# Factorial Typology--determining implicational universals?

For the implicational universal "if a language has voiced obstruents, then it must have voiceless obstruents," what would I have to observe from tableaux to verify its validity? The three main constraints of the tableux are Voiced Obstruents Prohibition, *Voiced Coda, and ID-IO(Voice). Thanks in advance!

FT refers to what can arise, given all possible orderings of constraints. Each ordering defines a language. Since the set of constraints is rather large, conventionally one focuses on the constraints of interest, by excluding any that don't seem relevant (e.g. *Round which prohibits round sound – not relevant to the issue at hand). Also in testing the implications of an ordering, you have to test it against all linguistically-possible inputs, for example /pa, p'a, ba, pʰa, ɓa, mpa, bʰa, ma/ and so on, even if some of those segments don't exist in the language.

If you have #1 = *Voiced-Obst (a standard stipulation) and #2 = ID-IO voice (also standard), there are only two orders, 1,2 and 2,1. the relevant candidate subset is the product of any input combined with any output, e.g. {pa, p'a}, {pa, pa}, {pa, ba}, {pa, ma}, {ba, pʰa}, {ba, ba}, {p'a, p'a}, {p'a, ba}, {p'a, pa} and so on, where the first string is the input the the second is the proposed output.

In the grammar where 2 > 1 (the faithfulness constraint is dominant), and since there are, for the sake of discussion, no other constraints, the winning candidates will be {pa, pa}, {ma, ma}, {ba, ba}, {p'a, p'a}, {ɓa, ɓa} and so on. When 1 > 2, the winners are {pa, pa}, {ma, ma}, {ba, pa}, {p'a, p'a}, {ɓa, p'a}: any voiced obstruent must be eliminated. Of course there are other constraints, so you ultimately have to throw in those constraints. For example, there would be a constraint *CG which prohibits glottalized consonants like implosives and ejectives, so if the language in question has no implosives or ejectives, the markedness constraint *CG would have to dominate the faithfulness constraint ID-IO(CG).

An implicational universal, under OT, is the result of all possible orderings of constraints yielding a particular fact pattern, such as that if a language has voiced obstruents, it also has voiceless obstruents. In order for the method to work, you also have to stipulate the non-existence of certain constraints, for example *Voiceless-Obstruent. If there were such a constraint, then ordering *Voiceless-Obstruent first would mean that all obstruents have to be voiced.

As for tableaux, you would create a set of meta-tableaux which contain just the segment of interest (not even the vowel) and just the constraints of interest, in both orders. The inputs of interest include (in the case of an IO constraint plus a markedness constraint) those with the prohibited value and those with the allowed value. If given all inputs and all ordering of those constraint, the voiced segment is not ever pointed at, you've derived the implicational universal.

As far as I can see, *Vioced-Coda is irrelevant, except by way of explaining how a language could exist with final devoicing, but that is a separate complication.