Object-Role Modeling (ORM) is a conceptual modelling language that is used to describe the structure and behaviour of complex systems. ORM is not typically considered a logical system in the same sense as first-order logic or fixed-point logic. Instead, it is a modelling language that can be used to represent concepts and relationships in a domain of interest.
While ORM is not a logical system, it is possible to map ORM models to various logical systems, including a first-order logical theory not supporting negation and theories under finite model theory. This is because ORM models can be expressed in terms of predicates and logical relationships, which can then be translated into the appropriate logical formalism.
For example, an ORM model that describes a set of entities and their relationships can be translated into a first-order logic theory that describes the properties of those entities and relationships. Similarly, an ORM model that describes a set of constraints or business rules can be translated into a theory under finite model theory that describes the properties of those constraints or rules.