Language, logic and ontology: uncovering the structure of commonsense knowledge

In Logic and Ontology Cocchiarella (2001) convincingly argues for a view of "logic as a language" in contrast with the (now dominant) view of "logic as a calculus". In the latter, logic is viewed as an "abstract calculus that has no content of its own, and which depends on set theory as a background framework by which such a calculus might be syntactically described and semantically interpreted." In the view of "logic as a language", however, logic has content, and "ontological content in particular." Moreover, and according to Cocchiarella, a logic with ontological content necessitates the use of type theory (and predication), as opposed to set theory (and set membership), as the background framework. An obvious question that immediately comes to mind here is the following: what exactly is the nature of this strongly-typed ontological structure that will form the background framework for a new logic that has content?