Graphs as relational structures: An algebraic and logical approach

Abstract

Relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied. We define operations on structures that are compatible with monadic second-order logic, and that are powerful enough to represent context-free graph- and hypergraphgrammars of various types, namely, hyperedge replacement. C-edNCE, and separated handle replacement ones. Several results on monadic second-order properties of the generated sets are obtained in a uniform way.