A phonological rule is a formal way of expressing a systematic phonological or morphophonological process or diachronic sound change in language. Phonological rules are commonly used in generative phonology as a notation to capture sound-related operations and computations the human brain performs when producing or comprehending spoken language. They may use phonetic notation or distinctive features or both.
John Goldsmith (1995) defines phonological rules as mappings between two different levels of sounds representation—in this case, the abstract or underlying level and the surface level—and Bruce Hayes (2009) describes them as "generalizations" about the different ways a sound can be pronounced in different environments. That is to say, phonological rules describe how a speaker goes from the abstract representation stored in their brain, to the actual sound they articulate when they speak. In general, phonological rules start with the underlying representation of a sound (the phoneme that is stored in the speaker's mind) and yield the final surface form, or what the speaker actually pronounces. When an underlying form has multiple surface forms, this is often referred to as allophony. For example, the English plural -s may be pronounced as [s] (in "cats"), [z] (in "cabs"), or as [?z] (in "buses"); these forms are all theorized to be stored mentally as the same -s, but the surface pronunciations are derived through a phonological rule.
In most dialects of American English, speakers have a process known as intervocalic alveolar flapping that changes the consonants /t/ and /d/ into a quick flap consonant ([?] in words such as "butter" (['b]) and "notable" (['nobl]).[note 1] The stop consonants /t/ and /d/ only become a flap in between two vowels, where the first vowel is stressed and the second is stressless. It is common to represent phonological rules using formal rewrite rules in the most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as
The rule given above for intervocalic alveolar flapping describes what sound is changed, what the sound changes to, and where the change happens (in other words, what the environment is that triggers the change). The illustration below presents the same rule, with each of its parts labelled and described.
Taken together and read from left to right, this notation of the rule for intervocalic alveolar flapping states that any alveolar stop consonant (/t/ or /d/) becomes a tap ([?]) in the environment where it is preceded by a stressed vowel and followed by an unstressed one.
Phonological rules are often written using distinctive features, which are (supposedly[note 3]) natural characteristics that describe the acoustic and articulatory makeup of a sound; by selecting a particular bundle, or "matrix," of features, it is possible to represent a group of sounds that form a natural class and pattern together in phonological rules. For example, in the rule above, rather than writing /t/ and /d/ separately, phonologists may write the features that they have in common, thus capturing the whole set of sounds that are stop consonants and are pronounced by placing the tongue against the alveolar ridge. In the most commonly used feature system, the features to represent these sounds would be [+delayed release, +anterior, -distributed], which describe the manner of articulation and the position and shape of the tongue when pronouncing these two sounds. But rules are not always written using features; in some cases, especially when the rule applies only to a single sound, rules are written using the symbols of the International Phonetic Alphabet.
Hayes (2009) lists the following characteristics that all phonological rules have in common:
Phonological rules can be roughly divided into four types: