323 Notes on Phonemic Theory in Terms of Set Theory

1. This page last updated 7 DE 06 1. Notes on Phonemic Theory Here I will discuss phonemic theory in terms of set theory. A phoneme is a set of allophones which are not contrastive and share a common phonological feature or features. For example [t] and [th]are not contrastive and they form a set containing apical voiceless stops. We may write the name of this with anything we want, but it is strongly advisable to use a symbol that can be associated with the set. Let us select ‘T’ for this set: E.g. T = {[t], [th]} or /T/ = {[t], [th]} It helps if the symbol comes close to the default. T is not complete. The two allophones are members of /T/, but there are at least two more allophones in the set: E. g. /T/ = {[t], [th],[€], [ʔ]} (the penultimate slot is a tap.) When completing exercises, I will expect phonemic notation, not phonetics ones, i.e. = [th] is incorrect for /T/. If a phonetic transcription is wanted, I will explicitly state that. Not that [th] in English is constrained to intervocalic positions after a stressed vowel (relatively standard) and in V _ V _ … Where the first vowel is stressed and the second one unstressed. This position is not common in Canadian dialects; it is an American pronunciation in some dialects. This allophone is much more restricted than [t]. Having the widest distribution, [t] is the default, which may write as ‘#[t]’. “#” is not a phonetic symbol but it simply means that [t] or whatever allophone is the default: E.g. T = {[th], [€], [ʔ], #[t]} 2. Morphophonemes Depending on one’s point of view, /s/ and /z/, for example, could be seen as two distinctive phonemes in all positions. This is the Bloch axiom: “Once a phoneme, 323 Notes on Phonemic Theory in Terms of Set Theory

2. always a phoneme.” Note that [z] belongs to two phonemes: /S/ and /Z/. The same will hold true for [d]: /D/ and /T/. Some now consider this axiom outdated. If no contrast exists between them in a certain position, then they may be members of the same phoneme set. The plays a role in two English paradigms involving [s] and [z]. Traditionally, the phonemic representation for dogs and cats is /dagz/ and /kæts/. The plural marker is /z/ and /s/, respectively. In this position, there can be no contrast between /z/ and /s/. Their phonetic representations are [z] and [s], which can be predicted. Suppose we consider the plural marker ‘s’. If ‘s’ occurs after a voiceless obstruent, then it is realized as [z]. This means that there is a set {[s], [z]}, whose distribution is determined by a preceding voiceless obstruent. What should we name this set? Let us call it /Z/: E.g. /KÆTZ / <--> [khæts]. Here the double ended arrow refers to mapping: the phonemic form is mapped to its phonetic form and vice versa. Where [s] and [z] do contrast, then /S/ is distinctive from /Z/: E.g. [hæwz] vs. [hæwz] = /HÆWS/ vs. /HÆWZ/ (houseN vs. houseV). Note that this contrast is not possible after voiceless obstruents. The set for /Z/ is given: E.g. /Z/ = {[s], #[z]} and /S/ = {#[s]}. [z] is the default since [z] everywhere else (not after a voiceless obstruent): E.g. sofas is /sofəz/ <--> [sówfəz] Mapping refers to the correspondence between one set and another related set. In the above example, /sofəz/ corresponds with [sówfəz]. /sofəz/ is mapped to [sówfəz], and [sówfəz] <--> /sofəz/. It is obvious that the two sets are related. Now can state that the plural morpheme in English is /Z/, and not as /s/, /z/ and /z/ as in traditional analyses. This leads to a state of greater elegance, since at least one awkward stop is removed. It is now possible to state that in terms of this theoretical framework, the sign for the English nominal plural is /Z/. This is one of two allomorphs. I will return to this shortly. 2. Morphophonemic Theory

3. Before we leave /S/, there is another case we must look at. It is well known now that a barred I [ɨ] appears phonetically between fricatives and a word-final [z]: [pʊšɨz]. This is predictable. Suppose we add [ɨz] to /Z/. And now let us put this in a mapping relation: E.g. /Z/ <--> [ɨz]/ ___##, where ## is a word boundary. Or E.g. /Z##/ <--> [ɨz##]. The former is the more traditional way of writing the rule. [ɨ] is not a distinctive phoneme in English. It only occurs in unstressed syllables in certain contexts, different from [ə] in many dialects of English. These two unstressed phones are often viewed as contrastive: E.g. Rosa’s = [rowzəz] and roses = [rowzɨz]. However, this differentiation is predictable. The first contains a stem final schwa [ə], whereas in the latter, [ɨ] is epenthetic: E.g. /ROZə/-/Z/ <--> [rówzəz]. Here, /z/ is adjoined to the stem and is spelled out as [z], as expected. In the latter case, rose = /ROZ/. When it is plural, the affix with the sign /Z/ is adjoined to the stem: E.g. /ROZ-Z/. The first /Z/ <--> [z], whereas the second /z/ <--> [ɨz]. Note that this schema will cause traditionalists either to turn over in their graves or cause them to lose more hair and risk having a stroke. The set /Z/ is now modified to include [ɨz]: E.g. /Z/ = {[ɨz], [s], [#z}]. The contexts for mapping the phoneme /Z/ to its allophones is well known. In a given context, on of the three allophones occurs. I will adopt the filtering or constraint method adopted in Optimality Theory. The first constraint states that sibilants (dental/apical/palatal fricatives and affricates) plus another sibilant cannot occur at the end of a word-form: 2. Morphophonemic Theory

4. Double Sibilant Constraint: *[+Sib][+Sib]##. ‘##’ indicates a word boundary, and ‘*’ an unacceptable string. I will illustrate this with roses. Recall that ‘/Z/ = {[ɨz], [s], #[z}]’. Suppose we select the default allophone [z]: E.g. *[rowzz]. The double word-final sibilant constraint is violated. That leaves two more allophones. If [s] is selected, we get: E.g. *[rowzs]. The same constraint is violated again. And other constraints, as well. That leaves [ɨz]: E.g. [rowzɨz]. The above constraint is not violated. Now consider the plural bats: Suppose the following is selected: E.g. *[bætz]. The above constraint is not violated, but theform is not acceptable. It is well-known that English syllables cannot end two obstruents with opposing signs of voice; that is [t] is voiceless and [z] is voiced. The constraint is: E.g. Opposite Voicing Signs Constraint: *X[αVoice — [-αVoice____ . If [s] is selected, this constraint is not violated as the sign of voice matches: E.g. [bæts]. This constraint blocks word-form strings like *[hîtd] and *[hîdt]. (See the verb hit below.) This constraint blocks a sequence of two phonetic segments each with opposing signs of [Voice] in word final position (actually, this should be syllable final position). The use of the Greek letter alpha ‘α’ has been around for roughly 40 years. It represents either a minus value or a plus value. In a rule or constraint, if ‘α’ means plus in the first form, it must be plus throughout. The placement of a minus sign immediately changes the sign. The in last constraint, if Voice is plus in the first feature, then it must be plus in the second feature. Since it is preceded by a minus sign, then its value is reversed becoming minus. As a consequence, a 2. Morphophonemic Theory

5. voiced and voiceless obstruent cannot occur at the end of a word, and a voiceless obstruent and a voiced one cannot occur at the end of a word. Other constraints will be introduced when needed. The past tense sign for regular English verbs is /D/. The classical English phoneme /d/ contains two allophones: [d] and the flap [€]. Note that [t] and [d] do not contrast when they follow voiceless obstruents: E.g. tacked = [thækt], tagged = thægd/ The phone [t] is added as a member of the phoneme set /D/: E.G. /D/ = {[€], [t], [th], [#d]}. /T/ has no [d] allophone: E.g. /T/ = {[ɾ], [t], [#th]}. If /D/ or /T/ follows an alveolar stop, an epenthetic vowel is inserted (in traditional phonology). alveolars: E.g. sited = [sajɾɨd], sided = [sa:j€ɨd]. The barred-i is predictable. I consider [ɨd] a member of the phoneme set /D/: E. g. /D/ = {[ɨd], [€], [t], [#d]}. Two alveolar stops cannot occur in word-final position: Double Stop Constraint: *[+Stop][+Stop]##. Thus *[sa:jdd], *[sajtd] and *[phɛtd] petted, for example, are not acceptable according the word-final double stop constraint. Note that this constraint is intended to block any sequence of double word-final stops, not just alveolar stops. The flap [€] presents an interesting problem. As an allophone of either /T/ or /D/, it must follow a stressed vowel and in some dialects, a stressed vowel and a consonant and another stressed vowel. The latter occurs in some American dialects, but I haven’t found it in any Canadian dialects, though it can’t be ruled out: E.g. city = [sɪ€i], caddy = [khǽ:€i], oddity = [á:€ɪɾ€], uppity = [ʌ́pɪ€I]. 2. Morphophonemic Theory

6. What is even more interesting flapping can be suppressed in which case [t] or [d] occurs in the appropriate position and aspiration of voiceless stops is not suppressed. In this case the speech rate is slowed down: E.g. city = [sɪthi], caddy = [khǽdi], oddity = [ádɪthi], uppity = [ʌ́phɪthi]: The Flapping Constraint: *{-[‘VɾV] or -[‘VCVɾV]}.1 The Flapping Constraint states that if a flap does not occur between vowels where the first one is stressed or in a second syllable where the vowel of the first one is stressed. The minus sign out side of the bracket states that if what follows inside the bracket is not true, then the constraint applies. If syllable initial [t] is not aspirated and the vowel, then the string fails: The Aspirated Stop Constraint; *$[+Stop, +Voiceless, -Aspirated] [+Vocalic, +Stressed]. E.g. *[táp] ‘top’, but [stáp] ‘stop’. Note these constraints are based on the same phonological principles that you might be familiar with.2 Consider mapping /Sɪ́TI/ ‘city’ to a phonetic realization: E.g. [sɪ́ɾi] or [sɪ́thi] but *[sɪ́ti], because initial [t] must be aspirated before a vowel (the final vowel must have some stress if flapping is suppressed. This could be a dialect constraint). Now consider a past tense form, for example, ‘potted’, stem =/PAT/: E.g. *[phathɨd], aspirated must occur before some degree of stress. *[phathd], two stops cannot occur at the end of a syllable, two stops cannot have opposing signs of voice at the end of a word (syllable) and an aspirated stop cannot occur before a consonant. *[phátt], two stops cannot occur at the end of a syllable. *[phátɾ], a flap must cannot occur at the end of a word, it is not between vowels. *[pháɾt], the same as above. *[pháɾɾ], the same as above. *[phátɨd], no constraints violated. Not all possible realizations of /T/ or /T/ are listed above, but the student should be able to figure out why other phonetic strings do not occur. 2. Morphophonemic Theory

7. The sign of the progressive participle is /iŋ/. There is an alternate sign that occurs in substandard English, which is frequently used: /ɨn/. I will not cover this here. The non-progressive participle is /n/ or /ø/ for strong verbs: E.g. with /n/: thrown, beaten, broken, ridden, written, spoken, hidden, lain, driven, done, gone, flown, been, chosen, slain, shown, shone, seen, … . with /ø/): drunk, sunk, swum, run, sung, hung, rung, flung, … . These are two allomorphs, although their distribution is nearly predictable. /ø/ occurs after a stem with a final nasal or final /k/ plus a nasal. /ɨn/ occurs elsewhere. A phonemic string can be mapped to a phonetic one and vice versa: E.g . /KÆTZ/ <--> [khæts]. /TÆKZ/ <--> [thæks]. We have discussed left to right. What about right to left? This falls in the realm of interpretation. A listener must interpret what a speaker says. Let us select the noun [thæks]. This one is interesting because the noun is ambiguous: it means either tax or tacks. If the argument that a speaker adds all inflected forms to his word-form lexicon (as opposed to his lexeme-based lexicon), then he could recognize both forms as extant words. In that case, he must depend on the context of the utterance to decide which one is the right one. This usually works, but it doesn’t always work. One interpretation leads to /TÆKS/, the other to /TÆK+Z/. It is from here he determines the lexical meaning. The morpheme /Z/ is interpreted as [+Pl] if he knows that /TÆK/ is a noun, or as [-Personal, -Pl] if he knows or has determined that the stem is a verb. Traditionally, a morphophoneme is a set of phonemes that alternate in a given paradigm. Generative Phonology tried to eliminate the level of the bi-unique phoneme. There have been several attempts to resurrect the traditional phoneme. I have attempted to put some of these alternation into a revised phonemic theory which is set oriented. Whether all such alternations can be relegated to this revised theory remains to be seen. 2. Morphophonemic Theory

8. 3. Verb Classes There are four classes of English verbs plus at least two verbs which straddle two of these classes. Each class is a distinct set. The first division is between strong verbs and non-strong verbs [±Strong]. These two classes show more differentiation than the smaller classes. In the strong class (this term is more or less traditional), the past tense word-form is always different from the non-progressive word-form: E.g. swim - swam - swum; run - ran - run; write - wrote - written; see - saw - seen. This class is also characterized by a vowel change in the past tense, an occasional vowel change in the non-progressive participle. Another occasional feature is the allomorph ‘-en’ in the non-progressive participle. The major feature of the non-strong [-Strong] class of verbs is the fact that the past tense forms and the non-progressive are phonologically identical marked with the suffix ‘-ed’: E.g. Type - typed - typed; walk - walked - walked; tame - tamed - tamed. The non-strong verbs can be divided into the weak (regular) verbs and the non-weak verbs. The non-weak verbs show some irregularity. The past tense and non-progressive participles are formed with either ‘-t’ or ‘-d’, forming two subclasses of verbs, the D-stems and the T-stems, named after which suffix is employed. Some of the verbs in in the non-weak verbs show a phonological vowel change: E.g. keep - kept - kept; deal-dealt - dealt; sleep - slept - slept; make - made - made. Stem final consonants are sometimes omitted in the past and non-progressive participle forms: E.g. Make - made - made; have - had - had; A few verbs show this in their orthographic system but not in their phonological sign: E.g. tell - told - told, sell - sold - sold. The following tree shows the four verb classes: 323-Notes on Phonemes and other things.ppt

9. 3. Verb Classes The feature [+Strong] refers to a marked class. The strong verbs are set off from the [-Strong] by having a past tense form that is different from the non-progressive participle. The [-Strong verbs by not distinguishing the sign of the past tense from the non-progressive participle. Of the four classes of verbs, the [+Weak] verbs are those that are regular. Strong verbs tend to have more unpredictable forms that the weaker ones. The weakest set is the class of regular verbs. At this time I have found no way to distinguish the D-class from the T-class using a binary feature system, though the T-class seems to be the marked one, since the other two classes are voiced ‘D’. This will take more contemplation and research. With exception of (recent) borrowings, it is impossible to determine which class a verb belongs to.This information must be listed in the lexicon. A sample of each verb class is given:

10. 3. Verb Classes Note that all verbs that are [+Weak] are [-Strong]. Since this predictable, it not necessary to include this information in the lexical entry. The rationale here is to keep the lexicon as simple as possible containing necessary information that is not predictable. The sign of the [-Weak] and [+Strong] verbs is left blank. In order to fill these cells in, unpredictable phonemic alternations must be discussed. Let us start with SLEEP. This verb shows an alternation of /i/ and /E/ in past tense and non-progressive participle forms. These two form a set, a set of vowels that alternate in the stems of certain verbs. We can write this set as {/i/, /E/}. However, it would is desirable to have a symbol to represent this morphophonemic set. Let us call it {E}. The curly brackets are necessary here because it is necessary to distinguish the phoneme /O/ from the morphophoneme {E}: E.g. E = {/I/, /E/}. Now we write the sign as ‘E’: /SL{E}P/. HOLD contains the alternating set {/O/, /E/. Suppose we call this ‘{O}’. E.g. {O} = {/O/, /E/}. HOLD now has the sign: /H{O}LD/. SWIM shows the alternation of /I/, /æ/, and /ʌ/. Let us represent this set as {ɪ}. One of the problems that we will be encountering is finding a grapheme to represent this set. We will run out of grapheme sooner or later to represent odd morphophonemic sets. {ɪ} is fine here since /I/

11. it represents a recurring set. That is, {î} occurs in some of the strong verbs: E.g. /SW{î, æ, ◊}M/, /DR{î, Æ, ◊}NK/, /S{î, Æ, ◊}NK, {ʃR{î, Æ, ◊}NK}, … 3. Verb Classes Later, it will be necessary to add complements and other required features used in syntax. 4. Morphophonemic Rules Morphophonemic rules in this approach (set theory) are not rules in the sense that take an input, apply a rule to it and get an output: A -> B / ___C, as in the standard approach. It is a selection process. Let’s go back to SL{E}P. When it comes up while determining the word-form, the is a choice to be selected: either /i/ or /E/. In order to do this we must set up a context for the alternate phonemes. /i/ is the default phoneme. All we need do is set up a context for /E/. /E/ occurs when the verb occurs in the past tense, passive voice, or perfect relevance: /slEpt/. The contextual rule is placed in the phonological component, as other verbs contain {E}: keep, kept; dream, dreamt; feel, felt; deal, dealt and so forth. The contextual rule takes the following form: Informal Mapping: Given {E}, select /E/ if the inflectional marker for the verb is [+Past], [-Passive] or [-Progressive]. To illustrate this, I will use the sign cell:

12. 4. Morphophonemic Mapping It is desirable to suggest a symbol for the set {/T/-W, /D/-W , #/D/+W}. The symbol {-S}    ([-Strong]) is proposed for this set.2: {-S}-Substitution: Weak Past Tense Set: {-S} = {/T/-W, /D/-W , #/D/+W}. The above figure is replaced with the abbreviated figure: The morphophonemic set {E} is restated formally: Morphophonemic mapping: {E} <--> {/œ/ / ____X — {-S}, #/I/}. ‘X’ represents a string of phonemes or morphophonemes that occurs before the first occurrence of {-S}. Thus the above figure is now mapped to: <-->

13. {-S} is mapped out in the last figure above. Let us assign a symbol to represent the set containing {[+Past], [+Passive] or [+Perfect]: Minus Strong Verb Class Set: {+D} = {[+Past], [+Passive], [+Perfect]}. [+D] has three signs. {/T/-W} is mapped to the features [-Weak, T]. Now the appropriate set can be determined. The same feature in the verb must agree with it in the suffix: 4. Morphophonemic Mapping <--> In a purely phonemic transcription, the result is /SLœPT/ <--> [slœpt].

14. If /I/ were chosen for /œ/ in SLEEP, the result would be unacceptable: *sleeped. In the present tense, there is no feature [+D] to which /œ/ should be linked. In this case, the default alternant must be /I/, since it has no contextual constraint: sleep, sleeps, and sleeping. Some new subfeatures have been introduced above. The feature [-Weak] marking the non-weak verb classes with the subfeature ‘T’ included. The non-weak stems show the alternation of a final stop and ‘ø’. Because of the proliferation of Single CAP letters to represent morphophonemic sets, I will assign a pair of CAPS to represent it: {TW}. I represents /T/-[Weak]. TW-Substitution: {TW} = {/ø/ / ___ {T, -Weak], #/T/. This can be read as follows: The morphophoneme {TW} is mapped to /ø/ if the verb stem is {T, -Weak}. Otherwise it is mapped to the default /T/. 4. Morphophonemic Mapping ↔ The sign /T/ plays a role in the non-weak phonological alternation. That ‘[-Weak], /T/’ is non-weak indicates that the stem is non-weak and subject to alternations. The final obstruent of a non-weak stem may be omitted phonetically. Alveolars are omitted and there is evidence that final /K/ is omitted. The set does not include labials stops. As long as this is predictable, this information need not be stored in each relevant lexeme, but is subject to the obvious phonemic-phonetic mapping:

15. 4. Morphophonemic Mapping Note that if we adopt the output constraint First, the sign ‘HîT-[+Pass] is mapped to /Hîø/3 because it occurs before {TW}. The constraint barring double alveolar stops at the end of a word blocks spelling {TW} out as /T/

16. ‘/ø/’ is selected because of the constraint barring double alveolar stops at the end of a word. The phoneme selected for the past tense is /T/. Therefore, /HîT/+[+Past] is spelled out as: /Hî{/T/, /ø/}/+ {/T/-W, /D/-W , #/D/+W} <--> /Hî{/T/, /ø/}/+ {/T/-W, /D/-W , #/D/+W} <-->/Hî{/T/, /ø/}/ - /T/} <--> /Hî-T/ <--> [hît]. The next problem is determine each step based on feeding and bleeding which means that extrinsically ordered rules might be omitted. Let us go through SLEEP to become more acquainted with this process. 4. Morphophonemic Mapping The morphophoneme ‘{T}’ here is technically a set containing {/T/, /ø/}. Morphophonemic Mapping: {T} ↔ {/ø/ / ____ - [+Apical, +stop]##}.

17. In the above diagram The final stem consonant is not /T/. Therefore, the stem before the inflectional suffix is {T}. SLEEP is [-Weak] verb and belongs to the T-class. The latter is linked to the morphophonemic sign in the affix. A link is established between the form-feature in SLEEP and {/T/-W}. This member of the set is selected: 4. Morphophonemic Mapping SLEEP-[+Past] can be spelled out: /SLœP-T/. Let us do another one, one with a stem final D: READ inflected for the passive voice. It belongs to the D-class: Referring now to {E}, /ɛ/ must be linked to [-Weak, D]. It succeeds and /œ/ is selected

18. 4. Morphophonemic Mapping It is thus phonemically spelled out as /RœD/, the remaining forms are spelled out phonemically as /RID/, /RIDZ/ and /RIDIñ/. Morpheme boundaries are not part of phonemic representation, although phonemes are conditioned by ‘#’ (clitics and type 2 affix boundaries) and ‘##’ (word boundary).

19. 4. Morphophonemic Mapping E.g. goose, geese; tooth, teeth; foot, feet; mouse, mice. There are two default vowels with /U/, and one with /Ʊ/. It is possible to define a set for the high back rounded vowels. Let {U} represent them: E.g. {U} = {/U/, /Ʊ/}. This idea simply will not work. It makes the grammar unnecessarily complex. That means there is one {/U/, /I/} and another set {/Ʊ/, /I/}. The first one occurs in two lexemes and the latter in just one lexeme. It is better just write the set in the lexical entry for these nouns. The lexical entry for FOOT would be: The lexeme still does not contain enough information to determine in which context /I/ occurs. Obviously, it occurs in the plural: This is still not enough to account for everything. In the plural there is no overt affix: /FIT/. The concept of an empty cell (phoneme) has been introduced earlier: /ø/. H’s proposal of a morphemic operator seems to be ill-thought out. It is difficult to incorporate his proposal into this scheme. Suppose we adopt the null phoneme hypothesis. There are now three allomorphs of the feature [+Pl]:

20. E.g. [+Pl] = {/ø/, /N/, #/Z/} The abbreviation [+Pl] must include a context in order to select the appropriate allomorph: E.g. [+Pl] = {/ø/ /___ [ø-class] nouns, /N/ /___ [N-class nouns, #/Z/} The ø-class of nouns includes all those will empty affixes in the plural (foot/feet), the N-class those with the suffix /N/ (ox, oxen; child, children; brother, brethren). Note that besides ø-class stems, there are ø-class stems that exhibit no morphophonemic change of the stem: deer/deer; sheep/sheep; elk/elk. These nouns have a null affix in the singular and in the plural. This leads to ambiguity: E.g. The deer eats the grass every day and looks at himself in the pool’s reflection. E.g. The deer eat the grass every day and look at themselves in the pool’s reflection. Deer in the first example is interpreted as singular because of the agreement with the verb and as plural in the second example, and the agreement with the anaphor in the second clause. Formally, both forms are /DEER—ø/. The remainder of irregular nouns with overt suffixes are formed similar to the above lexical entry. There are only two irregular adjective stems in the comparative and superlative. The procedure as above applies. Another type of alternation is the voiced alternation of final fricatives: E.g. elf, elves; shelf, shelves; dwarf, dwarves; house, houses; bath, baths; path, paths. There are three morphophonemic sets: {F} = {/V/, #/F/}, {S} = {/Z/, #/S/}, {Ɵ} = {/ð/, # /Ɵ/}. The voiced alternants occur when the function is [+Pl]. There exists another set: The entry for elf is the following: 4. Morphophonemic Mapping

21. E.g.: {FRV} = {/V/, /Ɵ/, /Z/, /Ʒ/}. This is a naturally occurring set in phonology, except not all voiced fricatives alternate with voiceless fricatives. /FRV/ represents the phonemic set of voiced fricatives. ‘FR’ stands for fricative, and ‘V’ stands for voiced. Its complementary set are the voiceless fricatives: E.g. : {FRVL} = {/F/, /ð/, /S/, /ʃ/}.The voicing rule is expressed in the following: Voiced Fricative Mapping for Nouns: {FRV} ↔ {/FRV/ / ____ — [+Pl]##/}, #/FRV/}. Otherwise, the default member applies. The lexical entry for elf and its mapping to its phonemic is now shown: E.g. ELF-[+PL] ↔ /ɛL{F}/-[+Pl] ↔ /ɛLV-[+Pl] ↔ /ɛLV-Z/. 4.2 Irregular Adjectives. Only three inflectional categories exist in English for adjectives: the positive, the comparative, and the superlative. The positive dgree is used in American grammas to mean the unmarked or plain degree in contrast to the comparative and superlative. I’m sure if this term is sued in Canadian grammars. First, they should be categorized by binary features. The feature [+Degree] includes the inflected and the periphrastic forms of the adjectives. The next division is [±Degree-affix]. [+Deg-affix] refers to adjectives and adverbs formed with the suffixes ‘-er’ and ‘-est’: warm, warmer, warmest; fast, faster, fastest (adjective and adverb). [-Deg-affix] refers to adjectives and adverbs for which the forms of the comparative and superlative are formed with the periphrastic forms more and most. At this time I will only cover the forms with the overt affixes as well as the positive degree. The positive degree is always /ø/, when the comparative and superlative forms are overt affixes. When degree category is formed periphrastically, there is no affix, overt or covert. The comparative sign is always /R/, even when the stem is irregular. The superlative is ‘-est’ with one exception: best. The problem is what is the phonemic form of the ending? 4. Morphophonemic Mapping

22. 4. Morphophonemic Mapping At this time it appears to be /ˆST/ (barred-I) ST/. If we assume that the phonemic form for the comparative and superlative stem is /Bîɛ{T}/. Previously, it was claimed that {T} <--> /ø/ before apical stops: Morphophonemic Mapping, ‘{T} ↔ {/ø/ /___ — [-Sonorant] ##, #/T/}. The above mapping rule is now expanded to include obstruents: E.g. {T} ↔ {/ø/ / ____ [-Sonorant] ##, #/T/} . This a noteworthy improvement as the mapping shows the true nature of some stops. In more advanced morphophonology some suffixes and prefixes are classified as type 1 or strong, since they trigger alternations that do not occur with type 2 or weak affixes.

23. The interpretation of a phonetic string occurs when the listener attempts to determine the phonemic string that is mapped with the phonetic string, which the listener hears. For example if a listener hears [t] in English, he will interpret it as /T/; if he hears [a], he will interpret it as /A/, and so forth. However, interpretation is not as easy as the above. Suppose the listener hears [laks]. It is possible that he will interpret it as /LAKS/ = ‘lox’. But he could also interpret it as /LOKZ/, in which case /Z/ can only be interpreted as [+Pl]. The astute listener will interpret it either way, in which case he must make a decision. In isolation, he has nothing to go on. In a context he should be able to make a decision: E.g. ‘He bought two [loks]’. (Here I am focusing on the last word-form.) The key word here for interpretation is some. Some is an indefinite quantifier. If the noun it modifies is a count noun, then the noun must be plural: E.g. Two locks (plural), *two lock. If the word is a mass noun, then the noun must be in the singular: E.g. Some lox, *two loxes, *some loxes. The astute listener will hear [laks] either as locks or lox. The complement of two must be plural. However, locks is a mass noun and cannot occur in the plural. The only possible interpretation is ‘locks’ if it is assumed the speaker is speaking grammatically. Let us do another one. [+Pl] is mapped to /Z/: /BAR/+[+Pl] <--> /BARZ/ (erasing morpheme boundaries). 5. A note on Interpretation

24. Now let us map the phonemic form back its morphological form. Probably the first task is to determine where there is a lexical stem /BARZ/. There is no known lexical item in standard English that would be spelled as barz. Hence, interpreting it as a lexical item fails. Next, other possibilities must be sought out. We can start at the right end or the left end. Let’s start at the right end. /Z/ matches the sign for [+Pl] for nouns, the sign for [-Pers] and [-Pl] for verbs. Going though verbs, the verb bar (BAR) is found: [-Pers], [-Pl] <--> /Z/ (This correspondence can be written in either direction.) Once we have determined that /Z/ has a correspondence, that means it is a separate morpheme: E.g. /BAR-Z/. By the above correspondence mapping, /Z/ <--> [-Pers], [+Pl]. Replace /Z/ with [-Pers], [+Pl]: E.g. /BAR/ — [-Pers], [+Pl]. The sign /BAR/ is part of the lexical entry for BAR: E.g. BAR — [-Pers], [+Pl]. However, we should continue checking the lexicon, because /BAR/ may show somewhere else, which in fact is does. It also occurs in the set of nouns in the lexicon: a bar. The fact that the noun stem BAR has several meanings has no bearing on interpreting /BAR/. There is a correspondence rule for /Z/ in the context of a noun. [+Pl] <--> /Z/. 5. A note on Interpretation

25. 5. A note on Interpretation /BARZ/ <--> /BAR-Z/ <--> /BAR/ — [+PL] <--> BAR — [+PL]. The rules for interpretation are rather complicated. As a person acquires speech, he also learns how to interpret words, phrases, clauses, and sentences. I will terminate this discussion here, leaving interpretation for another course. Go to Course Outline, Go to Chapter 1, Go to Chapter 2, Go to Chapter 4, Go to Chapter 5, Go to Exercise 3