Keywords

1 Syntagmatic Compositionality

At the phrasal/sentential level, linguistic structures are mostly compositional in their semantics: the content of a complex structure [X Y Z] is determined by the content of Y and Z and by the structure [X Y Z] itself. One must qualify this assertion because some expressions have semantic properties that are not directly determined by their superficial syntactic structure. For instance, the sentence At least one student read every book has a quantifier scope ambiguity that does not correspond to any ambiguity in its superficial constituent structure; to account for this ambiguity, one must assume that a sentence’s semantics is not determined by its superficial constituent structure, but depends on the postulation of covert quantifier raising (May 1985), a Cooper-style storage mechanism (Cooper 1983) or a Montague-style rule for “quantifying in” (Montague 1973). Still, this is one of a comparatively small number of well-delineated exceptions to the general pattern of sentential semantics, which is overwhelmingly compositional.

Given this fact, a natural assumption is that the semantics of individual word forms is itself compositional. Consider, for example, the Latin verb form laudābant ‘they were praising’, which might be assumed to have the constituent structure in Fig. 1. This structure seemingly affords a compositional account of the word form’s content, with each affix augmenting the content of the basic stem laudā-: the stem could begin with the denotation in (1a), which the successive suffixation of -bā and -nt would convert to (1b) then to (1c). Word forms such as laudābant present no obvious obstacle to assuming that morphological structure is semantically compositional. But many other word forms do.

Fig. 1
figure 1

Latin laudābant ‘they were praising’

Full size image

(1)

a.

laudā-

→ laudā-′ = λy . λx . x praises y

 

b.

laudā- + -bā

→ laudābā-′ = λy . λx . Past(ˆ[Imperfective(^[laudā-′(y)(x)])])

 

c.

laudābā- + -nt

→ λy . λZ ⊆ {z : z a 3rd-person referent} . Z ⊆ {z : laudābā-′(y)(z)}

Consider, for example, the partial paradigm of the Old English verb stelan ‘steal’ in Table 1. In this paradigm, the first-person singular present indicative form stele is identical to the singular present subjunctive form; by contrast, it is the second-person singular past indicative form stǣle that is identical to the singular past subjunctive form. Nothing in the morphological structure of either form entails that stele must be first-person singular if it is indicative but that stǣle must be second-person singular if it is indicative.

Table 1 Indicative and subjunctive forms of Old English stelan ‘steal’
Full size table

Consider, likewise, the Latin verb form capiēmus ‘we will be taking’. This is the first-person plural imperfective future indicative active form of capere ‘take’ (stem capi-), but there is no way to arrive at precisely this content in a compositional way. As an expression of first-person plural agreement, -mus appears

  • in both aspects (imperfective and perfective),

  • in all three tenses (past, present and future),

  • in the indicative and subjunctive moods, and

  • in the active and passive voices.

In the imperfective, -ē appears

  • in the future and past tenses,

  • in the indicative and subjunctive moods, and

  • in the active and passive voices.

Thus, the morphological structure of capiēmus underdetermines its content.Footnote 1 Even if one assumes that Latin verb forms are by default indicative and active, it is not obvious from its structure why capiēmus must be a future-tense form; it has no overt mark of the future tense, and the future cannot be seen as the default tense (since otherwise, capimus ‘we are taking’ should have a future- rather than present-tense interpretation).

Evidence of this sort makes it necessary to reappraise the notion of compositionality. In the syntactic domain, compositionality is a property of syntagmatic combinations: when two syntactic constituents combine in a particular way, their content combines in a particular way to determine that of the resulting combination. While complex word forms sometimes appear to exhibit this same property, they often fail to do so. Yet, word forms do seem to exhibit compositionality of a different kind.

2 An Alternative: Paradigmatic Compositionality

Paradigm-based approaches to inflectional morphology afford a different, paradigmatic conception of compositionality. In approaches of this sort, the inflectional paradigm of a lexeme L is a set of cells, where

  • each cell is the pairing 〈L, σ〉 of L with a complete morphosyntactic property set σ for which L is inflectable, and

  • each cell is realized by a word form either by stipulation or in accordance with a system of morphological rules.

In an approach of this sort, we may say that a word form is paradigmatically compositional if and only if its denotation conforms to the conventional semantics for the paradigm cell that it realizes.

Consider again the verb form laudābant. This verb form realizes cell (2a) in the paradigm of laudāre, and it is paradigmatically compositional because its denotation (2b) conforms to the conventional semantics for cell (2c) in (2d).

(2)

a.

〈laudāre, {3 plural past imperfective indicative active}〉

 

b.

Denotation of (a): λy . λZ ⊆ {z : z a 3rd-person referent} . Z ⊆ {z : laudābā-′(y)(z)}

 

c.

〈L, {3 plural past imperfective indicative active}〉

 

d.

Where lexeme L has denotation L′, cell (c) in L’s paradigm has the denotation

  

  λy . λZ ⊆ {z : z a 3rd-person referent} . Z ⊆ {z : Past(ˆ[Imperfective(^[L′(y)(z)])])}.

Even syncretic word forms may be compositional in this sense: the difference in content between 1sg present indicative stele and singular present subjunctive stele follows from the fact that they realize distinct cells in the paradigm of stelan:

(3)

a.

〈stelan, {1 sg present indicative}〉

  

Denotation: λy . λx ∈ {z : z a 1st-person referent} . x steals y

 

b.

〈stelan, {singular present subjunctive}〉

  

Denotation: λy . λx . ^[x steals y]

Similarly, the content of capiēmus ‘we will be taking’ follows from the fact that it realizes the cell in (4).

(4)

〈capere, {1 pl future imperfective active indicative}〉

 

Denotation:

 

   λy . λZ ⊆ {z : z a 1st-person referent} . Z ⊆ {z : Future(ˆ[Imperfective(ˆ[z takes y])])}

Though my concern here is with the role of paradigms in the semantic composition of inflected forms, I think that it is reasonable to suppose that the semantics of derived lexemes is also determined, at least in part, by their position in “derivational paradigms”; indeed, the rich theory of lexical semantics developed by Lieber (2004: esp. 37–43) involves a paradigmatic dimension of this kind.

3 The Dual Role of Cells in Paradigm-Based Theories of Morphology

The paradigmatic notion of compositionality presumes that a paradigm cell determines the semantic interpretation of the word form that realizes it. In inferential-realizational theories of inflectional morphology, a paradigm’s cells have another function—that of determining the morphology of the word forms that realize them. Combining these ideas, one might pursue the hypothesis that paradigm cells are the interface of inflectional morphology with semantics; according to this cell interface model, a paradigm’s cells have a dual role, being mapped on one hand to semantic representations and on the other hand to inflectional realizations, as in Fig. 2.

Fig. 2
figure 2

The nexus of semantic interpretation and inflectional realization in the cell interface model

Full size image

One potential objection to the cell interface model is that it does not seem reconcilable with the semantic scope of certain properties that are expressed inflectionally. For instance, the assumption that tense has scope over the entire sentence in (5) is not obviously consistent with the assumption that the past-tense operator enters into the sentence’s semantic composition as part of the denotation of deciphered. As an alternative, one might assume that in the semantic composition of a finite clause, tense composes with (and has scope over) the tense-neutral proposition expressed by that clause. On this view, a verb’s present and past verb forms (for example) would not differ in denotation, but only in their distribution, the former appearing in present-tense clauses, the latter in past-tense clauses. If this conclusion were valid, it would cast doubt on the claim that the verb forms deciphers and deciphered differ in their semantics because they occupy distinct cells in the paradigm of decipher (i.e. the claim that they are paradigmatically compositional).

(5)

Champollion deciphered the text.

This objection is flawed because it takes no account of the fact that the semantics of tense has three distinct components. In the logical representation of (5) in (6), past tense has a quantificational component (existential quantification over times), a temporal component (quantification is over members of the set of past times) and a situative component (quantification is over times at which Champollion deciphers the text). There is no obstacle to assuming that the denotation of the past-tense verb form deciphered includes the temporal and situative components of its past tense, as in (7). The temporal variable t that deciphered introduces may be bound by a quantifier at the clausal level (as in John never deciphered anything); but it may likewise remain free, as a case of temporal deixis (Partee 1973).

(6)

∃t[PAST(t) & AT(t, [Champollion deciphers the text])]

(7)

Denotation of deciphered : λyλx[PAST(t) & AT(t, [x deciphers y])]

An apparent objection to the denotation in (7) is that it fails to account for the fact that the past tense of deciphered can take scope over a quantified subject: sentence (8) can seemingly have the denotation in (9), which can be true even if the decipherer is no longer thirty years old, no longer in Grenoble, or no longer alive; yet this denotation cannot obviously be composed from (7).

(8)

A thirty-year-old man living in Grenoble deciphered the text.

(9)

∃t[PAST(t) & AT(t, ∃x[[x is a man, 30, living in Grenoble] & [x deciphers the text]])]

The defect in this reasoning stems from the fact that a quantified NP may have deictic temporal reference even if it contains no tense morphology (Enç 1986). Notwithstanding the fact that sentence (10) is in the present tense, the celebrity to whom it refers was a thirty-year-old living in Grenoble in the early nineteenth century; the logical representation of (10) should therefore be (11), whose unbound temporal variable t 1 has a contextually supplied value two centuries before the present. Correspondingly, the denotation of (8) can be represented as (12), which is fully consistent with the denotation of deciphered in (7).

(10)

That thirty-year-old man living in Grenoble is celebrated as the father of Egyptology.

(11)

(That x)[AT(t 1, x is a man, 30, living in Grenoble)

 

     & ∃t 2[PRESENT(t 2) & AT(t 2, x is celebrated as the father of Egyptology)]]

(12)

∃x[AT(t 1, x is a man, 30, living in Grenoble)

 

      & ∃t 2[PAST(t 2) & AT(t 2, [x deciphers the text]])]

Despite its initial plausibility, the cell interface model entails too tight a connection between semantics and inflectional morphology: in some instances, the morphosyntactic property set that determines a word’s semantic interpretation is apparently distinct from the set that determines its inflectional exponents—that is, the cell that determines a word form’s content cannot always be identified with the cell that determines its inflectional morphology. In the following sections, I discuss evidence from Latin and Kashmiri that demonstrates this point.

4 Latin Counterevidence to the Cell Interface Model

The notion that an inflected word form’s morphological realization is determined by the same set of morphosyntactic properties as its semantic interpretation is in many cases plausible, but many languages provide evidence that it is not always tenable. Latin verb morphology affords evidence of this sort. In their finite paradigms, Latin verbs inflect for person, number, tense, aspect, mood and voice. Table 2 exemplifies some of this inflection with the indicative imperfective part of the paradigm of monēre ‘warn’.

Table 2 Imperfective indicative forms of Latin monēre ‘warn’
Full size table

In this paradigm, the morphology of active forms (e.g. the forms in the left half of Table 2) is clearly distinguished from that of their passive counterparts (e.g. the forms in the right half of Table 2). There is, however, a class of deponent verbs that are distinguished by two special properties: (a) their paradigms lack forms receiving a passive interpretation, and (b) their active forms exhibit precisely the morphology that is ordinarily reserved for passive forms. Thus, the deponent verb verērī ‘fear, revere’ has the imperfective indicative forms in Table 3: these exhibit the same inflectional morphology as the passive forms of monēre, yet their interpretation is active and indeed transitive.Footnote 2

Table 3 Imperfective indicative forms of the Latin deponent verb
Full size table

A deponent verb’s semantics is apparently based on an active property set but its form is apparently based on a passive property set; this is prima facie counterevidence to the premise embodied by the cell interface model, that the same property set serves as the basis both for the semantics and for the inflectional realization of a given word form. I therefore now propose an alternative to the cell interface model.

5 The Paradigm Linkage Model

The paradigm linkage model of the interface of semantic interpretation with inflectional morphology is based on a simple idea: that a lexeme L has two distinct paradigms—one (L’s content paradigm) is the basis for the semantic interpretation and syntactic distribution of L’s word forms, while the other (the form paradigm of L’s stem) is the basis for the inflectional realization of these word forms. A lexeme L’s content paradigm is a set of content cells, each the pairing of L with a morphosyntactic property set with which L may be associated in syntax. By contrast, a stem Z’s form paradigm is a set of form cells, each the pairing of Z with a morphosyntactic property set for which Z is inflectable. In this model, the cell interface architecture exemplified in Fig. 2 is replaced by a framework in which (a) content cells are assigned semantic interpretations, (b) form cells are assigned inflectional realizations, and (c) for any word w, the interface of w’s content with its form is defined by a principle of paradigm linkage that relates w’s content cell to a particular form cell (the content cell’s form correspondent). This new architecture is exemplified in Fig. 3.

Fig. 3
figure 3

Semantic interpretation, paradigm linkage and inflectional realization in Latin

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In the simplest cases, a content cell’s morphosyntactic property set is identical to that of its form correspondent, as in Fig. 3; in such cases, the same property set determines both the interpretation and the inflectional realization of a given word form. But this framework accommodates cases in which a content cell’s property set is not identical to that of its form correspondent—in which a word form’s semantic interpretation and its inflectional realization do not proceed from the same property set. Figure 4 represents a case of this sort.

Fig. 4
figure 4

The semantic interpretation, paradigm linkage and inflectional realization of Latin deponents

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In this example, the content cells (A)–(C) are the basis for the semantic interpretation of three word forms (monēbit ‘s/he will warn’, monēbitur ‘s/he will be warned’, and verēbitur ‘s/he will fear’). Content cells (A) and (C) are alike in that—unlike (B)—they both receive active interpretations. By contrast, the three form cells (a)–(c) are the basis for the inflectional realization of the three word forms; form cells (b) and (c) are alike since—unlike (a)—they are both realized by means of passive morphology. The relation of paradigm linkage (represented by the dotted arrows in Fig. 4) is alike between (A) and (a) and between (B) and (b): in both instances, the content cell’s morphosyntactic property set is the same as that of its form correspondent. The relation between (C) and (c) is different: the content cell (C) has an active property set (accounting for its active interpretation) while the form cell (c) has a passive property set (accounting for its passive morphology).Footnote 3

In this new framework, a language’s morphological component requires (i) rules and principles that determine the morphological realization of each form cell, and (ii) rules and principles that regulate the relation of paradigm linkage that associates a content paradigm’s cells with their form correspondents. My main concern here is with rules of type (ii); I therefore provide only a skeletal summary of my assumptions about rules of type (i), which draw heavily on the work of Matthews 1972, Anderson 1992, Aronoff 1994, and Stump 2001.

I assume that a language’s inflectional morphology centers on the definition of its paradigm function—a function from form cells to their realizations. A language’s paradigm function is defined in terms of blocks of realization rules; in particular, the value PF(〈Z, σ〉) of a paradigm function PF applying to a form cell 〈Z, σ〉 is the result of applying a succession of rule blocks to 〈Z, σ〉. The application of a rule block n to any pairing 〈X, σ〉 of a stem X with a property set σ is the result of applying the most narrowly defined realization rule in n that is applicable to 〈X, σ〉.

Realization rules are of two kinds—rules of exponence and rules of referral. For present purposes, I shall focus on rules of exponence (but see Stump 1993, 2001: 218–230 concerning rules of referral). A rule of exponence introduces an inflectional exponent, and has the schematic form in (13), where X is a metalinguistic variable over stem forms, C is a category of stems, κ is a constraintFootnote 4 on morphosyntactic property sets (Gazdar et al. 1988) and f is a morphological operation. A rule of exponence in this form is applicable to the pairing 〈Z, σ〉 iff Z ∈ C and σ satisfies κ. In that case, the result of applying (13) to 〈Z, σ〉 is 〈f(Z), σ〉.

(13)

X, C, κ → f(X)

The Latin paradigms in Table 2 are defined by clause (14a) in the definition of the Latin paradigm function together with the realization rules in (14b).

(14)

Morphological realization rules for Latin verbs (partial definition)

 

a.

Paradigm function:

PF(〈Z, σ〉) = [iv : [iii : [ii : [i : 〈Z, σ〉]]]]

   

(where [n : 〈Z, σ〉] represents the result of applying to 〈Z, σ〉 the narrowest rule in Block n that is applicable to it)

 

b.

Realization rules

 
  

Block i

X, V, {past imperfective} → Xbā

   

X, V, {future imperfective} → XbI

  

Block ii

X, V, {1 sg} → Xō

   

X, V, {3 sg} → Xt

   

X, V, {1 pl} → Xmus

   

X, V, {2 pl active} → Xtis

   

X, V, {3 pl} → XUnt

  

Block iii

X, V, {2 pl passive} → Xminī

   

X, V, {pass} → XUrI

  

Block iv

X, V, {2 sg} → Xs

  

Sandhi:

 
  

\( \left[\mathrm{vowel}\right]\to \left[\mathrm{short}\right]/\mbox{\_\_}\left\{\begin{array}{c} \left[\mathrm{long}\kern0.5em \mathrm{vowel}\right] \\ r\# \\ t\# \\ \textit{nt} \end{array}\right\}\qquad \begin{array}{l} s \to \emptyset/\mbox{\_\_\_} r\# \\[5pt] U \to \emptyset/{\rm V}\mbox{\_\_\_},\ {\rm elsewhere}\ u \\[5pt] I \to \emptyset/\mbox{\_\_\_}\#,\ {\rm elsewhere}\ i \end{array} \)

The principles that regulate the mapping from paradigm cells to their realizations have been widely investigated. But what about the mapping from content cells to their form correspondents (= the relation of paradigm linkage)? I suggest that this relation involves interacting functions of three kinds.

  • A stem function Stem maps a content cell onto the stem form employed in its realization. In the default case, every cell in a content paradigm is mapped onto the same stem form.

  • One or more property mappings pm 1, …, pm n map each content cell’s morphosyntactic property set onto the property set of its form correspondent. In the default case, a content cell’s property set is identical to that of its form correspondent; that is, the default property mapping is an identity function.

  • A correspondence function Corr determines a content cell’s form correspondent by invoking the appropriate stem function and property mapping. In the default case, a lexeme L has a single stem form Z such that for each content cell 〈L, σ〉, Corr(〈L, σ〉) = 〈Stem(〈L, σ〉), pm(σ)〉 = 〈Z, σ〉.

A guiding assumption in this scheme is that content cells contain no information that is not relevant to the syntax or semantics of a lexeme’s word forms. Thus, the values of a language’s Stem, pm and Corr functions are not accessible to syntax or semantics. Moreover, inflection classes must be seen as classes of stems rather than classes of lexemes; as such, they never condition a word form’s syntax and semantics.

Consider how this scheme might be employed to define the Latin paradigm linkage in Fig. 4. By the partial definition in (15), the Stem function relates the lexemes monēre and verērī to their stems monē- and verē-. The property mapping pm defined in (16) has the effect of converting an active property set into a passive one. According to the definition of Corr in (17), this property mapping is only employed in defining the form correspondents of deponent verbs’ content cells.; otherwise, the form correspondent of a content cell 〈L, σ〉 is the form cell pairing Stem(〈L, σ〉) with σ.

(15)

The Latin Stem function (partial definition)

 

Stem(〈monēre, σ〉) = monē-

[‘warn’]

 

Stem(〈verērī, σ〉) = verē-

[‘fear, revere’]

(16)

The Latin property mapping pm

 

pm(σ:{active}) = [σ\{active}] ∪ {passive};

 

otherwise, pm(σ) = σ.

(17)

The Latin correspondence function Corr

 

If Stem(〈L, σ〉) is deponent, Corr(〈L, σ〉) = 〈Stem(〈L, σ〉), pm(σ)〉;

 

otherwise, Corr(〈L, σ〉) = 〈Stem(〈L, σ〉), σ〉.

This analysis accounts for the pattern of paradigm linkage in Fig. 4. In this Latin example, the morphosyntactic property sets of content cells sometimes differ from those of their form correspondents; nevertheless, the same inventory of property sets appears in both content cells and form cells. There are, however, cases in which a form cell’s property set includes one or more properties whose relevance is purely morphological and which are therefore absent from any content cell’s property set. I now turn to a case of this sort from Kashmiri.

6 Kashmiri Morphomic Tense Inflection

Kashmiri verbs fall into three main conjugations, with transitive verbs in Conjugation 1 and intransitive verbs in Conjugations 2 and 3; these conjugations are not clearly distinguished outside of the preterite tenses. Kashmiri verbs have three preterite tenses: a recent past, an indefinite past, and a remote past. In these tenses, transitive verbs exhibit both subject and object agreement; because this system of agreement presents complications that are orthogonal to our present concerns, our focus here will be on Conjugations 2 and 3.

The differences between these conjugations in the preterite tenses are evident in the paradigms of wup ‘burn inside’ (Conjugation 2) and wuph ‘fly’ (Conjugation 3); these preterite paradigms are presented in Table 4. One striking feature of these paradigms is that the tense morphology is more fully differentiated in masculine forms than in feminine forms: indeed, the feminine forms in Conjugation 2 fail to distinguish the indefinite past from the remote past, and the feminine forms in Conjugation 3 fail to distinguish the recent past from the indefinite past. Close comparison of these paradigms reveals an even more striking fact: the recent past forms in Conjugation 3 are morphologically like the indefinite past forms in Conjugation 2, and the indefinite past forms in Conjugation 3 are morphologically like the remote past forms in Conjugation 2. These correspondences are particularly clear in Table 5, where the two conjugations’ suffixal inflections are isolated.

Table 4 The preterite paradigms of two Kashmiri verbs
Full size table
Table 5 The preterite inflectional suffixes of two Kashmiri conjugations
Full size table

What this means is that from the point of view of content, there are three past tenses in Kashmiri (recent, indefinite and remote); but from the point of view of form, there are four past-tense patterns—(a) that of the recent past in Conjugation 2; (b) that of the recent past in Conjugation 3 and the indefinite past in Conjugation 2; (c) that of the indefinite past in Conjugation 3 and the remote past in Conjugation 2; and (d) that of the remote past in Conjugation 3. Suppose we name the four past-tense patterns ‘a’, ‘b’, ‘c’ and ‘d’ (as in Fig. 5). What is their significance?

Fig. 5
figure 5

The preterite morphomes ‘a’, ‘b’, ‘c’ and ‘d’ in Kashmiri

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The tense properties ‘a’, ‘b’, ‘c’ and ‘d’ are (in the terminology of Aronoff 1994) morphomic. Their significance is purely morphological: each participates in a uniform pattern of inflectional realization, yet none correlates exactly with any of the three past-tense categories of a Kashmiri verb. While a verb’s content cells are distinguished by the properties ‘recent past’, ‘indefinite past’ and ‘remote past’, the form correspondents of these cells are instead distinguished by the properties ‘a’, ‘b’, ‘c’ and ‘d’. Thus, Kashmiri verbs exhibit the pattern of paradigm linkage in Fig. 6.

Fig. 6
figure 6

The semantic interpretation, paradigm linkage and inflectional realization of preterite verb forms in Kashmiri

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Semantic interpretation proceeds from the content cells (A)–(C); (A) and (C) receive indefinite past interpretations, and (B), a remote past interpretation. Inflectional realization proceeds from the form cells (a)–(c); cells (b) and (c) receive the morphology associated with the {past c} morphome, while cell (a) receives the morphology associated with {past b}. The relation of paradigm linkage between (A) and (a) links indefinite past semantics to {past b} morphology; the relation between (B) and (b) links remote past semantics to {past c} morphology; and the relation between (C) and (c) links indefinite past semantics to {past c} morphology. In this way, the semantic parallelism between the indefinite past forms wupyōv ‘he burned inside’ and wuphyāv ‘he flew’ is reconciled with the orthogonal morphological parallelism between the {past c} forms wupyāv ‘he burned inside (long ago)’ and wuphyāv ‘he flew’.

This analysis may be fleshed out as follows. The mapping of a verbal lexeme’s content cells to their form correspondents is effected by the definitions in (18)–(20). By the definition in (18), the Stem function maps all of a verb’s preterite cells to the same stem. By the definition of Corr in (20), Conjugation 2 is associated with the property mapping pm2, which (according to (19)) maps the preterite properties ‘recent’, ‘indefinite’ and ‘remote’ to the morphomes ‘a’, ‘b’ and ‘c’ (respectively); by contrast, Conjugation 3 is associated with the property mapping pm3, which instead maps ‘recent’, ‘indefinite’ and ‘remote’ to the morphomes ‘b’, ‘c’ and ‘d’ (respectively). Finally, the form cells defined by (18)–(20) are realized by means of the rules in (21).

(18)

The Kashmiri Stem function (partial definition)

 

Stem(〈wup, σ〉) = wup

         [‘burn inside’]

 

Stem(〈wuph, σ〉) = wuph

         [‘fly’]

(19)

The Kashmiri property mappings pm2, pm3

 

pm2(σ:{tns:{recent}}) = σ:{tns:{a}}    pm3(σ:{tns:{recent}}) = σ:{tns:{b}}

 

pm2(σ:{tns:{indefinite}}) = σ:{tns:{b}} pm3(σ:{tns:{indefinite}}) = σ:{tns:{c}}

 

pm2(σ:{tns:{remote}}) = σ:{tns:{c}}  pm3(σ:{tns:{remote}}) = σ:{tns:{d}}

 

For other values of σ, pm2(σ) = pm3(σ) = σ.

(20)

The Kashmiri correspondence function Corr (partial definition)

 

If Stem(〈L, σ〉) belongs to Conjugation 2, Corr(〈L, σ〉) = 〈Stem(〈L, σ〉), pm2(σ)〉.

 

If Stem(〈L, σ〉) belongs to Conjugation 3, Corr(〈L, σ〉) = 〈Stem(〈L, σ〉), pm3(σ)〉.

(21)

Morphological realization rules for Kashmiri verbs (partial definition)

 

a.

Paradigm function:

PF(〈Z, σ〉) = [iv : [iii : [ii : [i : 〈Z, σ〉]]]]

 
 

b.

Realization rules

  
  

Block i

  X, V, {tns:{past d}} → Xi

 
  

Block ii

  X, V, {tns:{past a} agr:{sg masc}}

→ Xu

   

  X, V, {tns:{past a} agr:{3 sg masc}}

→ XU

   

  X, V, {tns:{past a} agr:{pl masc}}

→  XI

   

  X, V, {tns:{past a} agr:{sg fem}}

→ XÜ

   

  X, V, {tns:{past a} agr:{pl fem}}

→ Xɛ

   

  X, V, {tns:{past}}

→ Xy

   

  X, V, {tns:{past a}}

→ X

  

Block iii

  X, V, {tns:{past b} agr:{masc sg}}

→ Xō

   

  X, V, {tns:{past b} agr:{masc pl}}

→ Xē

   

  X, V, {tns:{past} agr:{masc}}

→ Xā

   

  X, V, {tns:{past} agr:{fem}}

→ Xēyɛ

   

  X, V, {tns:{past a} agr:{masc/fem}}

→ X

  

Block iv

  X, V, {agr:{1 sg}}

→ Xs

   

  X, V, {agr:{2 sg}}

→ Xkh

   

  X, V, {agr:{2 pl}}

→ Xwa

   

  X, V, {agr:{3 sg masc}}

→ Xv

   

  X, V, {agr:{3 pl masc}}

→ Xy

   

  X, V, {tns:{past a} agr:{3 sg/pl masc}}

→ X 

7 Wider Applications

The notion that the interface of a word’s semantic interpretation with its inflectional realization is mediated by a principle of paradigm linkage affords a new understanding of a number of problematic phenomena. As we have seen (§5), the paradigm linkage model makes it possible to see deponency as a characteristic of content paradigms; specifically, deponency is the characteristic of a content paradigm in which a cell 〈L, σ〉 has a form correspondent 〈X, pm(σ)〉 such that σ and pm(σ) have contrasting properties in one or more inflectional category. In the same way, defectiveness may be seen as the characteristic of any content paradigm containing a cell 〈L, σ〉 that lacks a form correspondent (i.e. that is such that Corr(〈L, σ〉) is undefined); for instance, the defectiveness of the English verbal lexeme used to may be modeled by means of a Corr function such that Corr(〈used to, σ〉) is undefined for various values of σ (e.g. {3 sg present indicative}, {present participle}, and so on).Footnote 5

Syncretism is likewise a characteristic of content paradigms in the paradigm linkage model, namely the characteristic of any content paradigm in which two or more cells have the same form correspondent; that is, L’s content paradigm exhibits syncretism if two of its cells 〈L, σ〉, 〈L, τ〉 are such that Corr(〈L, σ〉) = Corr(〈L, τ〉) = 〈X, ρ〉, for some specific stem X. The value of ρ is σ or τ in cases of directional syncretism, and is some neutralization of the distinction between σ and τ if the syncretism is nondirectional.

While the paradigm linkage model makes it possible to see deponency, defectiveness, and syncretism as properties of individual content paradigms, this model also elucidates certain relations between content paradigms. One such relation is the rather understudied relation of homomorphy—the relation among two or more content paradigms that correspond to a single form paradigm. Given any two corresponding content cells 〈L1, σ〉, 〈L2, σ〉 in a pair of homomorphic content paradigms, Corr(〈L1, σ〉) = Corr(〈L2, σ〉). Some examples of homomorphy in English are (22)–(26). In each of these examples, the (a) verb is distinguished from the (b) verb at the level of content paradigms (and are hence distinguished in syntax and semantics), but not at the level of form paradigms (so that the morphology treats them as the same verb).

(22)

a.

He wears/wore/has worn heavy boots.

 

b.

He wears/wore/has worn away the grass with all his marching.

(23)

a.

She sticks/stuck/has stuck me in the side with her pen.

 

b.

This glue sticks/stuck/has stuck to my fingers.

(24)

a.

He casts/cast/has cast spells on everyone.

 

b.

In every film, she casts/cast/has cast you as a small-time hood.

(25)

a.

She draws/drew/has drawn a new picture.

 

b.

She draws/drew/has drawn the curtain.

(26)

a.

He sews [soz] /sewed [sod] /has sewn [son] on another patch.

 

b.

He will reap what he sows [soz] /sowed [sod] /has sown [son].

8 Summary

Complex inflected forms often fail to exhibit semantic compositionality of the traditional, syntagmatic sort; they do, however, exhibit compositionality of a paradigmatic kind. According to the cell interface model, the same paradigm structure that serves as the basis for the semantic interpretation of a lexeme’s word forms also serves as the basis for their inflectional realization. But certain phenomena reveal that this model of the interface of inflectional morphology and inflectional semantics is too restrictive; in particular, phenomena such as Latin deponency and Kashmiri tense morphomes show that the properties that determine a word form’s semantic interpretation need not be those that determine its inflectional realization. The paradigm linkage model accommodates this fact about the morphology/semantics interface.

The evidence motivating this model reveals the architecture of a language’s inflectional morphology particularly clearly. Although a language’s inflectional morphology is sensitive to many of the same distinctions as the semantic component with which it interfaces, there are distinctions that are relevant to semantic interpretation but not to inflectional realization as well as distinctions to which inflectional realization is sensitive but which have no semantic significance. This mismatch between the content and form of a lexeme’s realizations is unexpected in a framework in which word structure is regulated by the same syntactico-semantic principles as the structure of phrases and sentences; they are, however, precisely what is expected when two autonomous components engage with each other. The principles of paradigm linkage are in this sense on a par with the principles that resolve discrepancies at the interfaces of other grammatical components. Just as a principle of English morphophonology resolves the unpronounceable morphological structure |twεlv-θ| as the pronounceable phonological structure /twεlfθ/, just as a principle of English interpretation resolves the ambiguous syntactic structure in (27) as the unambiguous semantic representations in (28), so the principles of paradigm linkage in Latin, Kashmiri and English resolve the realization of the content cells in (29a)–(31a) through the mediation of the form cells in (29b)–(31b).

(27)

Every kid read at least one book.

(28)

a.

(At least one book y)[(every kid x)[x read y]]

 

b.

(Every kid x)[(at least one book y)[x read y]]

(29)

a.

〈monēre, {3sg future indic active}〉

b.

〈monē, {3sg future indic active}〉

  

〈verērī, {3sg future indic active}〉

 

〈verē, {3sg future indic passive}〉

  

〈monēre, {3sg future indic passive}〉

 

〈monē, {3sg future indic passive}〉

(30)

a.

〈wup, {agr:{3sg masc} tns:{indef past}}〉

b.

〈wup, {agr:{3sg masc} tns:{past b}}〉

  

〈wuph, {agr:{3sg masc} tns:{indef past}}〉

 

〈wuph, {agr:{3sg masc} tns:{past c}}〉

  

〈wup, {agr:{3sg masc} tns:{remote past}}〉

 

〈wup, {agr:{3sg masc} tns:{past c}}〉

(31)

a.

〈stick 1 , {past tense}〉

b.

〈stick, {past}〉

  

〈stick 1 , {past participle}〉

  
  

〈stick 2 , {past tense}〉

  
  

〈stick 2 , {past particple}〉