Graphical systems such as Entity-Relationship Diagrams and Object-Role Modeling (ORM) are not typically considered formal systems of logic, although they do incorporate some logical concepts. As a graphical language, ORM, however, has a pedigree of being able to be mapped to a formal system of logic 
Formal systems of logic are mathematical systems that use a formal language and a set of rules for deriving logical conclusions. These systems are typically used in fields such as mathematics, philosophy, and computer science to reason about the properties of abstract concepts.
While ORM is a modelling language used primarily in the fields of database design and to capture business rules and uses graphical notation to represent objects types, and the relationships between them, it is not currently seen as a formal system of logic in the sense of being used in general use for deriving logical conclusions.
That is, ORM is useful for representing complex systems in a visual and intuitive way, but it is not intended for formal reasoning about the properties of those systems.
1. Enrico Franconi and Terry Halpin. ORM abstract syntax and semantics: non-normative glossary. Technical report, https://gitlab.com/orm-syntax-and-semantics/orm-syntax-and-semantics-docs, 2020.