Early formulations of situation semantics faced foundational problems when cast in standard well-founded set theory, especially when modelling information flow and self-referential structures. Building on Peter Aczel's work in non-well-founded set theory, Barwise and colleagues developed situation theory as a general theory of information with a rich ontology of situations, infons, types and constraints, and used it to reformulate the semantic programme.

Keith Devlin's work in the late 1980s and early