NACLO 2024 - Problem RFollow the Rules

In R1:

(a) has all double vowels like "really", "soaked", "oasis" replaced with the first vowel; this is rule 4
(b) has all "e" like "eggplant", "fuel", "efficiency" replaced with "a"; this is rule 5 (ignoring "e" before another vowel because "Earthling" remains unchanged)
(c) has all double consonants like "carrot", "trillion", "dollar" replaced with single consonant; this is rule 2
(d) has all final voiced consonants like "bad", "and", "lab" replaced with their voiceless counterparts; this is rule 1
(e) is therefore rule 3: initial "s" replaced with "z".

All this is just to get familiar with the rule notation and mechanics. Now onto real business.

For R2, we just look at the last rule and see what language contains the feature that was generated by that rule. Language A's last change is (17) → ei, so it should contain some "ei" bigrams. Only Portuguese has them. Language C's last change is (23) → dd, so it should contain some "dd" bigrams. Only Sardinian has them. That leaves B as Italian.

A: Portuguese
B: Italian
C: Sardinian

For R3, we can do it part-by-part. First consider Latin to Vulgar Latin. Take all Latin words and apply all the rules we already know.

(I will abbreviate [+Vow] and [+Const] as "V" and "C", but expand them in the final solution.)

Latin	h→∅	m→∅ / _#	(4)→(5) / _t	∅→i / #_sC
focum	focum	focu	focu	focu
bonum	bonum	bonu	bonu	bonu
ruptum	ruptum	ruptu	ruttu	ruttu
caballum	caballum	caballu	cavallu	cavallu
sonāre	sonāre	sonāre	sonāre	sonāre
pulvera	pulvera	pulvera	pulvera	pulvera
nivis	nivis	nivis	nivi	nivi
penna	penna	penna	penna	penna
sinum	sinum	sinu	sinu	sinu
fricāre	fricāre	fricāre	fricāre	fricāre
adoptāre	adoptāre	adoptāre	adottāre	adottāre
virdem	virdem	virde	virde	virde
arēna	arēna	arēna	arēna	arēna
cibus	cibus	cibus	civu	civu
habere	abere	abere	avere	avere
vanum	vanum	vanu	vanu	vanu
siccum	siccum	siccu	siccu	siccu
pilum	pilum	pilu	pilu	pilu
mittere	mittere	mittere	mittere	mittere
vīlla	vīlla	vīlla	vīlla	vīlla
lumbum	lumbum	lumbu	lumbu	lumbu
statum	statum	statu	statu	istatu
spatha	spata	spata	spata	ispata
pira	pira	pira	pira	pira
pullum	pullum	pullu	pullu	pullu
castellum	castellum	castellu	castellu	castellu
marītum	marītum	marītu	marītu	marītu
lūna	lūna	lūna	lūna	lūna

The first rule, (1)→∅ / _#, deletes something at the end. The only thing that got deleted is "s" as in "nivis" and "cibus". Therefore (1) = s.
The second rule, (2)→(3) / V_V, changes something between vowels—likely a consonant. This is b→u, as in cibu→civu and caballu→cavallu. It doesn't change the "b" in "lumbu" or "bonu" because they are not intervocalic.
The third rule, (4)→(5) / _t, changes something before "t". The only remaining change we haven't accounted for is ruptu → ruttu, so (4) = p, (5) = t.

Next, from Vulgar Latin to Italian (because the chain is shorter). Here, we can first back-deduce from e→∅ / #_sC. There are only two words that start with sC; and their Vulgar Latin form both start with "i", so we assume that this "i" changed into "e" which eventually gets dropped. The first rule that says change something into "e" should probably do that job. Indeed, all other "i" changed into "e" as well, such as siccu→secco, not just word initial. So (6) = i.

VL	i→e	(18)→(19) / (20)	e→∅ / #_sC
focu	focu	fuoco	fuoco
bonu	bonu	buono	buono
ruttu	ruttu	rotto	rotto
cavallu	cavallu	cavallo	cavallo
sonāre	sonāre	suonare	suonare
pulvera	pulvera	polvera	polvera
nivi	neve	neve	neve
penna	penna	penna	penna
sinu	senu	seno	seno
fricāre	frecāre	frecare	frecare
adottāre	adottāre	adottare	adottare
virde	verde	verde	verde
arēna	arēna	arena	arena
avere	avere	avere	avere
vanu	vanu	vano	vano
siccu	seccu	secco	secco
pilu	pelu	pelo	pelo
mittere	mettere	mettere	mettere
vīlla	vīlla	villa	villa
lumbu	lumbu	lombo	lombo
istatu	estatu	estato	stato
ispata	espata	espata	spata
pira	pera	pera	pera
pullu	pullu	pollo	pollo
castellu	castellu	castello	castello
marītu	marītu	marito	marito
lūna	lūna	luna	luna

Other than long vowel to short vowel, there's another universal sound change: all "u" become "o", except:

focu → fuoco (not foco)
bonu → buono (not bono)
sonāre → suonare (not sonare)
lūna → luna (not lona)

Because we have "u" sounds that survive (especially "luna"), the rule u→o should come very early, so that later "u" can be reinserted by other rules. Therefore, (7) = u, (8) = o. Once we have this, we can apply the V[+L]→V[-L] rule to get the before/after of the (18)→(19) / (20) change.

Before	After	Before	After
foco	fuoco	vano	vano
bono	buono	secco	secco
rotto	rotto	pelo	pelo
cavallo	cavallo	mettere	mettere
sonare	suonare	villa	villa
polvera	polvera	lombo	lombo
neve	neve	estato	estato
penna	penna	espata	espata
seno	seno	pera	pera
frecare	frecare	pollo	pollo
adottare	adottare	castello	castello
verde	verde	marito	marito
arena	arena	luna	luna
avere	avere

Therefore, this rule only changes "o" to "uo" in "foco", "bono", "sonare", but not "polvera", "lombo", or all word-final "o"s. The rule o→uo / _CV will do this job, although there are many other rules that could also explain the data at hand.

Now we know the three rewrite rules that lead to Western Romance, we can use that as the starting point for deducing Portuguese. The e→∅ / (16) rule deletes some "e"s; the only "e"s that are deleted are the word-final ones such as "frecare" and "adottare". However, the "e" in "verde" or "neve" are not deleted; only those after "r" are. So Therefore (16) = r_ (we don't have cases where "re" is not at the end, so I don't know if we also need # at the end).

WR	(14)→(15)	e→∅ / (16)	(17)→ei
foco	fogo	fogo	fogo
bono	bõo	bõo	bõo
rotto	roto	roto	roto
cavallo	cavalo	cavalo	cavalo
sonare	sõar	sõar	sõar
neve	neve	neve	neve
penna	pena	pena	pena
seno	s(17)o	s(17)o	seio
frecare	fregare	fregar	fregar
adottare	adotare	adotar	adotar
verde	verde	verde	verde
arena	ar(17)a	ar(17)a	areia
cevo	cevo	cevo	cevo
avere	avere	aver	aver
vano	vão	vão	vão
secco	seco	seco	seco
pelo	pelo	pelo	pelo
mettere	metere	meter	meter
villa	vila	vila	vila
lombo	lombo	lombo	lombo
estato	estado	estado	estado
espata	espada	espada	espada
pera	pera	pera	pera
pollo	polo	polo	polo
castello	castelo	castelo	castelo
marito	marido	marido	marido
luna	lũa	lũa	lũa

Skimming the data, there are three changes:

Voiceless stops become voiced stops, such as foco→fogo
Vowels followed by "n" become nasal vowels, such as bono→bõo
Double consonants become single consonants, such as cavallo→cavalo

We just need to devise the environment for each change.

The stop voicing change doesn't change "frecare" into "vrecare", or "espata" into "esbata", so it only applies intervocalicly. It also doesn't make "rotto" become "rodo", so this change has to happen before the consonant deduplication. Therefore, (9) = [+Stop -Voiced], (10) = [+Stop +Voiced], (11) = V_V (since the _V environment is not sufficient for this change)
The Vn→Ṽ rule doesn't change "penna" into "pẽna" or "pẽa", which means that it has to come before consonant deduplication too, and it should be restricted to the environment of pre-vowel, which does match the _V condition given in the problem. Therefore, (12) = Vn, (13) = Ṽ, (14) = C{2}, (15) = C{1}.

Finally, we still need to figure out what (17) is in (17)→ei. Applying all previous rules, we have seno→sẽo, arena→arẽa. Therefore (17) = ẽ. Indeed, we have no instance of ẽ in the final data.

Lastly, from Vulgar Latin to Sardinian.

VL	V[+L]→V[-L]	(21)→(22)	(23)→dd
focu	focu	focu	focu
bonu	bonu	bonu	bonu
ruttu	ruttu	ruttu	ruttu
cavallu	cavallu	caba(23)u	cabaddu
sonāre	sonare	sonare	sonare
pulvera	pulvera	pulbera	pulbera
nivi	nivi	nibi	nibi
sinu	sinu	sinu	sinu
fricāre	fricare	fricare	fricare
virde	virde	birde	birde
arēna	arena	arena	arena
civu	civu	cibu	cibu
avere	avere	abere	abere
siccu	siccu	siccu	siccu
pilu	pilu	pilu	pilu
mittere	mittere	mittere	mittere
vīlla	villa	bi(23)a	bidda
istatu	istatu	istatu	istatu
ispata	ispata	ispata	ispata
pira	pira	pira	pira
pullu	pullu	pu(23)u	puddu
castellu	castellu	caste(23)u	casteddu
lūna	luna	luna	luna

The answer is apparent: (21) = v, (22) = b, (23) = ll.

To recap:

(1) s
(2) b
(3) v
(4) p
(5) t
(6) i
(7) u
(8) o
(9) [+Stop -Voiced]
(10) [+Stop +Voiced]
(11) [+Vow]_[+Vow]
(12) [+Vow]n
(13) [+Vow +Nasal]
(14) [+Const]{2}
(15) [+Const]{1}
(16) r_
(17) ẽ
(18) o
(19) uo
(20) _[+Const][+Vow]
(21) v
(22) b
(23) ll

Finally, rewrite from Latin to Western Romance:

Rule	baculum	vīta	findāre
h→∅	—	—	—
m→∅ / _#	baculu	—	—
s→∅ / _#	—	—	—
b→v / V_V	—	—	—
p→t / _t	—	—	—
∅→i / #_sC	—	—	—
i→e	—	—	fendāre
u→o	bacolo	—	—
V[+L]→V[-L]	—	vita	fendare

Therefore, they become: bacolo, vita, fendare.