One common reaction to these observations is to acknowledge that as plausible as the axioms of traditional epistemic logics may appear, they formalize not our everyday understanding of knowledge but rather an idealized or ‘implicit’ notion more closely resembling ‘knowability in principle’ (e.g. Levesque 1984; Stalnaker 1991; 1999). Another reaction has been to attempt to modify the interpretation of the language of epistemic logic to mitigate the effects of (i) and (ii). This can be achieved by altering the account of semantic validity for the modal language in question – e.g. through the use of so-called impossible worlds (Rantala 1982), awareness models (Fagin and Halpern 1988), or local models (Fagin and Halpern 1988). But although these techniques can be used to circumvent particular cases of (i) and (ii), they also typically complicate the task of explaining why the set of sentences known by an agent may exhibit some potentially desirable closure properties (e.g. that knowledge of a conjunction entails knowledge of its conjuncts).