Logic

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

The next development of the propositional calculus is the predicate calculus. This considers the logical relationships that hold between predicate expressions, along with the quantifiers ∃x (“there is at least…

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…

A common extension to the standard formal languages outlined above is to introduce the technical machinery required to evaluate natural language arguments containing modal terminology (that is, talk of possibility…

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…

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…

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…

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…

¬ one-place logical connective read as “not” or as “is not the case” ~ alternative notation for “not” & two-place logical connective read as “and” ˄ and