If a theory of logic requires more input than can be gleaned from the sentences of the theory itself to have a logically consistent interpretation, then the theory may still have a logical signature without a complete or fully specified interpretation, or its logical signature must acknowledge the requirement of extra input to sentences of the theory complete the interpretation of sentences of the theory.

A logical signature specifies the syntax and semantics of the language used in the theory, including the set of symbols and operators used and the rules for constructing valid expressions and making inferences. This can be done independently of any particular interpretation of the theory, and is necessary for specifying the structure and rules of the theory.

However, an interpretation of the theory involves assigning a specific meaning to the symbols and operators used in the theory. This may require additional input beyond the sentences of the theory itself, such as external knowledge or the use of software to completely visualise sentences of the theory, in order to form an interpretation.

The use of software tools to help in the interpretation of sentences of a theory of logic may require additional assumptions or inputs that are not explicitly stated in the theory itself, and the interpretation may depend on the specific implementation of the software.

Where a theory of logic has a logically consistent interpretation with the help of external tools such as software, the logical signature of that theory must acknowledge the requirement of that external tool in the definition of the signature if there is to be a marriage between the interpretation and logical signature of that theory.

For instance, in some cases it is possible to express Object-Role Models, as a set of sentences, that at face value are ambiguous, as in where multiple potential join paths for a Join Subset Constraint exist. If software is required to disambiguate the ORM model, then the interpretation of the ORM model is not possible, in that case, without the software and whatever formal semantics operate over the intended signature  of ORM break down also without the signature intimating that software is required to disambiguate the ORM model.