Generalized constraint diagrams: the classical decision problem in a diagrammatic reasoning system

Constraint diagrams are part of the family of visual logics based on Euler diagrams. They have been studied since the 1990s, when they were first proposed by Kent as a means of describing formal constraints within software models. Since that time, constraint diagrams have evolved in a number of ways; a crucial re- finement came with the recognition of the need to impose a reading order on the quantifiers represented by diagrammatic syntax. This resulted first in augmented constraint diagrams and, most recently, generalized constraint diagrams (GCDs), which are composed of one or more unitary diagrams in a connected graph. The design of GCDs includes several syntactic features that bring increased expressivity but which also make their metatheory more complex than is the case with preceding constraint diagram notations. In particular, GCDs are given a second order semantics.