Semantics of Multimodal Network Models

A multimodal network (MMN) is a novel graph-theoretic formalism designed to capture the structure of biological networks and to represent relationships derived from multiple biological databases. MMNs generalize the standard notions of graphs and hypergraphs, which are the bases of current diagrammatic representations of biological phenomena, and incorporate the concept of mode. Each vertex of an MMN is a biological entity, a biot, while each modal hyperedge is a typed relationship, where the type is given by the mode of the hyperedge. The semantics of each modal hyperedge e is given through denotational semantics, where a valuation function f_{e} defines the relationship among the values of the vertices incident on e. The meaning of an MMN is denoted in terms of the semantics of a hyperedge sequence. A companion paper defines MMNs and concentrates on the structural aspects of MMNs. This paper develops MMN denotational semantics when used as a representation of the semantics of biological networks and discusses applications of MMNs in managing complex biological data.