Non-classical Logic

Non-classical logics are used to characterize phenomena with which classical logic has difficulty or to represent alternative views of reasoning. Relevant logic, for example, rejects the rule of classical logic that allows us to add new premises to an already valid inference to produce another valid inference. Relevant logic, as its name suggests, demands that all the premises of a valid argument be actually relevant to the derivation of the conclusion. In contrast, a weaker form of relevant logic – linear logic – is not supposed to represent an alternative view of valid inference, but rather describe relationships between different sorts of entities than classical (or relevant logic). Traditionally, logics are thought to represent relationships between propositions but linear logic represents relationships between resources and actions. The resulting logic is quite different from traditional logics and is interestingly related to the other logics that we will study such as relevant logic. A variant of linear logic, that we will also examine, is used to study the flow of information between agents.