Since Carnap (1947) and Montague (1974) a central current of formal semantics has modelled intensions as functions from possible worlds to extensions. Theorists of epistemic reasoning have also used worlds to analyse knowledge, belief, and inference (Halperin (1995)). Possible worlds pose a serious representability problem.

In Kripke frame semantics (Kripke (1959,1963)) they are equivalent to maximal consistent sets of propositions, which correspond to ultrafilters in a prelattice of propositions (Fox and Lappin (2005), Lappin (2015)). There is no obvious procedure for generating such a set effectively. If we try to substitute the set of possible situations (partial worlds) for the set of worlds, the representability difficulty becomes even more severe. I propose a non-modal characterisation of intensions, which adapts the distinction between operational and denotational meaning from the semantics of programming languages to the interpretation of natural languages. I then suggest an approach to epistemic reasoning that replaces worlds with probability models, specifically, with Bayesian networks. While these models pose complexity of representation issues, they can be dealt with through stratification, estimation, and approximation methods of the sort applied to a variety of other computational problems. By contrast, these techniques do not seem to be available for the representation of maximal worlds. I conclude with a brief discussion of how an operational approach to natural language intensions might be integrated into the proposed probabilistic view of epistemic reasoning through a suitable account of semantic learning.