November 2023

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…