Describes a type of semantic tool generalizing the notion of a possible world to permit representations of impossible states. Possible worlds are frequently described as states representing ways that the world could be; under this reading, impossible worlds are the ways that the world could not be. There exist many formal explications of the notion of an impossible world that require differing levels of divergence from the standard account of a possible world. In intensional analyses of counterpossible conditionals, impossible worlds are frequently proffered as the appropriate type of device for the evaluation of a conditional with an antecedent such as:
In such cases, all that is required of a possible world is that it does not verify all mathematical truths. In the more radical case of a counterlogical conditional, some revision to the truth conditions for logical connectives is often imposed. For example, the notion of a set-up can be considered an impossible world at which the truth condition for negation differs from that of classical negation but truth conditions for other extensional connectives remain standard. Impossible worlds feature in some semantics for conditional logics that employ a single absurd world at which every sentence is true.