattice, and parallel set inclusions tracking homomorphisms that connect distinct lattice fibers. In the time series model, the sets that appear within the set representation accumulate successive layers at each time point, establishing a mathematical model for historical phenomena.

Mathematics Subject Classification (2020):

• 06B75
• 06A15
• 68P05

Key words:

• Lattice
• quasilattice
• complex system
• historical science
• formal concept analysis