A theory whose sentences are well-formed formulae of a logical calculus, and in which axioms or rules governing particular terms correspond to the principles of the theory being formalized. The theory is said to be couched or framed in the language of a calculus, e.g. first-order predicate calculus. Set theory, mathematics, mechanics, and many other sciences may be developed formally, thereby making possible logical analysis of such matters as the independence of various axioms, and the relations between one theory and another.