Kopylov extends expected utility, multiple priors, and variational utility models to accommodate various framing patterns---such as partition dependence and availability biases in beliefs, comparative ignorance and source dependence in ambiguity attitudes. In these extensions, subjective beliefs, sets of beliefs, and variational costs may depend on the partition of the state space generated by (i) the evaluated prospect f, (ii) the pair f and g of compared prospects, and more broadly, by the entire set of feasible actions. The former type of framing violates monotonicity, while the latter is inconsistent with transitivity and the weak axiom of revealed preference. He relaxes these axioms to obtain partition-dependent beliefs, sets of beliefs, and variational costs in expected utility, multiple priors, and variational utility representations respectively.

Each of these functional forms is uniquely identified over all possible partitions of the state space.  In a related framework, he excludes the state space from the list of primitives altogether and derive subjective probabilistic distributions over the set of possible payoffs rather than states of the world. In this case, framing can satisfy both monotonicity and transitivity.