One of the most familiar non-classical logics is intuitionism, which, in simple terms, is based upon the rejection of the law of excluded middle: (P ∨ ¬P). There are both…

A relevance logic is motivated by the idea that the premises of a valid argument must be somehow “relevant” to its conclusion. The idea is motivated by the fact that…

The language sketched above is better referred to as first-order predicate calculus, as the language only quantifies over (first-order) individuals. A stronger language, second-order predicate calculus, can therefore be constructed…

Most non-classical logics are motivated by either philosophical considerations, such as the metaphysical status of the future, or technical concerns about the neutrality of the logical connectives or the notion…

While both the predicate calculus and the modal propositional calculus may be seen as extensions of the basic propositional calculus, there are also a variety of formal languages intended as…