We describe two different strategies for generating the morphology of Latin verbs. First, we hand-code default inheritance hierarchies in the KATR formalism, treating inflectional exponents as markings associated with the application of rules by which complex word forms are deduced from simpler roots or stems. The high degree of similarity among verbs of different conjugation classes allows us to formulate general rules; these general rules are, however, sometimes overridden by conjugation-specific rules. This approach allows linguists to gain an appreciation for the structure of verbs, gives teachers a foundation for organizing lessons in morphology, and provides students a technique for generating forms of any verb. Second, we start with a paradigm chart, then automatically remove common parts and redundant morphosyntactic property sets (columns), combine similar conjugations (rows), and generate the KATR theory that produces a complete table of forms for a set of lexemes. This second approach automatically determines principal parts (for Latin, we verify that there are four), groups inflection classes into super-classes, and builds full paradigm charts.
Two approaches to analyzing the morphology of Latin verbs
Recent research into the nature of morphology has demonstrated the feasibility of two alternative approaches to the definition of a language’s inflectional system. Central to both approaches is the notion of an inflectional paradigm. In general terms, the walk includes cells such as <WALK, {3rd singular present indicative}> and <WALK, {past}>,
whose
realizations are the word forms walks and walked.
Given this notion, one approach to the definition of a language’s inflectional system is the walks is deduced from
the cell <WALK, {3rd singular present indicative}> by means of the rule of -s suffixation, which applies to the root walk of the lexeme WALK to express
the property set {3rd singular present indicative}.
An alternative approach to the definition of a language’s inflectional
system is the hældon
healed (plural)
may be
deduced from the word form hælde
healed (3rd singular)
in accordance
with a general principle that in the inflection of a weak verbal lexeme L, the
realization of <L, {3rd singular past indicative}> and that of <L, {plural
past indicative}> stand in the relation Xde ↔ Xdon.
Despite their differences, both approaches are capable of generating
a language’s inflected forms. We demonstrate this claim for Latin. We
first present a realizational analysis of Latin in the KATR language
This research is part of a larger effort aimed at elucidating the morphological structure of natural languages. In particular, we are interested in identifying the ways in which default-inheritance relations describe a language’s morphology as well as the theoretical relevance of the traditional notion of principal parts.
As we demonstrate below, the realizational approach leads to a Latin KATR
theory that provides a clear picture of the morphology of Latin verbs. Different audiences might find different aspects of it attractive.
linguist can peruse the theory to gain an appreciation for the structure of Indo-European verbs in general and Latin verbs in particular,
with all exceptional cases clearly marked either by morphophonological
diacritics or by rules of sandhi, which are segregated from all the other rules.
teacher of the language can use the theory as a foundation for organizing lessons in morphology.student of the language can suggest verb roots and use the theory
to generate all the appropriate forms, instead of locating the right
paradigm in a book and substituting consonants.
The implicative approach that we demonstrate in this paper has several
benefits.
The purpose of the KATR theory described here is to generate verb forms
for Latin, specifically, the realizations of all combinations of the morphosyntactic properties of voice (active/passive), mood (indicative/subjunctive),
aspect (imperfective/perfective), tense (present/past/future), number (singular/plural), and person (1/2/3). The combinations form a total of 144
morphosyntactic property sets (MPSs). However, Latin has no future subjunctive, reducing the total to 120 MPSs.
Latin verbs consist of a sequence of morphological formatives, arranged
in five slots:
laudō, the stem is laud.issē.ā, and
for the present perfective subjunctive, it is ī.
ō. r for the passive voice.
To keep our discussion short, we omit the imperative and infinitive forms, although our complete KATR theory includes them without difficulty. For those forms that use a participle (such as the perfective passive), we limit ourselves to a single form, the masculine singular.
There are four frequently encountered conjugations, distinguished by
their theme vowel: first (ā: laudāre), second (ē: monēre), third (i: dūcere,
capere), fourth (ī: audīre). The third conjugation has two variants; in one (capere), the theme vowel is more pronounced.
Praise
A theory in KATR is a network of nodes. The network of nodes constituting our verb morphology theory is partially represented in Figure 1. The organizational principle in this network is hierarchical: The tree structure’s terminal nodes represent individual verbal lexemes, and each of the non-terminal nodes in the tree defines default properties shared by the lexemes that it dominates.
Each of the nodes in a theory houses a set of laudāre
praise
by a node:
Praise, has two rules, which we number for discussion purposes only. KATR syntax requires that a node be terminated
by a single period (full stop), which we omit here. Our convention is to
name the node for a lexeme by a capitalized English word (here Praise)
representing its meaning.
Rule 1 says that a query asking for the root of this verb should produce a
four-atom result containing l, a, u, and d. Rule 2 says that all other queries
are to be referred to the VerbA node, which we introduce below.
A <root> or <active indicative perfect present 1 sg>, addressed to a node such as Praise. In our
theory, the atoms in queries generally represent root, themeVowel), perfect, sg) or
A query addressed to a given node is matched against all the rules
housed at that node. A rule Praise, a query <root perfect>
is matched by Rules 1 and 2; a query <themeVowel> is only matched by
Rule 2.
Left-hand sides expressed with <pointed brackets>)
only match if their atoms match an initial substring of the query. Left-hand
sides expressed with {braces}) match if their atoms are all
expressed, in whatever position, in the query. We usually use set notation
for queries based on morphological formatives and morphosyntactic properties, where order is insignificant, but path notation for queries based on
surface forms, where order is significant.
When several rules match, KATR picks the best match, that is, the one
whose left-hand side uses up
the most of the query. This choice embodies Pāṇini’s principle, which entails that if two rules are applicable, the
more restrictive rule applies, to the exclusion of the more general rule. We
sometimes speak of a rule’s
In our case, Rule 2 of Praise only applies when Rule 1 does not apply,
because Rule 1 is always a better match if it applies at all. Rule 2 is called a
KATR generates output based on queries directed to nodes representing individual lexemes. Since these nodes, such as Praise, are not referred to by other nodes, they are called VerbA,
which are called Praise node.
Praise illustrates the strategy we term VerbA and
the nodes to which it, in turn, refers).
We refer to the individual segments of a morphological form by means
of particular atoms:
themeVowel is the vowel usually found after the root of a verb. stemImperfective, stemPerfective, and stemParticiple are the verb stems, usually including the theme vowel, that precede suffixes marking tense, number, person, mood, and aspect.
VerbA Node
We now turn to the VerbA node, to which the Praise node refers.
Praise node, VerbA defers most queries to its parent, in this case the node called Verb, as Rule 5 indicates.
Most of these rules are for provisioning. Rule 1 answers the
themeVowel query. We sometimes address this query to leaf nodes; the Praise node defers it to VerbA, which answers the query.
Rules 2-4 provision the three stems. The quoted path <root> in the
right-hand side directs a new query to the node to which the original query
was first addressed, in our case, Praise, which produces the four atoms
l a u d. The non-quoted path <themeVowel> directs a new query to the
current node, that is, VerbA, resolved by Rule 1. The right-hand side of the
rule in this case is equivalent to l a u d ā. Similarly, the right-hand side of Rule 3 is l a u d ā v, and the right-hand side of Rule 4 is l a u d ā t.
Rule 5 is a default rule, directing its query to the Verb node, with the
atom conj1 prepended to the query. Therefore, queries addressed to Verb contain not only morphosyntactic markers (such as present passive
) but
also informational markers (conj1
).
By way of contrast, we also present the VerbIO node, which applies to i-stem third-conjugation verbs such as facere and capere.
i or an e, depending on surrounding context, during a postprocessing step.
Rule 7 introduces the f a c to the AEE node to convert the a to ē, so the perfective stem of
facere becomes fēc. Here is that lookup node:
letter.
Rule 1 says that any query beginning with a
letter, then the atom a, then any letter, should evaluate to the two letters
surrounding ē instead.
Verb Node
Queries addressed to Praise are generally deferred to its parent, VerbA, which then defers them further to Verb.
$conj34) in the first singular imperfective. This rule is quite specialized, applying, for instance,
to dūcam
I will lead / may I lead.
Without this rule, we would produce dūcēo
I will lead.
Rule 2 indicates that there is no result for a query involving future subjunctive forms; Latin does not have these forms.
Rules 3 and 4 reflect to the Sandhi node as a postprocessing step after
assembling the components of a verb. The rule with the widest applicability, Rule 4, is the default rule. It combines the results of queries directed to the four nodes StemAspect, SuffixTense1, SuffixTense2, and SuffixPersonVoice, along with the marker wordEnd for postprocessing. Rule 3 generates forms for the perfective passive, which involve a participle, an adjectival end, and a specific form of the verb esse, which has its own node ToBe.
The Verb node invokes several auxiliary nodes.
=+= notation preserves all the elements of the
query path, including those otherwise removed by matching the left-hand
side of the rules.
SuffixTense1 node contains most tense information. It ranges
from very specific rules, like Rule 14, to fairly general rules, such as Rule 4,
which is overridden by more specific Rules 5-8.
ā or ī.
r for the passive) precedes the person suffix, as in laudāris
you (sg) are
praised,
whereas the voice suffix usually follows the person suffix, as in
laudāmur
we are praised.
r (Rule 2) but sometimes ur (Rule 3).
m (Rule 1) but
sometimes ō or ī.
I
as in laudābit
he will praise,
but sometimes u, as in laudābunt
they will
praise.
After we assemble the entire verb, we apply language-specific sandhi rules
to account for phonological alterations.
Sandhi works strictly from left to right, dealing
with a few atoms at a time. The first rule removes the wordEnd marker
if that is all that is left. The other rules simplify the beginning of the remaining string of letters and then use angle brackets to direct the modified
string back to the Sandhinode.
Rule 2 is quite general: if no more specific rule applies, it takes a single
letter from the query as output, and directs the remainder of the query
back to Sandhi. Rule 3 converts forms like *dūcimusr to *dūcimur. Rules 4-8 deal with the morphophoneme I, typically converting it to i (Rule 5),
but sometimes converting it to e or removing it entirely. Rules 9-18 deal
with two vowels in a row; typically, the second vowel is retained, and the
first either disappears or shortens. Rules 19 and 20 shorten long vowels
in certain contexts by applying to the Shorten rule, which we omit here.
Finally, Rules 22-24 introduce spelling rules. We include them in under the
rubric of sandhi.
We have been applying KATR to natural-language morphology for several years. In addition to Latin, we have built a complete morphology of
Hebrew verbs
Writing specifications in KATR is not easy. KATR is capable of representing elegant theories, but arriving at those theories requires considerable effort. Early choices color the structure of the resulting theory, and the author must often discard attempts and rethink how to represent the target morphology. The hardest choice is often whether to model a form by introducing a sandhi rule or a formative rule. An example is the -mur suffix that
marks first person plural passive. We choose to model this ending as Desinence node:
r appear due to the SuffixVoice node. In this case, we prefer
not to introduce a special rule in Desinence, partially because it looks so
similar to the existing Rule 4, and therefore seems unparsimonious, and
partially because we hypothesize that historically there really was some
form *-musr that eventually elided the two final consonants.
We start this analysis by presenting a paradigm of word forms for Latin verbs. Table 2 displays a subset of the entire paradigm that covers only the present indicative active forms. The roots of lexemes are abstracted away from this paradigm.
We have expanded the traditional four conjugations into 19 conjugations. They are mostly distinguished by forms not shown here, particularly by the perfect indicative active. For instance, a cIa verb such as iuvāre
help
forms the perfect stem by lengthening the middle vowel, as in iūvī
I helped,
whereas a cIb verb such as laudāre
praise
simply adds āvī to the stem to form the perfect 1 singular. For completeness, we even include conjugation cIIIs for the two exceptional verbs esse
be
and posse
be able.
The line marked CONJ simply lists the morphosyntactic property sets
for our convenience.
The line marked TEMPLATE indicates parts of the chart that are constant
within each column. For instance, the second-person singular is marked
with 1S1Cs. The 1S part means place the first stem here.
We choose to
make the first stem the present stem. Next, 1C means place the first entry in the column here.
Our Latin charts have only a single entry per column
in each row. When an entry is empty, we mark it with ∅. Finally, s means
place the letter
. All Latin verbs follow this strategy for building
the perfect indicative active 2nd person singular forms. s here
Our chart requires that each verb have five stems, possibly identical: present, perfect, supine, present first person, and present past subjunctive. For iuvāre help,
these stems are iuv, iū, iū, iuv, and iuv, respectively. For esse be,
the stems are es, fu, es, s, and es, respectively.
It often happens that a conjugation regularly refers one stem to another. For instance, class cIa refers the fourth and fifth stems to the first; class cIIIs refers the third to first. (For consistency, we always refer stems to earlier-numbered stems.) We represent stem referrals as an addendum to our chart, as in Table 3.
We then represent the lexicon by indicating the conjugation and stems of each verb as another addendum to the chart, as in Table 4.
The final section of the paradigm chart expresses rules of sandhi, as shown in Table 5.
These rules sometimes truly express sandhi, such as the rules for shortening long vowels before a final stop. Others are merely spelling rules, such as converting cs to x. We introduce a few in order to make our paradigm more regular, such as changing sb to r. In many cases, we indicate the situation that led us to introduce the rule by a comment starting with %.
Before analyzing the paradigm, we reduce it to its essence. The first reduction removes identical conjugations. This situation does not arise in Latin, but it does in French, where 71 of the 149 conjugations listed in the Larousse Dictionary are redundant after we present them on our paradigm form, and another 11 are identical except for stem-referral pattern.
The next step is to remove redundant columns (morphosyntactic property sets, or MPSs). For example, although the second and third person verb forms are different in the present indicative active, the columns associated with those forms are identical. The differences are all covered by the template and sandhi rules. Of the 92 MPSs in Latin, there are only 14 unique ones.
The last step is to remove essentially identical columns. Two columns are essentially identical if there is a one-to-one and onto mapping between the exponences (cell contents) found in those columns. For example, the future perfect indicative active 2nd singular MPS is essentially the same as another MPS. Our analysis reduces the chart from 92 MPSs to 9 important ones, which we call distillations.
We call the reduced paradigm chart the essence. The essence does not contain actual exponences; we substitute unique symbols instead. Table 6 presents the essence of the Latin paradigm. An entry like e4_2 means that this distillation is based on the fourth MPS (which happens to be PrIAc1p ) and has the second exponence found in that MPS (which happens to be ē).
Intuitively, a set of principal parts is a minimal subset of MPSs so that if one knows the exponences of those MPSs for a particular verb, one can deduce the verb's conjugation, from which one can deduce all the other MPSs of the verb. The practical utility of principal parts for language pedagogy has long been recognized. Generations of Latin students have learned that each verb in Latin has four principal parts (present indicative active first person singular, active infinitive, perfect indicative active first person singular, perfect passive participle (neuter nominative singular)). If one knows laudō, laudāre, laudāvī, laudātum, one knows enough to place the verb in conjugation 1, from which one can determine the exponences of all the other MPSs by reference to the paradigm chart.
We can define several kinds of principal-part systems
Static: a set of MPSs that applies for all verbs in the chart. Given the exponences of a verb for those MPSs, one can deduce its conjugation. Static principal parts are equivalent to the traditional understanding.Adaptive: a tree of MPSs. Given the exponence of a verb for the MPS at the root of the tree, one can select an appropriate subtree and recurse. The leaves of the tree are conjugations.Dynamic: a set of {MPS, exponence} pairs for each conjugation. If a verb agrees with a set of pairs, it belongs to the associated conjugation.
We have built a program that takes the essence of a paradigm and computes its principal-part systems. For Latin, we find that there are, in fact, four static principal parts, with ten variations, as shown in Table 7. It is a bit surprising that the infinitive does not figure into any of these variations. However, the paradigm from which we calculate this result places the infinitive MPS almost at the end. It turns out that the exponences for the infinitive are identical to the exponences for the imperfect subjunctive active first person singular. For laudō, for instance, both show ā, one using that exponence to form the infinitive laudāre, and the other to form the subjunctive laudārem. In turn the MPS for the imperfect subjunctive active first person singular is essentially identical to the MPS for the present indicative active second person singular. Therefore, the first variation in Table 7 is the traditional set of principal parts.
Our program computes one of the possible trees representing adaptive principal parts, as shown in Figure 2, which also shows a representative verb from each conjugation. Some conjugations can be determined with only two adaptive principal parts. For instance, if the present second person singular form uses ī, then the conjugation is cIa, as in iuvāre
help.
Others require three adaptive principal parts, such as dūcere
lead.
However, no conjugation needs four principal parts. This analysis shows that the most important distinction, the one at the top of the tree, is based on the present indicative active second person singular form, which we note above is essentially the same as the active infinitive form.
We also compute dynamic principal parts. Table 8 displays one set for each conjugation; in general, each conjugation has several variations. This analysis shows that many conjugations can be completely determined by a single principal part. For example, if the perfect indicative active 1 sg form of a verb is -āvī, the verb is in conjugation cIb. Only one conjugation, cIIIc, requires three exponences to determine all its forms.
Computing the adaptive principal parts produces one way to see the interrelation of the conjugations, as shown in Figure 2. We can compute the interrelation in a more direct way by using an algorithm based on Huffman encoding
This algorithm leads to multiple possible analyses, because we may be able to choose among several minimum pairs. Each analysis is a taxonomic tree. Figure 3 shows one tree that our program produces. The entries like e13_2 refer to the essence of Figure 3. They show in what way each node in the tree is distinguished from its siblings. For instance, conjugations cIIb and cIIe are distinguished by e37, which is perfect indicative active first person singular.
Figure 3 verifies that the usual conjugation nomenclature is reasonable. All three cI conjugations are close to each other, although cIa is a slight outlier. Conjugations cIIIa−d are very close to each other, but cIIIf (ferre) is significantly farther away. Conjugation cIIIs (esse) is still farther. Strangely, conjugation cIIIe (capere) is grouped with the cIV conjugations; apparently, i-stem third conjugation verbs share more connection with the fourth conjugation than the third.
We can generate a KATR theory directly from the paradigm of Table 2 along with the stem-referral rules of Table 3, and the lexicon of Table 4. We can take advantage of the grouping (Figure 3) to generate a fairly compact KATR theory. Figure 4 shows a fragment of the computed KATR theory.
The Help node introduces the three stems required by conjugation cIa. It refers all other requests to the CONJcIa node, which refers the remaining stems to the first stem. It also provisions the version of distillation e58 to have variant 1. It refers other requests to a chain of grouping nodes, here shown as Join12, Join15, Join17, and Join18, each of which provisions some distillations and hands of other requests to the next node in the chain. Finally, node Join18 refers all morphological queries to EXPAND. This node, of which we show only a small piece, combines the result of referring to nodes MPS1 through MPS92, for each one looking up the appropriate exponence. MPS1, which generates the present indicative active first person singular form, invokes node T02 with a parameter that depends on the value of the e1 distillation. Finally, the T02 node looks up the appropriate stem (in this case, stem 4) and combines it with the given ending.
Table 9 shows some of the output that KATR generates for this theory. We use such output to verify that we have correctly captured the original paradigm in our chart of Table 2.
This exercise demonstrates that both the realizational and the implicative approaches to defining language morphology lead to effective descriptions, as evidenced by the KATR theories they produce. An advantage of the realizational approach is that it allows us to apply language-specific knowledge and insight to create a default inheritance hierarchy that captures the morphological structure of the language, with slots pertaining to different morphosyntactic properties. However, as we have noted elsewhere
The implicative approach is much more automatic. One still needs to manually construct the initial paradigm, decide how many stems are needed (for Latin, we use five; for French, we use 15), and abstract as much information as possible into the templates for each MPS. After that, we can use automatic methods that reduce the paradigm chart to its essence, group conjugations, and generate an effective KATR theory. These steps take only a few seconds to complete (on a 1.8GHz Intel Pentium running Linux, only one second). It is a simple (albeit tedious) matter to verify that all the forms the KATR theory generates are accurate. The KATR theory itself is fairly compact, taking advantage of grouping. However, it is about twice the size of the hand-built theory (measured in characters). More important, it doesn't clearly delineate the slots of the exponences. It is therefore somewhat less satisfying, somewhat less informative, than the KATR theory we build manually following the realizational approach. We have applied the implicative approach to French (both as spelled and as pronounced), Hebrew, and Yiddish, as well as some lesser-known languages, such as Comaltepec Chinantec (Oto-Manguean, spoken in Oaxaca, Mexico), Fur (Nilo-Saharan, in Darfur), and Sora (Austro-Asiatic, India).
The implicative approach also has the advantage that it allows us to analyze the principal parts of the language based solely on the exponences in the paradigm chart. We have taken advantage of that ability elsewhere to characterize languages based on properties of their principal parts
As Latin developed into the Romance languages, its scheme of conjugations and principal parts evolved. Initial investigation of French, following the same implicative approach as that shown here for Latin, shows that 9 static principal parts are needed to distinguish the 67 distinct conjugations. Ignoring spelling and considering only pronunciation, we have been able to reduce this total to 7 principal parts distinguishing 35 conjugations. This investigation continues.
We would like to thank Lei Shen and Suresh Thesayi, who were instrumental in implementing our Java™ version of KATR. Nancy Snoke assisted in implementing our Perl/Prolog version.
This work was partially supported by the National Science Foundation under Grants IIS-0097278 and IIS-0325063 and by the University of Kentucky Center for Computational Science. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
- : A position in a full table of word forms, where the row is the inflection class (such as conjugation 1), and the column represents a set of morphosyntactic properties (such as first person singular present indicative active).
-
: An inflectional ending, usually added to a stem according to its syntactic context. For example,
amathe/she loves
has the desinence-t. - : A marker of a particular morphophonological property. For example, the fact that a verb is in conjugation 4 is a diacritic.
-
: The contents of a cell for a given lexeme, such as
amat. -
: A phonological unit whose phonemic expression depends on its context. For example in our Latin KATR theory, we use I as the phonological unit in conjugation 3 (i-stem) that is either expressed as the phoneme
i(as incapiōI grab
), as the phonemee(beforer, as incapereto grab
), or disappears entirely (such as beforeī, as incēpīI have grabbed
). - : A set of rules in a KATR theory to which a query is directed. The particular rule to apply depends on the query. Some nodes refer to others, leading to a hierarchical node structure.
-
: Rules of euphony or spelling. For example
ēōis pronouncedeō, as invideōI see,
andcsis spelledx, as indūxīI have led.