Variable set semantics for keyed generalized sketches: formal semantics for object identity and abstract syntax for conceptual modeling

We introduce a mathematical framework where a formal semantics for object identity can be built irrespectively to computer related things like object identifiers, memory allocations etc. Then, on this base, we build formal semantics for a few major constructs of conceptual modeling (CM) such as association, aggregation, generalization, isA- and isPartOf-relationships. We also give a formal meaning to the two fundamental dichotomies of CM: objects vs. values and entities vs. relationships.On the syntactical side, the language we use for specifying our formal semantic constructs is graph-based and brief: specifications are directed graphs consisting only of three kinds of items––nodes, arrows and marked diagrams. The latter are configurations of nodes and arrows closed in some technical sense and marked with predicate labels taken from a predefined signature. We show that this format does provide a universal abstract syntax for the entire CM-field. Then any particular CM-notation appears as a particular visualization superstructure (concrete syntax) over the same basic specification format as above.