Rule Application to Its Own Output

Abstract

Since the beginning of generative phonology, the principle of linear ordering has been assumed which was given in The Sound Pattern of English (hereafter SPE) as follows. (1) Principle of linear ordering Rules are applied in linear order, each rule operating on the string as modified by all earlier applicable rules. (SPE 341) For any number of phonological rules to follow this principle means that they should not violate the requirement of linearizability given below. (2) Requirement of linearizability (a) Assymetric: No rule both precedes and follows the same rule; that is, if (aRb), then it is not also the case that (bRa). (b) Irreflexive: No rule precedes itself; that is, there is no element a such that (aRa). (c) Transitive: Given the three rules R1, R2, and Ra, then if R1 precedes R2, and R2 precedes Ra, then R1 must also precede Ra; that is, if (aRb) and (bRc), then (aRc). (Anderson 1969). Principle (1) and Requirement (2) assert that rules be arranged in a single sequence and be applied one at a time from the beginning of the list toward the end, always to the results of the preceding rule without re-applying any rule which has already been applied. However, natural languages make the strict observance of this Markovian rhode of rule application difficult. We find the relaxation of this principle already in SPE. In case rules are formally related by parentheses, angled brackets, or variables, then the rules are applied disjunctively. When two rules are related by one of the above devices, then neither rule may be allowed to apply to the output of the other. The need of the principle of disjunctive ordering is attested by empirical data. Without this principle, for instance, the application so-called alpha switching rules will not terminate.