The generative power of rule orderings in formal grammars*

One way of 'restricting linguistic theory' is the L-view: place sufficient restrictions on the allowable rules of grammars so as to reduce their generative power. Another way is the G-view: disallow certain grammars, regardless of whether this results in a reduction of generative capacity. The present paper adopts the L-view and, consequently, investigates the generative power of various theories. One area in linguistics where restrictions on linguistic theory have been advocated is in the ordering (within the cycle) of the application of the rules which generate the language. We consider eight proposals: Total Ordering; Partial Ordering (= Total Ordering plus iterative application); Semi Ordering ( = Anderson's 'local ordering' without iterative application); Semi Partial Ordering ( = Semi Ordering plus iterative application); Unorder ings ( = Ringen 'Condition VI, unmodified'); Quasi Orderings ( = Ringen 'Condition VI, modified'); Random Orderings; and Simultaneous Application. If, for any grammar obeying rule ordering conditions A there is a grammar obeying rule ordering conditions B which contains exactly the same class of derivations, then rule ordering theory B is at least as powerful in strong generative capacity as rule ordering theory A. Similar considerations are used to define the notions of equivalent, more powerful, and noncomparable in strong generative capacity. A series of theorems are proved showing the relative strength of the eight rule ordering theories. Some linguists who advocate 'random ordering' actually have in mind random ordering plus some 'universal principles'. We investigate the effect of four of these principles from the standpoint of the L-view, showing that two of them are strongly equivalent to total orderings and that two of them are intermediate between total and partial orderings. We close with an indication of what the role of mathematical linguistics should be for the ordinary working linguist. Linguistics 18 (1980), 017-072. 0024-3949/80/0018-0017 $2.00 © Mouton Publishers, The Hague Brought to you by | University of Alberta Library