The simplest formal (logical) language is the propositional calculus. This considers the logical relationships that hold between complete propositions.

In the classical logics already discussed, the logical connectives are taken to be bivalent—that is, they allow of only two different truth values: true and false. One natural extension to…

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…