ABSTRACT
Deductive system of basic signs and rules that guarantees that mathematical or logical operations are carried out in a controlled, non-contradictory, mechanical fashion. Such basic signs may be letters, natural numbers, words, logical connectives, truth values, among others. Rules are, for example, arithmetical operations such as multiplication, addition, syntactic rules, rules for logical connections. The concept of calculus plays a basic role in the formalization of grammatical theories about natural languages to the degree that the models of generative language descriptions can be construed as calculus (or as algorithms instead of rules, if commands are operative). A generative grammar (e.g. transformational grammar) contains a finite set of objects (all words in a language) and rules (constituent structure rules, transformational rules ( transformation, recursive rules) by means of which an infinite set of sentences can be generated. The language of calculus is the formal language or artificial language of formal logic. ( also formalization, mathematical linguistics)
References
Carnap, R. 1937. Logical syntax of language. London. Curry, H.B. 1963. Foundations of mathematical logic. New York. Whitehead, A.N. and B.Russell. 1910-13. Principia mathematica, 3 vols. Cambridge.
