TABLE 2.

Some implicational laws observed in phonological acquisition and treatment, with examples of complex treatment targets for the associated errors.

Hierarchical properties of sound systems	Observed implicational relationships	Acquisition evidence	Examples of complex treatment targetsa
Phonetic inventory	A stridency and/or laterality distinction implies the phonetic occurrence of a liquid, which implies a fricative and/or affricate, which implies a voice distinction among cognate stops, which implies a nasal and glide.b	Tyler & Figurski, 1994	/s/ in contrast to /ɵ/
			/z/ in contrast to /ð/
			/r/ in contrast to /l/
Phonemic inventory	Consonants imply vowels.	Robb et al., 1999	Consonant excluded from the child’s phonemic inventory
	Affricates imply fricatives.	Dinnsen et al., 1992	/tʃ dʒ/
	Fricatives imply stops.	Dinnsen & Elbert, 1984	/f v ɵ ð s z ʃ ʒ/
	Voiced obstruents (i.e., stops, fricatives, affricates) imply voiceless obstruents.	McReynolds & Jetzke, 1986	/b d g/
			/v ð z ʒ/
			/dʒ/
	Liquids imply nasals.	Gierut et al., 1994	/l r/
	Velars imply coronals.	Stoel-Gammon, 1996	/k g/
Distributional properties	Fricatives in initial position imply fricatives in final position.	Ferguson, 1977	Word-initial /f v ɵ ð s z ʃ ʒ/
	Stops in final position imply stops in initial position.	Dinnsen, 1996	Word-final /p b t d k g/
	Word-initial /r/ implies post-vocalic /r/.	Smit, 1993a	Word-initial /r/
Syllable structure	Clusters imply singletons.	Gierut & Champion, 2001	Cluster, with exception of s+obstruent stop sequencesc
	Clusters imply affricates.	Gierut & O’Connor, 2002	Clusterc
	Clusters with a small sonority difference imply clusters with a greater difference.	Gierut, 1999	/fl- fr- ɵr- ʃr-/
	Fricative+Liquid clusters imply Stop+Liquid clusters.	Elbert et al., 1984	/fl- fr- ɵr- ʃr-/
	Liquid onset clusters imply a liquid in coda position.	Baertsch, 2002; Fikkert, 1994	/pl- pr- bl- br- tr- dr- kl- kr- gl- gr-/
			/fl- fr- ɵr- ʃr-/
Phonological processes	Stopping (e.g., [b] for /v/) implies liquid gliding (e.g., [w] for /r/).d	Dinnsen & O’Connor, 2001	/w/ in contrast to /r/ to eliminate liquid gliding
	Manner assimilation (e.g., [nʌn] “won”) implies liquid gliding (e.g., [w] for /r/).d	Dinnsen & O’Connor, 2001	/w/ in contrast to /r/ to eliminate liquid gliding
	Spirantization (e.g., [s] for /t/) implies place assimilation (e.g., [gɔg] “dog”).d	Dinnsen & O’Connor, 2001	/t d/ in contrast to /k g/ to eliminate place assimilation
	Progressive place assimilation (e.g., [bop] “boat”) implies regressive place assimilation (e.g., [gɔg] “dog”).d	Stoel-Gammon, 1996	Word-initial /t d/ in contrast to /k g/ to eliminate regressive place assimilation
	Velar fronting word-finally implies velar fronting word-initially.d	Morrisette et al., 2003	Word-initial /t d/ in contrast to /k g/ to eliminate velar fronting
	The absence of a voice contrast in final position implies the absence of a voice contrast in initial position.d,e	Dinnsen et al., 2001	Word-initial voiced obstruent in contrast to voiceless obstruent to eliminate devoicing
	Errors of weak syllable deletion in syllables beginning with an obstruent imply like errors in syllables beginning with a sonorant.d	Kehoe & Stoel-Gammon, 1997	Multisyllabic words containing unstressed syllables beginning with a sonorant (e.g., “ telephone,” “dinosaur”) to eliminate weak syllable deletion

^aAny one of the examples in the corresponding cell represents a complex treatment target.

^bThis is a relative markedness relationship that involves a chain of phonetic properties (see Dinnsen, 1992, for details). Phonetic inventories are determined by a two-time occurrence of a sound independent of context and accuracy (Stoel-Gammon, 1985), and distinctions are established by contrasts among phones in the inventory.

^c/sp- st- sk-/ are not true clusters, and therefore they pattern differently in typological markedness, speakers’ psycholinguistic judgments, and children’s learning in treatment. Treatment of these sequences has been experimentally shown to inhibit generalization learning (see Gierut, 1999; Gierut & Champion, 2001).

^dImplicational laws that pertain to phonological processes are formulated to reflect errors. This stands apart from all other implicational laws that are formulated in terms of accuracy and occurrence. Consequently, in laws involving processes, the markedness values are just the reverse, with the latter process being the crucial, more complex error to eliminate in treatment.

^eThis assumes that obstruents are phonotactically permissible in final position.