An important conceptual modeling activity in the development of database, object-oriented and agent-oriented systems is the capture and expression of domain constraints governing underlying data and object states. UML is increasingly used for capturing conceptual models, as it supports conceptual modeling of arbitrary domains, and has extensible notation allowing capture of invariant constraints both in the class diagram notation and in the separately denoted OCL syntax. However, a need exists for increased formalism in constraint capture that does not sacrifice ease of use for the analyst. In this paper, we codify a set of invariant patterns formalized here for capturing a rich category of propositional constraints on class diagrams. We use tools of Boolean logic to set out the distinction between these patterns, applying them in modeling by way of example. We use graph notation to systematically uncover constraints hidden in the diagrams. We present data collected from applications across different domains, supporting the importance of "pattern-finding” for n{\hbox{-}}{\rm{variable}} propositional constraints using general graph theoretic methods. This approach enriches UML-based conceptual modeling for greater completeness, consistency, and correctness by formalizing the syntax and semantics of these constraint patterns, which has not been done in a comprehensive manner before now.