All changes to the internal structure of phonological segments arise from combinations of rules based on two settheoretic operations: feature deletion by set subtraction and feature insertion by unification. Apparent cases of rules targeting underspecified segments reflect two kinds of vacuous rule application, one due to unification failure and the other due to vacuous unification. Despite this reduction of all segmentinternal changes to two basic mechanisms we can account for a wide variety of patterns, including the reciprocal neutralization and apparent exceptional behavior seen in Hungarian voicing assimilation.
We learn not to worry about purpose, because such worries never lead to the sort of delight we seek.
(Ontological) proliferation is the
But what if our approach is so narrow and reductive as to propose almost nothing about almost nothing? It is perhaps natural that such an anxiety arises from the combination of such a program of abstraction with the substance free approach I adopt (
I propose that the complex problem of modeling phonological phenomena can be fruitfully decomposed, and in this paper I examine only the segmentinternal changes effected by the most basic mappings (‘rules’). I argue that all changes to the internal structure of segments can be reduced to combinations of
In order to appreciate our narrow focus, let’s consider various aspects of a simple alternation, and see how they can be distinguished. The process in Lamba (
In light of all these questions, I focus here on just the narrow topic of
(1)  Assumptions based on previous work  
a.  Segment symbols are abbreviations for 

b.  Segments must be consistent (i.e. they don’t contain +F and –F for any feature).  
c.  Segments need not be complete—segments may lack a specification for some features. Assuming underspecification 

d.  Feature insertion rules involve unification (similar to set union) with a singleton set.  
e.  Feature deletion involves set subtraction and can affect several features at once.  
f.  Greek letter variables, also known as 

g.  Targets and environments of rules refer to natural classes, defined in a manner that slightly updates the traditional conception.  
h.  Rules are functions mapping between phonological representations, and the phonology of a language is a complex function composed of particular rules built from a toolkit of representational and computational primitives. For the most part, the rules developed here can be treated as functions mapping from strings of segments to strings of segments, however, where, e.g., syllable structure is referenced in a rule, mapping between more complex representations will be necessary. 
All of these points will be illustrated and elucidated as we proceed. As mentioned above, rules deleting and inserting full segments, tonal patterns and many other phenomena are not treated in this paper. The enviroments and conditions for processes such as longdistance vowel harmony are also not treated, but the intention is that the accounts of segment internal changes developed here will ultimately be part of a full analysis of such processes.
In this section, I provide more details concerning the list of assumptions given in the previous section. The term Logical Phonology is used here to situate the paper in a body of related work. Logical Phonology is an approach that is consistent with the notion of Substance Free phonology introduced by Hale & Reiss (
The basic toolkit of concepts used in this paper were developed in Bale et al. (
At the next level, we propose two kinds of phonological rules, ones that incorporate set subtraction and ones that incorporate unification. These operations replace the traditional ‘→’ of generative phonology rules. In subtraction rules, strings containing target segments (which are sets) are mapped to strings containing corresponding segments that are the result of subtracting a set of features (the structural change, in traditional terms) from the targets, when the targets appear in the environment specified by the rule. Rules that are built with unification are a bit more complex, since unification, as a mathematical notion, is a ‘partial’ operation, which means that it might not yield an output. When unification, as part of a phonological rule, fails to generate an output, the rule provides a default identity mapping: the rule’s output is identical to its input. In our model every rule applies to every string at the appropriate point in the derivation, although the application may be vacuous in several senses. In contrast to the adoption of standard math at level one, our level two discussion manifests our own version of phonological computation, including, for example, what happens when unification failure occurs as part of rule application.
At the third level, we discuss ‘processes’ in particular languages, such as final devoicing of obstruents or B
It is not unusual to get a
As a first approximation I treat segments as
(2)  Three simplifications  
a.  Not all features that are present are necessarily shown. This is just a matter of typographical convenience.  
b.  An actual feature set in a morpheme’s lexical representation may be associated with a timing slot, and the segment might be thought of as the timing slot combined with the feature set. Since our concern here is the range of segmentinternal changes, we can ignore timing slots, tones, syllable structure, etc., here.  
c.  We abstract away from contour segments like affricates, which potentially have a more complex structure (see 
Point (2a) is important to distinguish from our use of underspecification. The set of features in (3c) corresponds to neither /p/ nor /b/, but to a third possible segment,
(3)  Three labial oral stops  
a.  /p/ = {–V 

b.  /b/ = {+V 

c.  /B/ = {–S 
These segments all fulfill our assumed condition that segments be
Given our treatment of segments as sets of features, natural classes of segments, which are sets of segments, are fundamentally just sets of sets of features. For example, in a language containing the three oral labial stops,
(4)  Set of features that define the natural class containing only 

a.  {–S 
So, the set
(5) 
Because this notation is unwieldy, we make use of traditional square bracket notation to denote classes of segments in the target and environment of rules. The brackets are used to show that natural classes are of a different settheoretic type from the set of features in the structural change of a rule: the latter are sets of (valued) features, whereas the former are sets of sets of valued features, that is, sets of segments. To say it differently, (5) denotes the same natural class as (6), and both are different from the representation of the segment in (3c). They all list the same valued features, but the rest of the notation matters.
To be more precise, in (6), I’ve left implicit the second condition given in (5), the one that requires that a segment be in the inventory of the language in question—just keep in mind that the intensional natural class description in (6) may have the extension {
The treatment of natural classes sketched relies on the superset (or subset) relation. This fails for more complex representations, including ones that do not correspond to just single segments and those that involve
The basic set operations I attribute to phonological rules are
(7)  Examples of set subtraction  
•  { 

•  {+V 
In each of these examples, note that the subtrahend, the set that is being subtracted (the one on the right of the ‘–’ symbol) can contain elements that are not present in the minuend, the set on the left of the operator. Those elements are irrelevant to the outcome of the computation.
The second operation I use is unification, which is related to the familiar operation of set union.
(8)  Unification examples  
•  {+ 

•  {+ 
Because the output of unification may be undefined, it is called a
Our discussion makes use of three abstract segment symbols
(9)  Three abstract segments  
•  ∃! F s.t. 

The two segments differ w.r.t. exactly one feature.  
•  Δ = 

If you take –F from 

•  
The intersection of the two fully specified segments is the underspecified one. This follows from the definition of Δ.  
• 
The symbols
The use of symbols like
I treat phonological rules as functions mapping (in the simple cases considered here) strings of segments to strings of segments. As explained in Bale & Reiss (
(10)  Simple SMD 
The top row of the diagram shows segments that appear in URs, and the bottom row shows segments that occur in SRs. The arrows show the relations between the segments, with vertical arrows (most typically) showing identity mappings (or else the ‘evolution’ of a segment that doesn’t undergo split or merger with another segment). The diagram for (10) represents the very boring fact that underlying /s/ maps to surface [s] and underlying /š/ maps to surface [š].
An SMD for a language with a neutralization rule that merges
(11)  Segment mapping diagram (SMD) for neutralization: 
The diagonal arrow shows, on the one hand, the split of underlying /s/ into [s] and [š], and on the other hand, the partial merger of underlying /s/ and /š/ into [š]. As we will see, more elaborate SMDs can be used to track the derivational history of segments through multiple rules. In such diagrams, there will be intermediate levels between URs and SRs. Section 4 will show how a wide range of attested processes can be reduced to combinations of rules based on set subtraction and unification and described with such SMDs.
Since the focus in this paper is on segment internal changes, I adopt a simplified picture of rule environments. All the rules identify a target segment in input sequences that are defined by reference to at most one preceding and one following segment, or else by such a sequence enhanced by reference to syllable structure position such as O
Phonological processes are sometimes categorized as featurefilling vs. featurechanging. As the names suggest, a featurefilling process might replace sequences containing
Featurefilling rules consist of a natural class description of a target set of segments followed by the unification symbol (in place of the normal arrow symbol ‘→’), followed by the set which is the second argument of the unification operator (the set of valued features with which each member of the target set potentially unifies). For the environment segments, to the right of the slash ‘/’ I use
Developing the model sketched by Bale & Reiss (
(13)  Interpretation of rule (12)  
Rule (12) is the function that maps any finite string of segments 

•  I 

I 

•  O 
Note that the rule syntax makes use of unification, but the interpretation of the rule breaks unification down into normal set union along with the notion of consistency, as discussed above.
Let’s illustrate the application of such a rule by considering how it will affect input sequences containing
(14)  Applying rule (12)  
a.  If the input string is 

b.  If the input string is 

c.  If the input string is 

d.  The effect of the rule on any other sequence, say, 
To reiterate, the application of a phonological rule built from unification can be vacuous for three reasons: either the unification itself is vacuous, as in input
Let’s now look at a rule built with the set subtraction operator. Instead of using the unification symbol in place of the traditional arrow ‘→’, as we did above, this rule uses the set subtraction symbol ‘–’. Part of the motivation for the Logical Phonology approach I adopt is the recognition that phonological rules using ‘→’ actually encode very different basic operations. Our approach does away with such ambiguity and obviates the need for rule diacritics such as ‘featurefilling’ vs. ‘featurechanging’ labels invoked by authors such as McCarthy (
The other aspects of the rule match the example of the unificationbased rule above.
We can now consider the interpretation of this rule built with the subtraction operator.
(16)  Interpretation of rule (15)  
Rule (15) is the function that maps any finite string of segments 

•  I 

•  O 
Let’s illustrate the application of this rule using the same sequences we used for the unification rule above.
(17)  Applying rule (15)  
a.  If the input string is 

b.  If the input string is 

c.  If the input string is 

d.  The effect of the rule on any other sequence, say, 
The rule applies nonvacuously only in case (17c).
We can now see that a unification rule like (12) is sufficient to model a featurefilling process, for example by filling in +V
(18)
A featurefilling process
UR
Unification Rule (12)
—
—
SR
The dashes ‘—’ in this table reflect vacuous rule application. For input
To get a featurechanging process, we need to first apply a subtraction rule like (15) followed by a unification rule. Such a sequence of rules, (15) followed by (12), applied to
(19)
A featurechanging process
UR
Subtraction Rule (15)
—
—
Unification Rule (12)
—
SR
We will see that combining these simple mechanism with judiciously chosen underlying forms and the use of
Unification failure often turns out to allow quite streamlined accounts of phonological processes. We’ll start with a toy example and see more realistic cases later. Suppose a language has a threeway contrast of /p,b,B/, and that /B/ is the only segment underspecified for the feature V
This works, but note that unification of every other consonant in the language aside from /B/ with the set {+V
This also works, but since, by assumption all segments other than /B/, vowels and consonants, are specified for either +V
(22)  Third version of rule voicing /B/ to [b] 
[ ] ⊔ {+V 
As pointed out in Bale et al. (
We may be able to take this a step further. If it is truly the case that only /B/ is underspecified for voicing at this point in the derivation, then there may be no need for a context for the rule (but there may be a need—see below):
(23)  Fourth version of rule voicing /B/ to [b] 
[ ] ⊔ {+V 
This means “unify every segment that is a superset of the empty set with the set {+V
The interpretation of this rule is the following:
(24)  Interpretation of rule (23)  
Rule (23) is the function that maps any finite string of segments 

•  I 

•  O 
Of course, this rule might be ordered at the end of the derivation, after other tokens of underlying /B/ have been assigned a value for V
I have insisted that rules are functions that map any input representation to an output representation. Sometimes an input representation will be mapped to an identical output. This is necessary in order to treat the whole phonology as a composed function. The examples of rule semantics for a unificationbased rule and a subtractionbased rule have been formulated in terms of such functions. However in discussion, it is often convenient to focus on the mapping of target segments from input to output. This expository expedience should not be taken as a rejection of the nature of the rules indicated by the interpretations given above. As shown in Bale & Reiss (
In this section I provide a schematic SMD using the segment variable symbols
The SMD in (11) showing the partial neutralization of /s/ with /š/ did not take into account the discussion in section 3.3 about the twostep analysis of featurechanging processes. In order to reflect this view, a more complete SMD for simple neutralization would have an extra level as in (25).
(25)  Explicit SMD for featurechanging neutralization of 
As this SMD shows, in some environment, a first subtraction rule deletes the valued feature on
However, I will not generally reiterate in the SMDs
(26)  Less explicit SMD for featurechanging neutralization of 
I will also represent distinct rules at the same level in an SMD if there is no way to explicitly order them (as in the discussion of Turkish stops below).
If a language has a sequence of rules just like in the previous case, but without having any underlying tokens of
(27)  Featurechanging allophony 
The only difference from the previous case is that there are no underlying tokens of
For a concrete example of the relationships and mappings manifested in (27), let’s suppose that Modern Greek [x] contains the specification +B
In some cases, it is not possible to choose an underlying form based on elsewherecase reasoning. In other words, it may be clear that
(28)  Featurefilling allophony of 
An example of this situation might be found in the English distribution of laterals. In some English dialects, dark [ɫ] occurs in codas and light [l] occurs in onsets, so both can be derived from a lateral unspecified for one (or more) features. Strictly speaking, the SMD in such a case should have a separate level corresponding to each of the two rules (one for featurefilling in onsets and another in codas), but since it is not possible to determine the mutual ordering of the two rules, we’ll maintain the simple SMD of (28).
If we flip the SMD for featurechanging allophony (27) upside down we get a situation that initially looks implausible. There are two underlying segments, but only a single surface correspondent. This SMD models the logical structure of featurechanging absolute neutralization which potentially corresponds to situations like the harmonically irregular vowels of Hungarian, like the [i:] in
(29)  Featurechanging absolute neutralization of 

•  Rules: A subtraction rule for 
The SMD is just like that of featurechanging neutralization in (26), aside from the lack of an identity mapping for
The next pattern is just like featurefilling allophony (28) but with the addition of
(30)  Threetotwo featurefilling mapping  
•  Rules: Two unification rules—one for Δto 
This structure corresponds to Inkelas and Orgun’s (
(31)  Turkish stops  
a.  Nonalternating voiceless: – V 

[sanat] ‘art’, [sanatlar] ‘artplural’, [sanatɯm] ‘art1sg.poss’  
b.  Nonalternating voiced: +V 

[etyd] ‘etude’, [etydler] ‘etudeplural’, [etydym] ‘etude1sg.poss’  
c.  Alternating: (no specification for V 

[kanat] ‘wing’, [kanatlar] ‘wingplural’, [kanadɯm] ‘wing1sg.poss’ 
For Turkish, we need one featurefilling unification rule to insert +V
In (32) we repeat the logical structure shown in (30) but with the Turkish segments filled in, along with the environments of the two featurefilling rules responsible for the nonidentity mappings.
(32)  Segment mapping (noncrucial rule ordering ignored here) 
As mentioned above, we assume that all rules are ordered in a grammar, but the two rules here cannot be ordered by the analyst.
We now turn to an SMD that has the exact same threetotwo structure of the previous example involving Turkish stops, but where we can make use of a single rule to account for both mappings by introducing
(33)  Three segments mapping to two with 
This SMD models the harmonic alternations of Turkish vowels seen in the plural suffix:
(34)
Turkish plurals
Trigger vowel
S
P
G
Suffix form
[i]
ip
ipler
‘rope’
[ler]
[e]
ek
ekler
‘joint’
[y]
gül
güller
‘rose’
[œ]
öç
öçler
‘revenge’
[ɯ]
kıl
kıllar
‘body hair’
[lar]
[a]
sap
saplar
‘stalk’
[u]
pul
pullar
‘stamp’
[o]
son
sonlar
‘end’
The alternating vowel can be posited to be underlyingly /A/, a nonhigh, nonround vowel, lacking specification for B
(35)  Segment mapping with an 
So, there are two diagonal arrows in (35) but they reflect the mapping of a single rule (36) that uses
(36)  [–H 
Application of this rule to a sequence with fully specified /e/ or /a/ in target position will result in vacuous application, either via vacuous unification or unification failure. If /A/ is the target, the rule will fill in a value for B
The examples of the Turkish stops and vowels just given lead to the consideration of similar patterns involving allophony, rather than neutralization. Note that the analysis of the Turkish stop /D/ is parallel to the syllable structure based analysis of the lateral allophones of English given in section 4.3. It should be possible to have a language like Turkish, but without the underlying
I haven’t yet found such a case based on
(37)  One segment mapping to two with 
If we allow crossfeatural use of
(38)  [+C 
Odden points out that the Tswana surface distribution can be handled by choosing either segment as the underlying form: “There is no evidence to show whether the underlying segment is basically /l/ or /d/ in Tswana, so we would be equally justified in assuming either” a rule that turns /d/ to [l] or a rule that turns /l/ to [d], since “[s]ometimes, a language does not provide enough evidence to allow us to decide which of two (or more) analyses is correct”. Odden is writing here in Chapter 2 of an undergraduate textbook, so he doesn’t mention the third option, suggested here, that neither of the surface forms is identical with the underlying form. It is hard to imagine how allophonic patterns derived from underspecified segments could be excluded in any systematic manner, so the formal approach we have adopted helps us to formulate a topic for empirical exploration—a noncrossfeatural
Another pattern that can be usefully identified using symbols in the logical relationship of
(39)  Schematic reciprocal neutralization 
This generic pattern can be illustrated with separate rules or with a single set of rules using
Hungarian
(40)  Reciprocal neutralization SMD: 
Both /t/ and /d/ surface unchanged in final position, as in
(41)
Reciprocal neutralization in Hungarian
Noun
In N
From N
To N
kuːt
kuːdbɔn
kuːttoːl
kuːtnɔk
‘well’
kaːd
kaːdbɔn
kaːttoːl
kaːdnɔk
‘tub’
byːn
byːnben
byːntøːl
byːnnek
‘crime’
However, /t/ undergoes voicing assimilation to a following [b], or other voiced obstruent, and surfaces as [d], as in [kuːdban]. Similarly, /d/ undergoes voicing assimilation to a following [t], or other voiceless obstruent, and surfaces as [t], as in [kaːttoːl]. As illustrated by [byːntøːl] and [kuːtnɔk], sonorants like /n/ neither assimilate nor trigger assimilation.
First, I posit a feature deletion rule based on set subtraction, as we have seen above:
This rule deletes the voicing value on an obstruent if the following obstruent has a different value.
This rule maps
We can combine the two rules into a single SMD:
(44)  Revised reciprocal neutralization SMD: 
The SMD looks complex, but we have seen all the parts before.
It turns out that there is more to Hungarian voicing assimilation. The consonants written
My goal here is not to delve into the phonetic factors and diachronic factors that may have led to the synchronic behavior of Hungarian
Data illustrating the interaction of
(45)  
a.  Target: 

b.  Nontrigger: 

We see in (45a) that Hungarian
However, if we assume that
The SMD in (46) shows the derivation of /V/ to both [v] and [f] by the same two rules we used in the previous section. Again, the deletion rule (42) applies vacuously, since /V/ has no voicing value. The voicing of the following obstruent is indicated by the environments denoted ‘___p’ vs. ‘___b’. This value is filled onto the segment corresponding to underlying /V/ by rule (43) at this point in the derivation.
(46)  
The behavior of /V/ is formally identical to other featurefilling processes we have seen, such as the behavior of Turkish /A/ in (35).
Note that turning an underlying /V/ into an [f] involves rule (43). The same rule is responsible for turning
Now consider what happens when /V/ is on the right side of a cluster, in the position of a potential trigger for voicing assimilation. A voiceless segment before a
(47)  SMD for 
The two rules account for the outcome of obstruent clusters which do not contain
The system of two rules developed thus far fails to account for a
(48)  [ –S 
However, this rule can be made even more economical if we assume that at the end of the derivation every segment, consonant or vowel, other than the outputs of underlying prevocalic or wordfinal /V/’s has a specification for V
(49)  [ ] ⊔ {+V 
See the discussion around the rule in (22) to confirm that the effect of rule (49) is to unify every segment that is a superset of the empty set (that is, every segment) with the set {+V
Why is
Other approaches to the behavior of
It may be useful to show graphically that in developing an account of Hungarian our model has not gotten any more complicated than what we used to account for the various languages above. In order to present an SMD for Hungarian, we will adjust our interpretation of the symbols
(50)  SMD for ‘normal’ obstruents and /V/ in Hungarian 
The first
Two simple stipulations are needed to extend the analysis of Hungarian to the underlying consonant surfacing as a voiceless glottal fricative [h] in onsets, written
Rule (51) will not delete voicing on /V/ because there is none. It won’t delete voicing on /H/ because the rule specifies that the target must be +C
Since the segment /H/ will not lose its –V
The slightly revised deletion rule (51) is not quite the only change needed to account for clusters containing
(53)  [ ] ⊔ {+C 
In onset position, we can follow the
(54)  [ ] ⊔ {–C 
Let’s (arbitrarily) assume that feature filling for C
(55)  [ ] ⊔ {–C 
Alternatively, we could leave
Recall that the focus of this paper is on changes within segments. In order to illustrate the logic of our set theoretic approach we have made several simplifications. For example, we have only considered clusters of two consonants, but Hungarian has clusters of three consonants, with the rightmost member determining the outcome of the whole cluster, so that it looks like voicing assimilation works iteratively from right to left, e.g.,
Let’s first consider the clusters of fully specified segments, corresponding to the discussion of simplified Hungarian in section 5. The derivations are in (57), using the same abbreviations that I will now explain and use in the subsequent tables.
In the tables below (57)–(60), a dash ‘–’ indicates, as is traditional, an identity mapping from the next cell up in the table, when the structural description of a rule is not met. For example, underlying /tp/ is unchanged by the first rule (51), since the segments do not disagree in voicing. The rule conditions are not met and this is denoted with the endash ‘–’.
In the same column, the row corresponding to the rule (52) that potentially inserts voicing value is marked with ‘vac.’, indicating the vacuous
The next cell down is marked ‘un.fail’ for unification failure. This is the row corresponding to the default rule (49) that fills in +V
(56)  Three kinds of vacuous rule application:  
a.  – : Input string does not match rule structural description, so target segment is unaffected  
b.  vac. : Unification is vacuous, so rule application does not affect target segment  
c.  un.fail : Unification fails because of feature value conflict, so (by definition) input representation is mapped to identical output representation 
I call all three of these situations “vacuous rule application” rather than, for example, saying that the rule does not apply in situation (56a) for reasons discussed in Bale & Reiss (
Here are the derivations for clusters of fully specified segments:
(57)
Derivations for Hungarian fully specified sequences
UR
tp
tb
dp
db
(51) Delete –
–
Db
Dp
–
(52) Insert
db
tp
(49) Fill +V
(53) Fill +C
(55) Fill –C
SR
tp
db
tp
db
Since the examples in (57) involve only fully specified segments after the application of rule (52), the last three rules, which are all fillin rules, can have no effect on their inputs. The situation changes as we consider additional inputs with underspecified segments. Let’s first consider derivations whose inputs contain /V/ as the first segment of an obstruent cluster (/Vp/ and /Vb); the second segment of an obstruent cluster (/tV/ and /dV/); or elsewhere (/V/).
(58)
Derivations for Hungarian sequences with /V/
UR
Vp
Vb
tV
dV
V
(51) Delete –
–
–
–
–
–
(52) Insert
fp
vb
–
–
–
(49) Fill +V
tv
dv
v
(53) Fill +C
(55) Fill –C
SR
fp
vb
tv
dv
v
None of the clusters or the single consonant /V/ meet the conditions for the first rule (51), which looks for a mismatch in voicing values on adjacent obstruents, so we have ‘–’ across the row. However, the feature filling rule (52) in the second row provides underlying /V/ with a voicing value that agrees with the following obstruent, so we get [f] before [p] and [v] before [b].
The next row corresponds to rule (49) which fills in +V
Consider the next row, corresponding to rule (53), which fills in +C
Finally, in the last row, rule (55) ‘tries’ to fill in –C
Now we turn to the derivation of forms with /H/ in the input. We consider /H/ as the first or second member of a cluster between vowels, so in coda or onset position, with the other segment either voiceless or voiced. We also need to consider /H/ on its own, not adjacent to another obstruent, in both onset and coda position.
(59)
Derivations for Hungarian sequences with /H/
UR
Hp
Hb
tH
dH
Hons
Hcod
(51) Delete –
–
–
–
DH
–
–
(52) Insert
tH
–
–
(49) Fill +V
(53) Fill +C
xp
xb
–
x
(55) Fill –C
th
th
h
SR
xp
xb
th
th
h
x
Because rule (51), the first rule, requires that the lefthand member of an input sequence be specified +C
The only nonvacuous application in the next row, for the rule (52) that copies a voicing value from the righthand member of a sequence to the left, is the case where derived [D] becomes [t] before the voiceless /H/.
At this point in the derivation, all segments in this table are specified as either +V
In the next row, rule (53) fills in +C
The next row shows that any remaining /H/ becomes –C
Finally, let’s show derivations for clusters /HV/ and /VH/:
(60)
Derivations for Hungarian sequences /HV/ and /VH/
UR
HV
VH
(51) Delete –
–
–
(52) Insert
–
fH
(49) Fill +V
Hv
(53) Fill +C
xv
(55) Fill –C
fh
SR
xv
fh
For the second column, forms like
The point of the epigraph to this paper “We learn not to worry about purpose, because such worries never lead to the sort of delight we seek” is that this work is the antithesis of that exhorted by Prince & Smolensky (
Instead, the Logical Phonology approach I assume here (developing work such as
Phoneticians, acquisitionists and historical linguists get their thrills, their delight, in various ways that bear on the particularities of the “welter of descriptive complexity” we see in phonological systems—
Recall that combinatorics is our friend: the model proposed is in the spirit of Gallistel & King (
A machine with a very rich store of symbols must have a means of forming them out of a not too numerous store of atomic data. No language in the world has a word for the message, “After the circus, I’m going to the store to get a quart of skim milk.” No system for representing discrete numbers represents 1,342,791 with a single digit or number name. Minimizing the number of atomic data is desirable in any symbol system as it reduces the complexity of the machinery required to distinguish these data. This is why computers use just two atomic data and likely why nucleotide sequences use only four.
The Logical Phonology model derives the commonalities among languages as well as the welter of descriptive complexity, the superficial variety we observe, via combinatoric explosion over a small inventory of elements and operations. The model of innate mechanisms is small, with not much “attributed to genetic information.” In other words, we are aiming to minimize our ontological commitments for UG, and intensionally define a set of possible human languages rich enough to contain the superficial variety we observe. I offer this simple model of segmentinternal changes as a form of effective data compression in the spirit of Chaitin (
I explore an alternative with just one operation, priority union, in Reiss (
We could add an ellipsis “⋯” to each of the following three feature specifications to indicate that the listed features are not the only ones we assume to exist, and are not the only ones we assume to be specified on these segments. For example, let’s suppose that all three of the labial stops contain the specification –L
This probably captures the typically implicit notion of natural class held by most working phonologists, but a survey of texts reveals a surprising amount of inconsistency in the formalization of natural classes and in the view of their role in phonology. For example, Odden (
There are, of course, a whole slew of grammatical approaches based on unification, in phonology, syntax, semantics and discourse analysis. Our version of unification is a simple version of the others because we are working only with sets. When dealing with treelike representations, unification cannot be defined in terms of set union, although the relevant intuitions are similar.
Suppose you want to define a complex function
In other work (
The use of set substraction in phonological rules appears to allow the second argument to contain more than one element—there is no restriction to singleton sets (
This condition, the absence of an elsewhere case, might be too strict. Consider the alternating nasal segment appearing at the end of certain prefixes in Malay, such as [mem, men, meŋ]. These alternants are distributed according to the place of articulation of the root initial segment. Simplifying a bit, [mem] occurs before labial obstruents, [men] occurs before coronal obstruents, and [meŋ] occurs before velar obstruents and before vowels. It is an open question whether the velar nasal before vowels is a direct reflex of the underlying segment, thus, an elsewhere form, or else the result of a set of default, feature fillin rules.
To be clear, I am not arguing here for the crossfeatural use of
The analysis in this section and the next builds on work with Alëna Aksënova and Maxime Papillon. Hungarian forms are given in orthographic or IPA representation, or both. In underlying forms, suffix vowel harmony variants are given with their surface vowel, since the present discussion is concerned only with consonant interactions.
It is tempting to further simplify the rule by deleting the voicing value of any preobstruent obstruent, irrespective of the value on the following obstruent, leading to a Duke of York gambit in cases where the two had the same value for voicing to begin with. However, we cannot state such a deletion rule, because we don’t use existential
Note that the rule does not need to ‘know’ whether the righthand obstruent indeed differs in its voicing value from the target to its left. Consider the input
A reviewer asks whether breaking down featurechanging into two steps is like failing to unify the treatment of Russian voicing assimilation, as discussed in Morris Halle’s (
The squiggly arrow ‘⟿’ should be read as ‘leads to’, meaning that the form on the lefthand side, which may be either a UR or a subsequent form in the derivation, comes out via the application of one or more rules as the form on the righthand side, which is a later stage of the derivation, and is potentially the SR. The negated form ‘⟿̸’ implies that no subsequence (including the full sequence) of the rules maps the representation on the lefthand side to the one on the righthand side.
For some Hungarian speakers,
See Siptár & Törkenczy (
This analysis follows Siptár & Törkenczy (
Note again that I am not going to formulate rules for the velar vs. glottal distinction between [x] and [h].
See Siptár & Törkenczy (
I am grateful to Maxime Papillon, Alan Bale, Marjorie Leduc, David TaChun Shen, Armel Jolin, Veno Volenec, Rim Dabbous, Alëna Aksënova, Fatemeh Mousavi and Hisako Noguchi for discussion and corrections of the paper itself, and also for playing a role in developing many of the ideas here over several years. Péter Siptár deserves special recognition as a pure scientific soul who generously advised me on the data, analysis and exposition of an account of Hungarian at odds with his own. I also thank the three anonymous
The author has no competing interests to declare.