The linguistic phenomena of temporal presuppositions and
counterfactuals, situated on the boundary line between semantics and
pragmatics, are common to many languages, and the computational
treatment of such phenomena is difficult because of their nonmonotonic
aspect.

These phenomena are presented through a corpus of examples; they are
studied emphasizing the various types of knowledge underlying them;
and the fragment of language that encloses such phenomena is defined
in a way not dependent from a specific language. Then, Recursive
Models, a formalism for modeling the semantics of utterances
containing temporal presuppositions and counterfactuals, are proposed,
described from both functional (by formal specifications) and
structural points of view, and compared with related work.  Finally,
the adequacy of Recursive Models is empirically verified: TOBI
(Temporal presuppositions and counterfactuals: an Ontological Based
Interpreter), a system that interacts with the user in natural
language using the recursive models, is illustrated. TOBI is not based
on a deductive system, but uses the more primitive and flexible notion
of model-based evaluation; its architecture, flow of control and
internal data structures are presented.