An Externalist Way to Avoid Logical Omniscience Without Getting Logically Ignorant

Two well-known approaches to the problem of logical omniscience, impossible-worlds semantics and awareness structures, are described. Both approaches can be used to model logically ignorant agents, but both also have drawbacks when it comes to making a distinction between knowledge and veridical belief, modelling rational agents and explaining the appropriate conditions on models to do so. An alternative way to distinguish knowledge from both fallible and veridical belief, using non-normal modal logic and conditional logic, is introduced, explained and applied to model weakly rational agents.