A Computational Approach to Biblical Hebrew Conjugation

Joachim Lambek and Noson S. Yanofsky

November 19, 2006

Abstract We study the Hebrew verb as it occurs in the Torah, according to the Masoretic tradition. Potentially, each verb has 7 × 2 × 10 = 140 finite conjugational forms corresponding to seven patterns, two tenses and ten persons. We present a simple computational method for generating these conjugational forms step by step.

1 Introduction

In J. Weingreen’s authoritative A Practical Grammar For Classical Hebrew [11], he writes (page vii) “Hebrew grammar is essentially schematic and, starting from simple primary rules, it is possible to work out, almost mathematically, the main groups of word-building.” We claim that the adverb “almost” in his assertion can be removed. We shall present such a scheme in a mathematical language. The mathematics involved is that of a finitely generated partially ordered semi-group, also called “semi-Thue system” by mathematicians, “rewrite system” by computer scientists and “production grammar” (Chomsky’s Type zero) by linguists.

We do not intend to offer any new discoveries about biblical Hebrew grammar. No new grammatical rule will be introduced, nor will we offer any deep insight that has been overlooked in millennia of work by the Hebrew grammarians. We simply aim at a clear mathematical way of presenting the rules of conjugation for a small fragment of biblical Hebrew. This presentation is concise, exact (perhaps too exact for the text evaluated) and intended to be an easily intelligible expression of the rules. We hope that the rules presented here are an improvement over the usual paradigm tables or the long English statements explaining them. The improvements will be seen with the ease that the examples are computed. We should add that in order to calculate a word form, one always applies the first rewrite rule that is applicable.

We accept the traditional grammar as presented, say, in the admirable text of Weingreen [11], with only minor quibbles. We have also consulted the classical treatment by Gesenius [7]. What we are concerned with is the computational aspect: how could a speaker of biblical Hebrew calculate the correct verb form in a step by step manner? Phonological reasons for some of the grammatical rules will be offered when they are apparent.

While our goal is to be as inclusive as possible, we are ignoring many different parts of Hebrew conjugation. There will be no discussion of the cohortative, imperative, jussive, infinitive, or participle tenses. In general, we ignore the modifications of the verb form when it is followed by a pronominal suffix. We also — perhaps in error — wave our hands at accents and whether or not a syllable is open or closed. There are some grammatical constructions and rules that are dependent on these factors. For example, without considering if a syllable is open or closed, it is hard to tell if a shewa is vocal or silent. Similarly, an accent on a verb can move when there is a prefixed waw. We suspect that the accents can be computed from the phonological rules rather then the other way around. Because of space and time considerations, we choose to work with the fragment of biblical Hebrew conjugation dealing with the “finite” forms of the verb.

Like classical Latin [9], biblical Hebrew is an inflected language. It has 140 finite verb forms, constructed from seven patterns, two tenses and ten persons, while Latin has 90 finite verb forms, constructed from three patterns (amo, amavi, amor), five tenses and six persons. One thing both languages have in common is that not every verb possesses all possible patterns. Thus, Latin memini and nascor exist only in the second and third pattern respectively; similarly in Hebrew, many verbs fail to possess a full complement of all seven patterns.

We mention two points of difference between Latin and Hebrew. In Latin, each pattern displays a separate conjugation paradigm, whereas in Hebrew, all patterns are conjugated exactly alike, thus making Hebrew computationally easier to manipulate than Latin. On the other hand, Latin pattern 1 determines the semantics of patterns 2 and 3; but in Hebrew, the meanings of the other patterns cannot always be inferred from that of pattern 1. For example, nikbad, the alleged passive of kābad “to be heavy”, can unpredictably mean “to gain honor”^{1}. The passive of pāqad “to visit” is the seemingly unrelated nipqad ”to be lacking”. (We have here represented each verb by the third person singular of the past tense.)

2 The Hebrew Consonants

To make this paper accessible to readers not familiar with Hebrew, we do not use Hebrew grammatical terminology in the metalanguage, although we sometimes mention the Hebrew word for completeness. We present Hebrew letters in Roman transliteration. Concerning the consonants, we adopt the transliteration system A of the Encyclopedia Judaica (volume VIII page 79):

’ b g d h w z h. \begin{matrix}t \\ . \end{matrix} y k l m n s ‘ p s. q r š ś t

Some sample transliterations are

Aleph ’ Bet b Dalet d
H .et \begin{matrix}h \\ . \end{matrix} Tet \begin{matrix}t \\ . \end{matrix} Kaph k
Samek s ‘Ayin ‘ S.ade \begin{matrix}s \\ . \end{matrix}
Qoph q Šin š Śin ś
Taw t

We follow the Gileadites^{2} in maintaining the distinctions between the letters š and ś, which were not distinguished in the original text. Essentially the Hebrew consonants aim to represent what are called “phonemes” in modern linguistics. We will not distinguish between the plosives b g d p k t and their spirant (fricative) allophones b^{h} g^{h} d^{h} t^{h} p^{h} k^{h} t^{h} (denoted by \underline{b}, \underline{g}, etc in the Encyclopedia). Plosives will automatically appear at the beginning of a word (denoted by # if necessary), after certain prefixes (in which case we place the symbol + between the prefix and the stem), and after another consonant. Otherwise, the letter b, g, etc. should be read as spirants b^{h}, g^{h} etc. In particular, when we have two consecutive consonants, the former is a spirant, if possible, and the latter is a plosive, if possible. A problem may arise when the first consonant has no spirant allophone. However, we will ignore such marginal phenomena.

3 The Masoretic vowels

Apparently, biblical Hebrew contained three basic vowel phenomes^{3} a, i and u, like modern standard Arabic. (Note moslem = muslim). These were not written originally, although they might be revealed by attached consonants h, y and w respectively^{4}.

The vowel system now in use goes back to the Tiberian Masoretes^{5} (around 800 A.D.), who were closer in time to us than to Ezra (around 600 B.C.), the traditional final editor of the Torah. They claimed to preserve the original pronunciation in all its nuances^{6}; but can they really be trusted after such a long time spread?^{7} Still, it is difficult to ignore them now. Rather than to question them, we aim to formulate the grammar implied in their system of spelling.

The Masoretes essentially acknowledge seven short and five long ^{8} vowels:

a  ā(h)
ä  ȧ  ey  ow
e  o  iy  uw
i  u

They failed to distinguish between ā (qāme\begin{matrix}s \\ . \end{matrix} − gadol) and ȧ (qāmes. − katan). These have indeed complementary distribution, the former occurs only in open syllables and the latter before two consecutive consonants. Both ä and ȧ might have been allophones of a, although later they became allophones of e and o respectively. In pattern 4, the so called hoph‘al, there is even a variation between ȧ and u.

The Masoretes occasionally also admitted the long vowels äy (\begin{matrix}s \\ . \end{matrix}ere−yud) and äh perhaps representing the same sound. In addition, they had a symbol, the shewa, for the so called schwa, a neutral vowel recognized by modern linguists. We shall denote this with a raised ( )^{e}. They introduced a very

short a, ä and ȧ (\begin{matrix}h \\ . \end{matrix}atep − pata\begin{matrix}h \\ . \end{matrix}, \begin{matrix}h \\ . \end{matrix}atep − segol and \begin{matrix}h \\ . \end{matrix}atep − qāme\begin{matrix}s \\ . \end{matrix}) which we

shall denote by raised ^{a}, ä and ȧ.

The Masoretes also admitted a silent shewa between two consecutive consonants. This we shall omit in our transliteration. Although they used the same symbol for both vocalic and silent schwa, there are standard rules to distinguish them.^{9}

4 Vowel transformations

It is not clear to us how exactly the phoneme-allophone distinction may be incorporated into a computational description of Hebrew. What seems important is that a certain symbol (a), is to be pronounced differently in different contexts. In fact we require the following rule:

(V) ⟶ \{ \begin{matrix}V & before CC′ or C# \\ ( )^{V} & before CV′ \\ ( )^{e} & before CV̄′ \end{matrix} (4.1)

where V = a, ä or ȧ. Here C and C′ denote consonants, V and V′ short vowels, V̄′ a long vowel, and # denotes the space between words. The way to read this is that (a) becomes a, ( )^{a} or ( )^{e} depending on what follows, and similarly for (ä) and (ȧ). If she wishes, the reader may take (a) to be a phoneme with three allophones.

We shall also postulate

(V) ⟶ \{ \begin{matrix}V & before CC′ or C# \\ ( )^{e} & before CV′ or CV̄′ \end{matrix} (4.2)

where V = e, i, o or u, except when C or C′ = w or y or when C = C′. We shall deal with these exceptional cases later.

Unfortunately, (e) must be distinguished from a related symbol (é) which will turn into a different vowel before two consecutive consonants:

(é) ⟶ \{ \begin{matrix}a & before CC′ \\ e & before C# \\ ( )^{e} & before CV′ or CV̄′ \end{matrix} (4.3)

In order not to make our notation too cumbersome, we shall henceforth drop the parentheses around (a), (e), etc. But this will imply that, before a vowel takes its final form, we will have to look at two or three letters following it (three because a long vowel may be represented by two letters).

5 The Hebrew verb

Most Hebrew verbs are presented by three consonants, called “radicals”, and two vowels, which we call “characteristic vowels”. This triliteralness^{10} is a defining property of all Semitic languages. Three consonants may determine a verb and one forms related words by placing different vowels between these consonants. This is in stark contrast to non-Semitic languages such as English, where the words boot, bait, but, bat, bet, boat, bit, etc. have nothing to do with each other.

A verb V will be presented as follows:

V = F MLα_{1}, α_{2}

where F, M, and L stand for the F irst, Middle, and Last radical respectively and α_{1} and α_{2} are equal to a, é or o. The characteristic vowels appear in pattern 1 of the verb only, α_{1} in the future and α_{2} in the past. For example, Weingreen discusses four verbs, in our notation:

q\begin{matrix}t \\ . \end{matrix}loa, q\begin{matrix}t \\ . \end{matrix}nao, kbdaé, y\begin{matrix}t \\ . \end{matrix}baa

( they mean, respectively, “to kill”, “to be small”, “to be heavy”, “to be good”). The third person masculine singular of the future and of the past in pattern 1 is seen as follows

yiq\begin{matrix}t \\ . \end{matrix}ol / qā\begin{matrix}t \\ . \end{matrix}al

yiq\begin{matrix}t \\ . \end{matrix}an / qā\begin{matrix}t \\ . \end{matrix}on

yikbad / kābed

yiy\begin{matrix}t \\ . \end{matrix}ab / yātab.

Unfortunately, it must be admitted that different scholars are not necessarily in agreement. Thus Gesenius writes q^{e}\begin{matrix}t \\ . \end{matrix}āl and Halkin [8] writes kābad. We prefer Weingreen, who asserts that the vowels oa characterize “active” verbs, that is verbs denoting an action, and that ao, aé and aa characterize “stative” verbs, that is verbs denoting a state^{11}.

The characteristic vowels may be affected by phonological rules. For example, there is an active verb šl\begin{matrix}h \\ . \end{matrix}aa “to send” in which the o has been replaced by a, in view of the fact that \begin{matrix}h \\ . \end{matrix} is a guttural consonant.

If we look at the first person singular of the past tense of pattern 1, we find that é ⟶ a in kbdaé

kābédtiy ⟶ kābadtiy.

This follows from rule (4.3).

In the third person feminine, the characteristic vowel α_{2} turns into a schwa and we obtain

qā\begin{matrix}t \\ . \end{matrix}^{e}lāh, qā\begin{matrix}t \\ . \end{matrix}^{e}nāh, kāb^{e}dāh, yāt^{e}bnāh,

from rule (4.1).

6 The Conjugation formula

We distinguish 140 possible finite verb forms C_{i,j,k}(V) for every verb V where

i = 1, 2m, 2f, 3m, 3f, 4, 5m, 5f, 6m, 6f

denotes the three persons singular followed by the three persons plural, and m stands for masculine, f for feminine;

j = 1, 2

denotes the future (also called “imperfect” or “incomplete”) tense and the past (also called the “perfect” or “complete”) tense respectively;

k = 1, 2, …, 7

denotes the seven patterns (also called the “forms”, “conjugations,” or “binyanim”). The 140 verb forms are calculated by the formula

C_{i,j,k}(V) ⟶ P_{i,j}S_{j,k}(V)Q_{i,j} (6.1)

where P_{i,j} and Q_{i,j} are given by the following table.

Table I Prefixes and Suffixes

i P_{i,1} Q_{i,1} P_{i,2} Q_{i,2}
1 ’  ∅  ∅ tiy
2m t  ∅  ∅ tā
2f t iy  ∅  t
3m y  ∅  ∅  ∅
3f t  ∅  ∅ \overline{a}h
4 n  ∅  ∅ nuw
5m t uw ∅ täm
5f t n\overline{a}h ∅ tän
6m y uw ∅ uw
6f t n\overline{a}h ∅ uw

The table encapsulates a number of rewrite rules such as P_{1,1} ⟶ ’, and Q_{1,1} ⟶ ∅ (the empty string). Note, in particular, that P_{i,2} ⟶ ∅ for all i, hence for j = 2 conjugation rule (6.1) may be simplified to

C_{i,2,k}(V) ⟶ S_{2,k}(V)Q_{i,2}. (6.2)

The seven patterns S_{j,k}(V) are given by the following table:

Table II Stem Rewrite Rules

k Pattern Future S_{1,k}(V)  Past S_{2,k}(V)
1  qal  iF Mα_{1}L  [F āMα_{2}L]
2 niph‘al  niF F āMéL  niF MaL
3 hiph‘il  haF M[ey]L  hiF M[ay]L
4 hoph‘al  hȧF MaL  hȧF MaL
5 pi‘el  iF aMMeL  F iMMéL
6 pu‘al  iF uMMaL  F uMMaL
7 hitpa‘el hit + F aMMéL hit + F aMMéL

(Recall from Section 5 that V = F MLα_{1}α_{2} and from Section 2 that we place the symbol + between prefix and stem.)

Halkin differs from Weingreen in his treatment of S_{1,7}(V). In our notation, he would put

S_{1,7}(V) ⟶ hit + F aMMel,

replacing é by e.

The patterns^{12} usually have the following shades of meaning:

Pattern

Simple Intensive Causative Reflexive
Active  qal k = 1 pi‘el k = 5 hiph‘il k = 3
Passive niph‘al k = 2 pu‘al k = 6 hoph‘al k = 4 hitpa‘el k = 7

Before embarking on any actual calculations, we must state a number of phonological rewrite rules:

h ⟶ \{ \begin{matrix}∅ & after C \\ h & otherwise \end{matrix} (6.3)

n ⟶ \{ \begin{matrix}∅ & after C \\ n & otherwise \end{matrix} (6.4)

’i ⟶ \{ \begin{matrix}’ä & before CC′ \\ & & except when C or C′ = y or w \\ ’^{a} & before CV \end{matrix} (6.5)

When a verb is prefixed with something that ends in a t, the following rule holds^{13}

t + C ⟶ \{ \begin{matrix}Ct & if C = š, ś or s \\ C\begin{matrix}t \\ . \end{matrix} & if C = \begin{matrix}s \\ . \end{matrix} \\ CC & if C = \begin{matrix}t \\ . \end{matrix}, d, z or n (often) \\ tC & otherwise \end{matrix} (6.6)

[ey] ⟶ \{ \begin{matrix}e & after CC′ \\ iy & otherwise \end{matrix} (6.7)

[ay] ⟶ \{ \begin{matrix}a & after CC′ when unstressed \\ iy & otherwise \end{matrix} (6.8)

[F āMV L] ⟶ \{ \begin{matrix}F^{e}MȧL & when V = o before täm or tän \\ F^{e}MV L & when V = a, or é before täm or tän \\ F āMV L & otherwise \end{matrix} (6.9)

(The third case also allows V = ā in anticipation of Section 10.)

7 Sample calculations for regular verbs

In the following sample calculations, we will show how to calculate C_{i,j,k}(V) when V is a regular (aka “strong”) verb. This means that none of the three radicals is n, w or y, nor a guttural ’, h, h., ‘ (and sometimes r). We follow Weingreen and look at the verb q\begin{matrix}t \\ . \end{matrix}loa “to kill”^{14} in all seven patterns. Most of our rules will be illustrated by taking i = 1 and 6f. When j = 2, we will occasionally also look at i = 3m and 5m to illustrate the rôle of rewrite rules replacing é by e, ā by ( )^{e} and o by ȧ in certain contexts. The number below the arrow ⟶_{(#)} is the rule number in this paper. We only supply it when the rule is not obvious.

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’iq\begin{matrix}t \\ . \end{matrix}olQ_{1,1}

⟶_{(6.5)} ’äq\begin{matrix}t \\ . \end{matrix}olQ_{1,1} ⟶ ’äq\begin{matrix}t \\ . \end{matrix}ol

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tiq\begin{matrix}t \\ . \end{matrix}olQ_{6f,1} ⟶ tiq\begin{matrix}t \\ . \end{matrix}olnāh

C_{1,2,1}(V) ⟶ S_{2,1}(V)Q_{1,2} ⟶ [qā\begin{matrix}t \\ . \end{matrix}al]Q_{1,2} ⟶ [qā\begin{matrix}t \\ . \end{matrix}al]tiy

⟶_{(6.9)} qā\begin{matrix}t \\ . \end{matrix}altiy

C_{5m,2,1}(V) ⟶ ⋯ ⟶ [qā\begin{matrix}t \\ . \end{matrix}al]täm ⟶_{(6.9)} q^{e}\begin{matrix}t \\ . \end{matrix}altäm

Computational Hebrew Conjugation 11 By contrast, for V′ = q\begin{matrix}t \\ . \end{matrix}nao “to be small”, we have

C_{5m,2,1}(V′) ⟶ ⋯ ⟶ [qā\begin{matrix}t \\ . \end{matrix}on]täm ⟶_{(6.9)} q^{e}\begin{matrix}t \\ . \end{matrix}ȧntäm

Returning to V = q\begin{matrix}t \\ . \end{matrix}loa,

C_{6f,2,1}(V) ⟶ ⋯ ⟶ [qā\begin{matrix}t \\ . \end{matrix}al]uw ⟶_{(6.9)} qā\begin{matrix}t \\ . \end{matrix}aluw ⟶_{(4.1)} qā\begin{matrix}t \\ . \end{matrix}^{e}luw

C_{1,1,2}(V) ⟶ P_{1,1}S_{1,2}(V)Q_{1,1} ⟶ ’S_{1,2}(V)Q_{1,1} ⟶ ’niqqā\begin{matrix}t \\ . \end{matrix}élQ_{1,1}

⟶_{(6.4)} ’iqqā\begin{matrix}t \\ . \end{matrix}élQ_{1,1} ⟶_{(6.5)} ’äqqā\begin{matrix}t \\ . \end{matrix}él ⟶_{(4.3)} ’äqqā\begin{matrix}t \\ . \end{matrix}el

C_{6f,1,2}(V) ⟶ ⋯ ⟶ tiqqā\begin{matrix}t \\ . \end{matrix}élnāh ⟶_{(4.3)} tiqqā\begin{matrix}t \\ . \end{matrix}alnāh

C_{1,2,2}(V) ⟶ S_{2,2}(V)Q_{1,2} ⟶ niq\begin{matrix}t \\ . \end{matrix}alQ_{1,2} ⟶ niq\begin{matrix}t \\ . \end{matrix}altiy

C_{6f,2,2}(V) ⟶ ⋯ ⟶ niq\begin{matrix}t \\ . \end{matrix}aluw ⟶_{(4.1)} niq\begin{matrix}t \\ . \end{matrix}^{e}luw

C_{1,1,3}(V) ⟶ P_{1,1}S_{1,3}(V)Q_{1,1} ⟶ ’haq\begin{matrix}t \\ . \end{matrix}[ey]lQ_{1,1} ⟶_{(6.3)} ’aq\begin{matrix}t \\ . \end{matrix}[ey]lQ_{1,1}

⟶ ’aq\begin{matrix}t \\ . \end{matrix}[ey]l ⟶_{(6.7)} ’aq\begin{matrix}t \\ . \end{matrix}iyl

C_{6f,1,3}(V) ⟶ ⋯ ⟶ taq\begin{matrix}t \\ . \end{matrix}[ey]lnāh ⟶_{(6.7)} taq\begin{matrix}t \\ . \end{matrix}elnāh

C_{1,2,3}(V) ⟶ S_{2,3}(V)Q_{1,2} ⟶ hiq\begin{matrix}t \\ . \end{matrix}[ay]lQ_{1,2} ⟶ hiq\begin{matrix}t \\ . \end{matrix}[ay]ltiy ⟶_{(6.8)}

hiq\begin{matrix}t \\ . \end{matrix}altiy

C_{6f,2,3}(V) ⟶ ⋯ ⟶ hiq\begin{matrix}t \\ . \end{matrix}[ay]luw ⟶_{(6.8)} hiq\begin{matrix}t \\ . \end{matrix}iyluw

This example forces us to add the proviso “when unstressed” in case 1 of (6.8), otherwise we would have obtained hiq\begin{matrix}t \\ . \end{matrix}aluw ⟶ hiq\begin{matrix}t \\ . \end{matrix}^{e}luw instead.

C_{1,1,4}(V) ⟶ P_{1,1}S_{1,4}(V)Q_{1,1} ⟶ ’S_{1,4}(V)Q_{1,1} ⟶ ’hȧq\begin{matrix}t \\ . \end{matrix}alQ_{1,1}

12 Lambek and Yanofsky

⟶_{(6.3)} ’ȧq\begin{matrix}t \\ . \end{matrix}alQ_{1,1} ⟶ ’ȧq\begin{matrix}t \\ . \end{matrix}al

C_{6f,1,4}(V) ⟶ ⋯ ⟶ tȧqtalQ_{6f,1} ⟶ tȧq\begin{matrix}t \\ . \end{matrix}alnāh

C_{1,2,4}(V) ⟶ S_{2,4}(V)Q_{1,2} ⟶ hȧq\begin{matrix}t \\ . \end{matrix}alQ_{1,2} ⟶ hȧq\begin{matrix}t \\ . \end{matrix}altiy

C_{6f,2,4}(V) ⟶ ⋯ ⟶ hȧq\begin{matrix}t \\ . \end{matrix}aluw ⟶_{(4.1)} hȧq\begin{matrix}t \\ . \end{matrix}^{e}luw

C_{1,1,5}(V) ⟶ P_{1,1}S_{1,5}(V)Q_{1,1} ⟶ ’S_{1,5}(V)Q_{1,1} ⟶ ’iqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}elQ_{1,1}

⟶_{(6.5)} ’^{a}qa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}elQ_{1,1} ⟶ ’^{a}qa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}el

C_{1,2,5}(V) ⟶ S_{2,5}(V)Q_{1,2} ⟶ qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,2} ⟶ qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}éltiy ⟶_{(4.3)} qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}altiy

C_{3m,2,5}(V) ⟶ ⋯ ⟶ qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}él ⟶_{(4.3)} qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}el

C_{6f,2,5}(V) ⟶ ⋯ ⟶ qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}éluw ⟶_{(4.3)} qi\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}^{e}luw

C_{1,1,6}(V) ⟶ P_{1,1}S_{1,6}(V)Q_{1,1} ⟶ ’S_{1,6}(V)Q_{1,1} ⟶ ’iqu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alQ_{1,1}

⟶_{(6.5)} ’^{a}qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alQ_{1,1} ⟶ ’^{a}qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}al

C_{6f,1,6}(V) ⟶ ⋯ ⟶ tiqu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alQ_{6f,1} ⟶_{(4.2)} t^{e}qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alQ_{6f,1} ⟶ t^{e}qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alnāh

C_{1,2,6}(V) ⟶ ⋯ ⟶ S_{2,6}(V)Q_{1,2} ⟶ qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alQ_{1,2} ⟶ qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}altiy

C_{6f,2,6}(V) ⟶ ⋯ ⟶ qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}aluw ⟶_{(4.1)} qu\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}^{e}luw

C_{1,1,7}(V) ⟶ P_{1,1}S_{1,7}(V)Q_{1,1} ⟶ ⋯ ⟶ ’hit + qa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,1}

⟶_{(6.3)} ’it + qa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,1} ⟶_{(6.6)} ’itqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,1} ⟶_{(6.5)} ’ätqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,1}

⟶ ’ätqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}él ⟶_{(4.3)} ’ätqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}el

C_{6f,1,7}(V) ⟶ ⋯ ⟶ titqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élnāh ⟶_{(4.3)} titqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}alnāh

C_{1,2,7}(V) ⟶ ⋯ ⟶ hit + qa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,2} ⟶_{(6.6)} hitqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}élQ_{1,2}

⟶ hitqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}éltiy ⟶_{(4.3)} hitqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}altiy

C_{6f,2,7}(V) ⟶ ⋯ ⟶ hitqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}éluw ⟶_{(4.3)} hitqa\begin{matrix}t \\ . \end{matrix}\begin{matrix}t \\ . \end{matrix}^{e}luw

8 Quadriliterals

While most verbs have exactly three consonants, there are some with four. Weingreen mentions only one such verb explicitly, namely krs.s.; but implicitly he allows that others appear in late Biblical Hebrew such as qwwm and mwtt, in certain patterns of otherwise triliteral verbs. In modern Hebrew, as in modern standard Arabic, quadriliterals proliferate (see Halkin [8]). Both Hebrew and Arabic apply the same trick to derive the conjugation of quadriliterals from triliterals. Noting that in patterns 5,6 and 7 of regular verbs the medial consonant is doubled, all one has to do is to replace MM by M_{1}M_{2}, where M_{1} ≠ M_{2}. It follows that quadriliterals can exist only in patterns 5,6 and 7.

For example, here is how we can calculate pattern 5 of V = krsm “to gnaw”. (There is no need for characteristic vowels, which appear only in pattern 1.)

C_{1,1,5}(V) ⟶ P_{1,1}S_{1,5}(V)Q_{1,1} ⟶ ’S_{1,5}(V)Q_{1,1} ⟶ ’ikarsemQ_{1,1} ⟶_{(6.5)} ’^{a}karsemQ_{1,1} ⟶ ’^{a}karsem

C_{6f,1,5}(V) ⟶ ⋯ ⟶ tikarsemQ_{6f,1} ⟶_{(4.2)} t^{e}karsemQ_{6f,1} ⟶ t^{e}karsemnāh

C_{1,2,5}(V) ⟶ ⋯ ⟶ kirsémQ_{1,2} ⟶ kirsémtiy ⟶_{(4.3)} kirsamtiy

C_{3m,2,5}(V) ⟶ ⋯ ⟶ kirsém ⟶_{(4.3)} kirsem

C_{6f,2,5}(V) ⟶ ⋯ ⟶ kirsémuw ⟶_{(4.3)} kirs^{e}muw

This verb is found in the Bible with a pronominal suffix: y^{e}kars^{e}männāh “he (a boar) doth ravage it (a vine)” (Psalms 80:14). We shall not analyze pronominal suffixes here.

Several other quadraliteral verbs found in the Bible are

• ru\begin{matrix}t \\ . \end{matrix}^{a}paš “To grow fresh again” (Job 33:25). Chomsky [6] on page 216 footnote 349, mentions a source which explains the hatef-patah. under the t. due to euphonic difficulties in the transition from t. to p. There are many who say that the word is not a quadriliteral but is in fact a portmanteau word combined of two other words. (See the commentaries ad loc. and on the Babylonian Talmud Nedarim 41a.) There are still others who think that the r is a dittographic from the previous word.

• m^{e}kurbāl “to clothe” (I Chronicals 15:27) which is similar to the passive particle (hence the m^{e}) of the pual.

• paršez “to spread” (Job 26:9). Some authors say that this is an infinitive absolute of the piel pattern.

There are no five-letter verbs in Biblical Hebrew. In contrast, there are many in modern Hebrew. There are numerous quadriliterals and five-letter nouns in Biblical Hebrew.^{15}

9 Weak Verbs and Weak Verbs with F = n

Triliteral verbs are said to be “weak” if they contain the gutturals ’, h, \begin{matrix}h \\ . \end{matrix}, ‘ and sometimes r, the assimilable n or the semi-consonants y or w. As Weingreen puts it: “weak verbs [...] are explained rationally by the simple method of applying to these verbs the ordinary rules governing ‘peculiar’ letters and working out the forms which they, respectively, assume.” In other words, weak verbs are conjugated like regular ones and then transformed with the help of appropriate phonological rules. In principle, these rules are not restricted to verbal contexts, but these are the only contexts we have looked at here. How this program is carried out in detail will occupy most of the remaining sections of this paper.

Special considerations must also be given to verbs where two contiguous radicals coincide. We will look at this in Section 15.

In the present section we consider the case F = n. When the letter n occurs as the first radical of a verb, and sometimes elsewhere, it may be assimilated to the following consonant. We will write (n) for the assimilable n, to distinguish it from the usual letter n. It obeys the following rule:

V (n)C ⟶ \{ \begin{matrix}V nC & if C is a gutteral \\ V nn & if C = (n) \\ V CC & otherwise \end{matrix} (9.1)

(n) ⟶ n before a vowel or # (9.2)

We also note that, in unstressed syllables,

V CC ⟶ uCC if V = o or ȧ (9.3)

The restriction to unstressed syllables is necessary in view of qā\begin{matrix}t \\ . \end{matrix}onnuw

and tiq\begin{matrix}t \\ . \end{matrix}onnāh.

We will now calculate some representative finite forms of the verb V = (n)ploa “to fall”.

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’i(n)polQ_{1,1} ⟶_{(6.5)} ’ä(n)polQ_{1,1} ⟶_{(9.1)} ’äppolQ_{1,1} ⟶ ’äppol

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tippolnāh

C_{1,2,1}(V) ⟶ S_{1,2}(V)Q_{1,2} ⟶ [(n)āpal]Q_{1,2} ⟶_{(9.2)} [nāpal]Q_{1,2} ⟶ [nāpal]tiy ⟶_{(6.9)} nāpaltiy

C_{5m,2,1}(V) ⟶ ⋯ ⟶ [nāpal]täm ⟶_{(6.9)} n^{e}paltäm

C_{6f,2,1}(V) ⟶ ⋯ ⟶ nāpaluw ⟶_{(4.1)} nāp^{e}luw

C_{1,1,2}(V) ⟶ P_{1,1}S_{1,2}(V)Q_{1,1} ⟶ ’S_{1,2}(V)Q_{1,1} ⟶ ’i(n)(n)āpélQ_{1,1} ⟶_{(6.5)} ’ä(n)(n)āpélQ_{1,1} ⟶_{(9.1)} ’ännapélQ_{1,1} ⟶ ’ännapél ⟶_{(4.3)} ’ännapel C_{6f,1,2}(V) ⟶ ⋯ ⟶ tinnāpélnāh ⟶_{(4.3)} tinnāpalnāh

C_{1,2,2}(V) ⟶ S_{2,2}(V)Q_{1,2} ⟶ ni(n)palQ_{1,2} ⟶_{(9.1)} nippalQ_{1,2} ⟶ nippaltiy

C_{1,1,3}(V) ⟶ P_{1,1}S_{1,3}(V)Q_{1,1} ⟶ ’S_{1,3}(V)Q_{1,1} ⟶ ’ha(n)p[ey]lQ_{1,1} ⟶_{(6.3)} ’a(n)p[ey]lQ_{1,1} ⟶_{(9.1)} ’app[ey]lQ_{1,1} ⟶ ’app[ey]l ⟶_{(6.7)} ’appiyl

C_{1,2,3}(V) ⟶ S_{2,3}(V)Q_{1,2} ⟶ hi(n)p[ay]lQ_{1,2} ⟶_{(9.1)} hipp[ay]lQ_{1,2} ⟶ hipp[ay]ltiy ⟶_{(6.8)} hippaltiy

C_{1,1,4}(V) ⟶ P_{1,1}S_{1,4}(V)Q_{1,1} ⟶ ’S_{1,4}(V)Q_{1,1} ⟶ ’hȧ(n)palQ_{1,1} ⟶_{(6.3)} ’ȧ(n)palQ_{1,1} ⟶_{(9.1)} ’ȧppalQ_{1,1} ⟶_{(9.3)} ’uppalQ_{1,1} ⟶ ’uppal

C_{1,2,4}(V) ⟶ S_{2,4}(V)Q_{1,2} ⟶ hȧ(n)palQ_{1,2} ⟶_{(9.1)} hȧppalQ_{1,2} ⟶_{(9.3)} huppalQ_{1,2} ⟶ huppaltiy

Weingreen lists no other pattern for this verb, but Halkin considers pattern 7 (hitpa‘el) which contains no surprises. But recall that he has e in place of é in table II, and so he obtains

C_{6f,1,7}(V) ⟶ tit + (n)appelQ_{6f,1} ⟶_{(6.6)} tit(n)appelQ_{6f,1} ⟶_{(9.2)} titnappelQ_{6f,1} ⟶ titnappelnāh where we would expect titnappalnāh.

There is one verb in which the letter l is similarly assimilable, lq\begin{matrix}h \\ . \end{matrix}aa “to take”. Note that α_{1} = a rather than o since \begin{matrix}h \\ . \end{matrix} is a guttural.

There is one common verb in which both the first and the last radical is an assimilable n, the verb (n)t(n)éa “to give”. This is an example of a doubly weak verb about which we shall see more of in Section 16. For some reason, α_{1} = é rather then o. At the beginning, this verb is treated like (n)ploa, so we only have to look at the end of the calculations.

C_{1,1,1}(V) ⟶ ⋯ ⟶ ’ätte(n) ⟶_{(9.2)} ’ätten C_{6f,1,1}(V) ⟶ ⋯ ⟶ titté(n)nāh ⟶_{(9.1)} titténnāh ⟶_{(4.3)} tittannāh

C_{1,2,1}(V) ⟶ ⋯ ⟶ nāta(n)tiy ⟶_{(9.1)} nātattiy

C_{3m,2,1}(V) ⟶ ⋯ ⟶ nāta(n) ⟶_{(9.2)} nātan

C_{6f,1,2}(V) ⟶ ⋯ ⟶ ’ännaté(n) ⟶_{(9.2)} ’ännatén ⟶_{(4.3)} ’ännaten

C_{3m,2,2}(V) ⟶ ⋯ ⟶ nitta(n)tiy ⟶_{(9.1)} nittattiy

10 Weak verbs with guttural radicals

The gutturals (also called “laryngals”) in Hebrew are ’, h,\begin{matrix}h \\ . \end{matrix},‘. Here ’ and ‘ can be subclassified as weak gutturals in contrast to h and \begin{matrix}h \\ . \end{matrix} which are called strong gutturals. Because there is latitude about the level of “gutturalness”, there is latitude about the extent that each letter follows the guttural rules.

Although r is technically not a guttural, it still follows several guttural rules.

In Hebrew a guttural can not be doubled^{16} (i.e., accept a dagesh). Rather than extending the guttural, we lengthen the vowel before the guttural:

iGG ⟶ eG (10.1)

uGG ⟶ oG (10.2)

aGG ⟶ āG (10.3)

(Note that the vowel before a doubled consonant other then n is always a, i or u in unstressed syllables.)

Gutturals cannot even be immediately followed by another consonant. Thus, we have (except for G = r)

V GC ⟶ V GV C when V = ä, a, ȧ, (10.4) assuming that C ≠ G. Recalling that, for such V, V ⟶ ( )^{V} , by (4.1) we infer that

V GC ⟶ V G^{V} C (10.5)

before a short vowel V′.

There is also a rule introducing a so-called furtive a at the end of a verb form:

V̄ G ⟶ V̄ aG before #, when V̄ is any long vowel. (10.6)

Furthermore, there is a rule which transforms the vowel i before a preliminary guttural-consonant combination:

iGC ⟶ \{ \begin{matrix}äGC & after ’ or h or in pattern 1 of stative verbs \\ aGC & otherwise, \end{matrix} (10.7)

assuming that C ≠ G.

It follows from (10.7) and (10.4) that

iGC ⟶ äGäC or aG^{a}C before V′ (10.8)

in the two cases respectively.

Which gutturals may occur in different places of a triliteral verb? One considers the following cases:

F = G = ’, h, \begin{matrix}h \\ . \end{matrix} or ‘,

with exceptions when ’ is quiescent or when \begin{matrix}h \\ . \end{matrix} is harsh.

M = G = ’, h, \begin{matrix}h \\ . \end{matrix}, ‘, r,

where r is perhaps pronounced as in Parisian French (see sec. 22q,r of [7]).

L = G = ‘ or \begin{matrix}h \\ . \end{matrix}

L = ’ is quiescent and L = h really stands for L = y or L = w, as we shall see in Section 14 below.

The letter \begin{matrix}h \\ . \end{matrix} is harsh in some exceptional verbs and can be followed by a consonant after all, as in the future yä\begin{matrix}h \\ . \end{matrix}šak “he will be dark” of the stative verb \begin{matrix}h \\ . \end{matrix}škaé “to be dark” or the future ya\begin{matrix}h \\ . \end{matrix}mod “he will be desired” of the active verb \begin{matrix}h \\ . \end{matrix}mdoa“to be desired”.

The letter ’ is always quiescent before # or constants, that is, it does not count as a consonant when applying rule (4.1). We postulate:

a’ ⟶ \{ \begin{matrix}ā’ & before # or ] \\ e’ & before C ≠ h \end{matrix} (10.9)

ā’, e’, é’ ⟶ ä’ before nāh (10.10)

Here are some sample calculations. First consider F = G, e.g. for V = ‘mdoa “to stand”.

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’i‘modQ_{1,1} ⟶_{(10.7)} ’ä‘modQ_{1,1} ⟶_{(10.5)} ’ä‘ämodQ_{1,1} ⟶ ’ä‘ämod

C_{6f,1,1}(V) ⟶ ⋯ ⟶ ta‘modQ_{6f,1} ⟶_{(10.5)} ta‘^{a}modQ_{6f,1} ⟶ ta‘^{a}modnāh

C_{1,1,2}(V) ⟶ P_{1,1}S_{1,2}(V)Q_{1,1} ⟶ ’S_{1,2}(V)Q_{1,1} ⟶ ’ni“āmédQ_{1,1} ⟶_{(6.4)} ’i“āmédQ_{1,1} ⟶_{(10.1)} ’e‘āmédQ_{1,1} ⟶ ’e‘āméd ⟶_{(4.3)} ’e‘āmed

C_{3m,2,3}(V) ⟶ P_{3m,2}S_{2,3}(V)Q_{3m,2} ⟶ hi‘m[ay]dQ_{3m,2} ⟶_{(10.8)} hä‘äm[ay]dQ_{3m,2} ⟶ hä‘äm[ay]d ⟶_{(6.8)} hä‘ämiyd

As an example of a weak verb with M = G, take V = brkaa “to bless”,

C_{1,1,5}(V) ⟶ P_{1,1}S_{1,5}(V)Q_{1,1} ⟶ ’ibarrekQ_{1,1} ⟶_{(6.5)} ’^{a}barrekQ_{1,1} ⟶_{(10.3)} ’^{a}bārekQ_{1,1} ⟶ ’^{a}bārek

C_{1,2,5}(V) ⟶ S_{2,5}(V)Q_{1,2} ⟶ birrékQ_{1,2} ⟶_{(10.1)} berékQ_{1,2} ⟶ beréktiy ⟶_{(4.3)} beraktiy

C_{1,1,6}(V) ⟶ ⋯ ⟶ ’iburrakQ_{1,1} ⟶_{(6.5)} ’^{a}burrakQ_{1,1} ⟶_{(10.2)} ’^{a}borakQ_{1,1} ⟶ ’^{a}borak 20 Lambek and Yanofsky

As an example of a weak verb with L = G, take V = šl\begin{matrix}h \\ . \end{matrix}aa “to send”.

C_{1,1,3}(V) ⟶ ⋯ ⟶ ’hašl[ey]\begin{matrix}h \\ . \end{matrix}Q_{1,1} ⟶_{(6.3)} ’ašl[ey]\begin{matrix}h \\ . \end{matrix}Q_{1,1} ⟶ ’ašl[ey]\begin{matrix}h \\ . \end{matrix}

⟶_{(6.7)} ’ašliy\begin{matrix}h \\ . \end{matrix} ⟶_{(10.6)} ’ašliya\begin{matrix}h \\ . \end{matrix}

C_{3m,2,3}(V) ⟶ ⋯ ⟶ hišliy\begin{matrix}h \\ . \end{matrix} ⟶_{(10.6)} hišliya\begin{matrix}h \\ . \end{matrix}

As an example of a weak verb in which L is a quiescent ’, take V = m\begin{matrix}s \\ . \end{matrix}’aa “to find”.

C_{1,1,1}(V) ⟶ ⋯ ⟶ ’äm\begin{matrix}s \\ . \end{matrix}a’ ⟶_{(10.9)} ’äm\begin{matrix}s \\ . \end{matrix}ā’

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tim\begin{matrix}s \\ . \end{matrix}a’nāh ⟶_{(10.10)} tim\begin{matrix}s \\ . \end{matrix}ä’nāh

C_{1,2,1}(V) ⟶ ⋯ ⟶ [mā\begin{matrix}s \\ . \end{matrix}a’]tiy ⟶_{(10.9)} [mā\begin{matrix}s \\ . \end{matrix}ā’]tiy ⟶_{(6.9)} mā\begin{matrix}s \\ . \end{matrix}ā’tiy

C_{1,1,2}(V) ⟶ ⋯ ⟶ ’ämmā\begin{matrix}s \\ . \end{matrix}é’ ⟶_{(4.3)} ’ämmā\begin{matrix}s \\ . \end{matrix}e’

C_{1,1,2}(V) ⟶ ⋯ ⟶ nim\begin{matrix}s \\ . \end{matrix}a’tiy ⟶_{(10.9)} nim\begin{matrix}s \\ . \end{matrix}e’tiy

C_{6f,1,3}(V) ⟶ ⋯ ⟶ tam\begin{matrix}s \\ . \end{matrix}e’nāh ⟶_{(10.10)} tam\begin{matrix}s \\ . \end{matrix}ä’nāh

In five exceptional verbs ’bdaā “to perish” (or “to lose”), ’bhaa “to be willing”, ’klaa “to eat”, ’mraa “to say” and ’phaa “to bake” F = ’ is quiescent. This affects the conjugational form but only for j = 1 (future) and k = 1 (qal).

i’C ⟶ \{ \begin{matrix}oC & after ’ \\ o’C & otherwise \end{matrix} (10.11) Here are some sample calculations for V = ’klaa, C_{1,1,1}(’klaa) ⟶ P_{1,1}S_{1,1}(’klaa)Q_{1,1} ⟶ ’iS_{1,1}(’klaa)Q_{1,1} ⟶ ’i’kalQ_{1,1}

⟶_{(10.11)} ’okalQ_{1,1} ⟶ ’okal C_{3f,1,1}(’klaa) ⟶ P_{3f,1}S_{1,1}(’klaa)Q_{3f,1} ⟶ tS_{1,1}(’klaa)Q_{3f,1} ⟶ ti’kalQ_{3f,1} ⟶_{(10.11)} to’kalQ_{3f,1} ⟶ to’kal

C_{6m,1,1}(’klaa) ⟶ P_{6m,1}S_{1,1}(’klaa)Q_{6m,1} ⟶ yS_{1,1}(’klaa)Q_{6m,1} ⟶ yi’kalQ_{6m,1} ⟶_{(10.11)} yo’kalQ_{6m,1} ⟶ yo’kaluw ⟶_{(4.1)} yo’k^{e}luw.

For j ≠ 1 or k ≠ 1, the regular conjugations will work. The other verbs with F = ’ quiescent are treated similarly, except that the two with L = h ( or rather L = y in line with Section 14) are doubly weak and fall under Section 16.

When one of the root letters is a guttural, the changes to the stem rewrite rules can be seen by looking at the guttural rules. Not every case requires a change. We have summarized which rewrites change in the following table. The table is split into two parts depending on which of the first two root letters is a guttural.

Table IIa Stem Rewrite Rules For Guttural Verbs

k Future S_{1,k}(V) Past S_{2,k}(V)

F=G

1  iGMα_{1}L  [GāMα_{2}L]
2  niGGāMéL ⟶_{(10.1)} neGāMéL  niGMaL
3 haGM[ey]L ⟶_{(10.4)} haGaM[ey]L  hiGM[ay]L
4  hȧGMaL ⟶_{(10.4)} hȧGȧMaL  hȧGMaL ⟶_{(10.4)} hȧGȧMaL
5  iGaMMeL  GiMMéL
6  iGuMMaL  GuMMaL
7  hit + GaMMéL  hit + GaMMéL

M=G

1  iF Gα_{1}L  [F āGα_{2}L]
2  niF F āGéL  niF GaL
3  haF G[ey]L  hiF G[ay]L
4  hȧF GaL  hȧF GaL
5  iF aGGeL ⟶_{(10.3)} iF āGeL  F iGGéL ⟶_{(10.1)} F eGéL
6  iF uGGaL ⟶_{(10.2)} iF oGaL  F uGGaL ⟶_{(10.2)} F oGaL
7 hit + F aGGéL ⟶_{(10.3)} hit + F āGéL hit + F aGGéL ⟶_{(10.3)} hit + F āGéL

The only changes when L = G depend on and must take account of the suffixes and cannot be summarized in our table.

11 Weak verbs with F = y or w

According to Weingreen, there are two types of verbs with F = y or F = w. The former occurs in the stative verb y\begin{matrix}t \\ . \end{matrix}baa“to be good” and requires the following phonological rules:

ay ⟶ ey (11.1)

hiy ⟶ hey (11.2)

Note that ’iy does not change.

F = w occurs only in patterns 2,3 and 4. It is replaced by F = y in patterns 5,6 and 7 (not discussed by Weingreen) and by F = (y) in pattern 1, where (y) is a potential y. An example is the verb (y)šbéa/wšb/yšb. We require the following phonological rules:

iw ⟶ ow except before w (11.3)

aw ⟶ ow except before w (11.4)

ȧw ⟶ uw (11.5)

i(y) ⟶ e (11.6)

#(y) ⟶ #y. (11.7)

Here are some sample calculations for V = y\begin{matrix}t \\ . \end{matrix}baa:

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’iy\begin{matrix}t \\ . \end{matrix}abQ_{1,1} ⟶ ’iy\begin{matrix}t \\ . \end{matrix}ab

C_{1,1,3}(V) ⟶ P_{1,1}S_{1,3}(V)Q_{1,1} ⟶ ’S_{1,3}(V)Q_{1,1} ⟶ ’hay\begin{matrix}t \\ . \end{matrix}[ey]bQ_{1,1}

⟶_{(6.3)} ’ay\begin{matrix}t \\ . \end{matrix}[ey]bQ_{1,1} ⟶_{(11.1)} ’ey\begin{matrix}t \\ . \end{matrix}[ey]bQ_{1,1} ⟶ ’ey\begin{matrix}t \\ . \end{matrix}[ey]b ⟶_{(6.7)} ’ey\begin{matrix}t \\ . \end{matrix}iyb

C_{6f,1,3}(V) ⟶ ⋯ ⟶ tay\begin{matrix}t \\ . \end{matrix}[ey]bQ_{6f,1} ⟶_{(11.1)} tey\begin{matrix}t \\ . \end{matrix}[ey]bQ_{6f,1}

⟶ tey\begin{matrix}t \\ . \end{matrix}[ey]bnāh ⟶_{(6.7)} tey\begin{matrix}t \\ . \end{matrix}ebnāh

Actually, Weingreen lists tey\begin{matrix}t \\ . \end{matrix}abnāh on page 268, but we cannot reconcile this with our rules. However, Gesenius on page 523 agrees with us. The following calculations are for the verb V = (y)šbéa/wšb/yšb “to sit” for patterns 1 / 2,3,4 / 5,6,7 respectively.

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’i(y)šébQ_{1,1} ⟶_{(11.6)} ’ešébQ_{1,1} ⟶ ’ešéb ⟶_{(4.3)} ’ešeb

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tešébQ_{6f,1} ⟶ tešébnāh ⟶_{(4.3)} tešabnāh

C_{1,1,2}(V) ⟶ P_{1,1}S_{1,2}(V)Q_{1,1} ⟶ ’S_{1,2}(V)Q_{1,1} ⟶ ’niwwāšéb ⟶_{(6.4)} ’iwwāšéb ⟶_{(4.3)} ’iwwāšeb

C_{1,2,2}(V) ⟶ S_{2,2}(V)Q_{1,2} ⟶ niwšabQ_{1,2} ⟶_{(11.3)} nowšabQ_{1,2} ⟶ nowšabtiy

C_{1,1,3}(V) ⟶ ⋯ ⟶ ’awš[ey]bQ_{1,1} ⟶_{(11.4)} ’owš[ey]bQ_{1,1} ⟶ ’owš[ey]b ⟶ ’owšiyb

C_{1,2,3}(V) ⟶ ⋯ ⟶ hiwš[ay]bQ_{1,2} ⟶_{(11.3)} howš[ay]bQ_{1,2} ⟶ howš[ay]btiy ⟶_{(6.8)} howšabtiy

C_{1,2,4}(V) ⟶ S_{2,4}(V)Q_{1,2} ⟶ hȧwšabQ_{1,2} ⟶_{(11.5)} huwšabQ_{1,2} ⟶ huwšabtiy

C_{1,1,5}(V) ⟶ ⋯ ⟶ ’^{a}yaššebQ_{1,1} ⟶ ’^{a}yaššeb

C_{1,2,5}(V) ⟶ ⋯ ⟶ yiššébQ_{1,2} ⟶ yiššébtiy ⟶_{(4.3)} yiššabtiy

12 Weak verbs with M = y or w

Most difficult among weak verbs are those whose middle radical y or w is unable to decide whether it is a consonant or a vowel. Weingreen discusses the following three examples: qwmoa, šyméa and kwn, the last not known in pattern 1.

To start with, we require the following rewrite rules:

iCwo ⟶ āC[uw] (12.1)

iCwé ⟶ āC[ey] (12.2)

iCwa ⟶ āC[ow] (12.3)

We have already discussed the symbol [ey] in Section 6 and we now introduce the following rules for evaluating [uw] and [ow].

[uw] ⟶ \{ \begin{matrix}o & before CC′ \\ uw & before CV̄ or C# \end{matrix} (12.4)

[ow] ⟶ \{ \begin{matrix}ȧ & before Ctäm \\ o & before CC′ otherwise \\ uw & before CV \\ ow & before CV̄ or C# \end{matrix} (12.5)

We can now make some sample calculations for V = qwmoa “to arise”.

C_{1,1,1}(V) ⟶ P_{1,1}S_{1,1}(V)Q_{1,1} ⟶ ’S_{1,1}(V)Q_{1,1} ⟶ ’iqwomQ_{1,1} ⟶_{(12.1)} ’āq[uw]mQ_{1,1} ⟶ ’āq[uw]m ⟶_{(12.4)} ’āquwm

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tāq[uw]mnāh ⟶_{(12.4)} tāqomnāh

At least, this is the form presented by Halkin, but Weingreen follows a different strategy for avoiding the impossible combination wmn and obtains t^{e}quwmāynāh instead. Calculating C_{6f,1,1}(V′) for V′ = šyméa “to place”, both authors obtain tāšemnāh, easily calculated with the help of our old rules for evaluating [ey], as well as the alternative form t^{e}šiymäynā. We will now discuss how the alternative forms are to be constructed. The following rules introduce so-called “buffer vowels” between two consonants C′ and C′′, hence we postulate: before C′′.

āC[uw]C′ ⟶^{e} CuwC′äy (12.6)

āC[ey]C′ ⟶^{e} CiwC′äy (12.7)

āC[ow]C′ ⟶^{e} CuwC′o (12.8)

āC[ay]C′ ⟶^{e} CiyC′ow (12.9)

To handle the past tense, we require furthermore:

āwa, āya ⟶ \{ \begin{matrix}ā & before CV̄ or C# \\ a & before CC′ \end{matrix} (12.10)

ewa ⟶ a before CC′ (12.11)

allowing us to calculate C_{1,2,1}(V) ⟶ S_{2,1}(V)Q_{1,2} ⟶ [qāwam]Q_{1,2} ⟶ [qāwam]tiy

⟶_{(6.9)} qāwamtiy ⟶_{(12.10)} qamtiy

C_{3m,2,1}(V) ⟶ ⋯ ⟶ qāwam ⟶_{(12.10)} qām

C_{5m,2,1}(V) ⟶ ⋯ ⟶ [qāwam]täm ⟶_{(6.9)} q^{e}wamtäm ⟶_{(12.11)} qamtäm

Similarly we obtain šamtiy, šām and šamtäm. To deal with the second pattern, we require another rule:

āwé ⟶ [ow]. (12.12)

We will now calculate C_{1,1,2}(V). But since V = qwmoa does not possess a passive, we replace it by V′ = kwn (the characteristic vowels being irrelevant.)

C_{1,1,2}(V′) ⟶ ⋯ ⟶ ’äkkāwén ⟶_{(12.12)} ’äkk[ow]n ⟶_{(12.5)} ’äkkown

C_{6f,1,2}(V′) ⟶ ⋯ ⟶ tikkāwénnāh ⟶_{(12.12)} tikk[ow]nnāh ⟶_{(12.5)} tikkonnāh

At least, this is Halkin’s result. Weingreen, unaccountably, omits this form.

C_{1,2,2}(V′) ⟶ S_{1,2}(V′)Q_{1,2} ⟶ nikwanQ_{1,2} ⟶_{(12.3)} nāk[ow]nQ_{1,2} ⟶ nāk[ow]ntiy ⟶_{(12.8)} n^{e}kuwnotiy

C_{3m,2,2}(V′) ⟶ ⋯ ⟶ nāk[ow]n ⟶_{(12.5)} nākown

C_{3f,2,2}(V′) ⟶ ⋯ ⟶ nāk[ow]nt ⟶_{(12.8)} n^{e}kuwnot

C_{4,2,2}(V′) ⟶ ⋯ ⟶ nāk[ow]nnuw ⟶_{(12.8)} n^{e}kuwnonuw

For the third and fourth pattern, we require new rewrite rules:

\begin{matrix}aCw & ⟶ & āC \\ iCw & ⟶ & eC \\ ȧCw & ⟶ & uwC \end{matrix} \} before [ey] or [ay] (12.13)

C_{1,1,3}(V) ⟶ P_{1,1}S_{1,3}(V)Q_{1,1} ⟶ ’S_{1,3}(V)Q_{1,1} ⟶ ’haqw[ey]mQ_{1,1} ⟶_{(6.3)} ’aqw[ey]mQ_{1,1} ⟶_{(12.13)} āq[ey]mQ_{1,1} ⟶ ’āq[ey]m ⟶_{(6.7)} ’āqiym

C_{6f,1,3}(V) ⟶ ⋯ ⟶ tāq[ey]mnāh ⟶_{(6.7)} tāqemnāh though Weingreen offers the alternative t^{e}qiymäynāh, which may be justified by (12.7).

C_{1,2,3}(V) ⟶ ⋯ ⟶ hiqw[ay]mQ_{1,2} ⟶_{(12.13)} heq[ay]mQ_{1,2} ⟶ heq[ay]mtiy ⟶_{(6.8)} heqamtiy where again Weingreen offers the alternative h^{a}qiymowtiy, although we would predict ( )^{e} instead of ( )^{a} by (12.8).

Computational Hebrew Conjugation 27 C_{6f,2,3}(V) ⟶ ⋯ ⟶ heq[ay]muw ⟶ heqiymuw C_{1,1,4}(V) ⟶ ⋯ ⟶ ’ȧqwamQ_{1,1} ⟶_{(12.13)} ’uwqamQ_{1,1} ⟶ ’uwqam C_{6f,1,4}(V) ⟶ ⋯ ⟶ tuwqamnāh C_{1,2,4}(V) ⟶ ⋯ ⟶ huwqamQ_{1,2} ⟶ huwqam C_{6f,2,4}(V) ⟶ ⋯ ⟶ huwqamuw ⟶_{(4.1)} huwq^{e}muw The pattern 5,6 and 7 for verbs with medial y or w were only used in late

biblical times. Due to a reluctance to double the medial y or w, the triliteral root qwmoa was replaced by the quadriliteral qwmm. See Section 8 above.

13 Weak verbs with M = (w), a potential w

The stative verbs m(w)taé“to die” and b(w)šao “to be ashamed” require special consideration. Here (w) denotes a potential w, to be distinguished from an actual w and subject to the following rewrite rules:

ā(w)o ⟶ [ow] (13.1) ā(w) ⟶ ∅ when not followed by o (13.2)

e(w) ⟶ ∅  before ȧ  (13.3)
(w) ⟶ w  otherwise.  (13.4)

Here are some sample calculations: C_{1,1,1}(V) ⟶ ⋯ ⟶ ’im(w)atQ_{1,1} ⟶ ’ām(w)atQ_{1,1} ⟶ ’āmwatQ_{1,1}

⟶ ’ām[uw]tQ_{1,1} ⟶ ’ām[uw]t ⟶_{(12.4)} ’āmuwt

C_{6f,1,1}(V) ⟶ ⋯ ⟶ tām[uw]tnāh ⟶_{(12.4)} tāmotnāh with an alternative t^{e}muwtäynāh by (12.6).

28 Lambek and Yanofsky

C_{1,2,1}(V) ⟶ S_{2,1}(V)Q_{1,2} ⟶ [mā(w)ét]Q_{1,2} ⟶ [mā(w)ét]tiy ⟶_{(6.9)} mā(w)éttiy ⟶_{(13.2)} méttiy ⟶_{(4.3)} mattiy

C_{3m,2,1}(V) ⟶ ⋯ ⟶ mā(w)ét ⟶_{(13.2)} mét ⟶_{(4.3)} met C_{6f,2,1}(V) ⟶ ⋯ ⟶ mā(w)étuw ⟶_{(13.2)} métuw ⟶_{(4.3)} metuw Pattern 2 does not exist for m(w)taé. For patterns 3 and 4, we adopt the

rules:

aC(w) ⟶ āC

iC(w) ⟶ eC  before [ey] or [ay]

uC(w) ⟶ uwC

(13.5)

C_{1,1,3}(V) ⟶ ⋯ ⟶ ’am(w)[ey]tQ_{1,1} ⟶_{(13.5)} ’ām[ey]tQ_{1,1} ⟶ ’ām[ey]t ⟶_{(6.7)} ’āmiyt

C_{6f,1,3}(V) ⟶ ⋯ ⟶ tām[ey]tnāh ⟶_{(6.7)} tāmetnāh with the alternative t^{e}miytäynāh by (12.7).

C_{1,2,3}(V) ⟶ ⋯ ⟶ him(w)[ay]tQ_{1,2} ⟶_{(13.5)} hem[ay]tQ_{1,2} ⟶ hem[ay]ttiy ⟶_{(6.8)} hemattiy

C_{6f,2,3}(V) ⟶ ⋯ ⟶ hem[ay]tuw ⟶_{(6.8)} hemiytuw C_{1,1,4}(V) ⟶ ⋯ ⟶ hum(w)atQ_{1,2} ⟶_{(13.5)} huwmatQ_{1,2} ⟶ huwmattiy

C_{6f,2,4}(V) ⟶ ⋯ ⟶ huwmatuw ⟶_{(4.1)} huwm^{e}tuw To obtain patterns 5 and 6, we must replace the triliteral m(w)taé by the

quadrilitiral mwtt.

Next, consider V = b(w)šao. Then we calculate:

C_{1,1,1} ⟶ ⋯ ⟶ ’ib(w)ašQ_{1,1} ⟶_{(13.1)} ’eb[ow]šQ_{1,1} ⟶ ’eb[ow]š ⟶_{(12.5)} ’ebowš

C_{6f,1,1}(V) ⟶ ⋯ ⟶ teb[uw]šnāh ⟶_{(12.4)} tebošnāh

C_{1,2,1}(V) ⟶ ⋯ ⟶ bā(w)ošQ_{1,2} ⟶ b[ow]šQ_{1,2} ⟶_{(13.1)} b[ow]štiy ⟶_{(12.5)} boštiy

C_{3m,2,1}(V) ⟶ ⋯ ⟶ [bā(w)oš]Q_{5m,2} ⟶ [bā(w)oš]täm ⟶_{(6.9)} b^{e}(w)ȧštäm ⟶ b^{e}(w)ȧštäm ⟶ bȧštäm

14 Weak verbs with L = y or w

As already mentioned, the traditional L = h should really be treated as L = y or w. For example, consider V = qlyéa. The easiest way to describe the conjugation of these verbs is by revising Table II above as follows:

Table IIb Stem Rewrite Rules for L = y or w

k Pattern Future S_{1,k}(V)  Past S_{2,k}(V)
1  qal  iF M[äy]  [F āM[iy]]
2 niph‘al  niF F āM[äy]  niF M[iy]
3 hiph‘il  hiF M[äy]  hiF M[iy]
4 hoph‘al  hȧF M[äy]  hȧF M[iy]
5 pi‘el  iF aMM[äy]  F iMM[iy]
6 pu‘al  iF uMM[äy]  F uMM[iy]
7 hitpa‘el hit + F aMM[äy] hit + F uMM[iy]

where

[äy] ⟶ \{ \begin{matrix}∅ & before a long vowel \\ äh & before # \\ äy & before nāh \end{matrix} (14.1) and

[iy] ⟶ \{ \begin{matrix}∅ & before uw \\ ^{e}t & before āh \\ āh & before # \\ iy & otherwise \end{matrix} (14.2) When k = 3 to 7, iy may or must be replaced by ey; see Weingreen pages

218 to 220 for details .

Sample calculations for V = glyéa : C_{1,1,1}(V) ⟶ ⋯ ⟶ ’ägläh C_{2f,1,1}(V) ⟶ ⋯ ⟶ tigl[äy]iy ⟶_{(14.1)} tigliy C_{6f,1,1}(V) ⟶ ⋯ ⟶ tigl[äy]nāh ⟶_{(14.1)} tigläynāh C_{1,2,1}(V) ⟶ ⋯ ⟶ gā[iy]tiy ⟶_{(14.2)} gāliytiy C_{3m,2,1}(V) ⟶ ⋯ ⟶ gāl[iy] ⟶_{(14.2)} gālāh C_{3f,2,1}(V) ⟶ ⋯ ⟶ gāl[iy]āh ⟶_{(14.2)} gāl^{e}tāh C_{6f,2,1}(V) ⟶ ⋯ ⟶ gāl[iy]uw ⟶_{(14.2)} gāluw C_{5m,2,1}(V) ⟶ ⋯ ⟶ [gāl[iy]]täm ⟶_{(14.2)} [gāliy]täm ⟶_{(6.9)} g^{e}liytäm

15 Weak verbs with M = L

The so-called “doubled” verbs with M = L give rise to a number of complications. Weingreen treats two examples: the active verb sbboa and the stative verb qllaa, the former only in patterns 1,2 and 3, the latter only in pattern 1. Are we to infer that then verbs are regular in patterns 5,6 and 7?

Let us consider V = sbboa. A straight forward calculation would yield C_{1,1,1}(V) ⟶ ’äsbob. It is difficult to see why this form was not acceptable to the ancient Hebrews, but apparently it was not. In fact, Weingreen offers two alternatives for C_{1,1,1}(V), namely ’āsob and ’ässob. The second form suggests that we are dealing with a different verb altogether, namely ssboa with M = F. Perhaps the verb in question originally had only two radicals and the doubling of M was merely a device to force it into the triliteral straightjacket. The second alternative seems to be acceptable for the entire future of pattern 1, and its conjugation is quite regular. For the first alternative, which applies also to the past of pattern 1 and to both tenses of patterns 2,3 and 4, the easiest way is to rewrite Table II as follows:

Table IIc Stem Rewrite Rules for M = L

k Pattern Future S_{1,k}(V) Past S_{2,k}(V)
1 qal āF α_{1}(MM) F α_{2}(MM)
2 niph‘al niF F a(MM) nāF a(MM)
3 hiph‘il hāF e(MM) heF e(MM)
4 hoph‘al huwF a(MM) huwF a(MM)

where

(CC) ⟶ \{ \begin{matrix}C & before # \\ CC & before a long vowel \\ CCäy & before nāh \\ CCow & otherwise \end{matrix} (15.1)

The äy and ow serve as long buffer vowels.

We present some sample calculations for V = sbboa, but with some question marks that will require an explanation.

32 Lambek and Yanofsky C_{1,1,1}(V) ⟶ ⋯ ⟶ ’āso(bb) ⟶_{(15.1)} ’āsob C_{6f,1,1}(V) ⟶ ⋯ ⟶ tāso(bb)nāh ⟶_{(15.1)} tāsobbäynāh ⟶^{?} t^{e}subbäynāh

C_{1,2,1}(V) ⟶ ⋯ ⟶ sa(bb)tiy ⟶_{(15.1)} sabbowtiy C_{3m,2,1}(V) ⟶ ⋯ ⟶ sa(bb) ⟶_{(15.1)} sab C_{6f,2,1}(V) ⟶ ⋯ ⟶ sa(bb)uw ⟶_{(15.1)} sabbuw C_{1,1,2}(V) ⟶ ⋯ ⟶ ’ässa(bb) ⟶_{(15.1)} ’ässab C_{3m,1,2}(V) ⟶ ⋯ ⟶ yissa(bb) ⟶_{(15.1)} yissab C_{6f,1,2}(V) ⟶ ⋯ ⟶ tissa(bb)nāh ⟶_{(15.1)} tissabbäynāh C_{1,2,2}(V) ⟶ ⋯ ⟶ nāsa(bb)tiy ⟶_{(15.1)} nāsabbowtiy ⟶^{?} n^{e}sabbowtiy

C_{3m,2,2}(V) ⟶ ⋯ ⟶ nāsa(bb) ⟶_{(15.1)} nāsab C_{6f,2,2}(V) ⟶ ⋯ ⟶ nāsa(bb)uw ⟶_{(15.1)} nāsabbuw C_{1,1,3}(V) ⟶ ⋯ ⟶ ’āse(bb) ⟶_{(15.1)} ’āseb C_{6f,1,3}(V) ⟶ ⋯ ⟶ tāse(bb)nāh ⟶_{(15.1)} tāsebbäynāh ⟶^{?} t^{e}sibbäynāh

C_{1,2,3}(V) ⟶ ⋯ ⟶ hese(bb)tiy ⟶_{(15.1)} hesebbowtiy ⟶^{?} h^{a}sibbowtiy C_{3m,2,3}(V) ⟶ ⋯ ⟶ hese(bb) ⟶_{(15.1)} heseb

C_{1,1,4}(V) ⟶ ⋯ ⟶ ’uwsa(bb) ⟶_{(15.1)} ’uwsab

C_{6f,1,4}(V) ⟶ ⋯ ⟶ tuwsa(bb)nāh ⟶_{(15.1)} tuwsabbäynāh

C_{1,2,4}(V) ⟶ ⋯ ⟶ huwsa(bb)tiy ⟶_{(15.1)} huwsabbowtiy

C_{3m,2,4}(V) ⟶ ⋯ ⟶ huwsa(bb) ⟶_{(15.1)} huwsab

C_{6f,2,4}(V) ⟶ ⋯ ⟶ huwsa(bb)nāh ⟶_{(15.1)} huwsabbäynāh

The question marks in the above calculations indicate a missing explanation for the change of the two vowels before the long buffer vowels is reached. The problem is that our system does not take the accent of the vowel into account. We can fix the problem but our solution seems a bit ad hoc. We are forced to adopt the following awkward revisions:

\begin{matrix}āF oMM & ⟶ & ^{e}F uMM \\ āF aMM & ⟶ & ^{e}F aMM \\ āF eMM & ⟶ & ^{e}F iMM \\ eF eMM & ⟶ & ^{a}F iMM \end{matrix} \} before a long buffer vowel äy or ow (15.2)

What is the rationale behind these revisions? First, the initial vowel must be shortened when too far removed from the stressed syllable, and so ā ⟶^{e}, and e ⟶^{a}. Second, as we have already noticed, when unstressed, o ⟶ u and e ⟶ i before CC. We had hoped that the verb V′ = qllaa “to be light” would be covered by the same rules. Unfortunately, we cannot explain why C_{1,1,1}(V′) ⟶ ’eqal rather than ’āqal as expected, except by modifying Table IIc accordingly.

16 Doubly weak verbs

Doubly weak verbs are verbs that have two radicals that are weak. Its seems that one has to work with the rules of each radical one at a time. All our examples worked by applying the rules from left to right.

We begin with the verb that starts with an assimilative F = (n) and concludes with a guttural L = ‘. The verb is V = (n)g‘aa “to touch”.

C_{1,2,1}(V) ⟶ ⋯ ⟶ [(n)āga‘]Q_{1,2} ⟶_{(6.9)} (n)āga‘Q_{1,2} ⟶_{(9.2)} nāga‘Q_{1,2} ⟶ nāga‘tiy

C_{3f,1,1}(V) ⟶ ⋯ ⟶ ti(n)ga‘Q_{3f,1} ⟶_{(9.1)} tigga‘Q_{3f,1} ⟶ tiygga‘Q_{3f,1} ⟶ tiygga‘

C_{3f,1,3}(V) ⟶ ⋯ ⟶ tha(n)g[ey]‘Q_{3f,1} ⟶_{(6.3)} ta(n)g[ey]‘Q_{3f,1} ⟶ tagg[ey]‘Q_{3f,1} ⟶ tagg[ey]‘ ⟶_{(6.8)} taggiy‘ ⟶_{(10.6)} taggiya‘

C_{6f,2,3}(V) ⟶ ⋯ ⟶ hi(n)g[ay]‘Q_{6f,2} ⟶_{(9.1)} higg[ay]‘Q_{6f,2} ⟶ higgiy‘Q_{6f,2} ⟶ higgiy‘uw

Another doubly weak verb is V = (n)ś’aa “to raise”. We require a new rule supplementing (4.1):

a ⟶ ā before ’. (16.1)

C_{1,1,1}(V) ⟶ ⋯ ⟶ ’i(n)śa’Q_{1,1} ⟶_{(6.5)} ’ä(n)śa’Q_{1,1} ⟶_{(9.1)} ’äśśa’Q_{1,1} ⟶ ’äśśa’ ⟶_{(15.2)} ’äśśā’

C_{1,2,1}(V) ⟶ ⋯ ⟶ [(n)āśa’]Q_{1,2} ⟶_{(6.9)} (n)āśa’Q_{1,2} ⟶_{(9.2)} nāśa’Q_{1,2} ⟶ nāśa’tiy ⟶_{(15.2)} nāśā’tiy

C_{2m,2,2}(V) ⟶ ⋯ ⟶ ni(n)śa’Q_{2m,2} ⟶_{(9.1)} niśśa’Q_{2m,2} ⟶_{(10.9)} niśśe’Q_{2m,2} ⟶ niśśe’tā

Now let us calculate a doubly weak verb with F = (y)/w. The verb is V = (y)d‘aa/wd‘aa“to know”.

C_{3f,1,1}(V) ⟶ ⋯ ⟶ ti(y)da‘Q_{3f,1} ⟶_{(11.6)} teda‘Q_{3f,a} ⟶ teda‘

C_{3f,1,2}(V) ⟶ ⋯ ⟶ tniwwādé‘ ⟶_{(6.4)} tiwwādé‘ ⟶_{(4.3)} tiwwāda‘

C_{3f,1,7}(V) ⟶ ⋯ ⟶ thit+waddé‘ ⟶_{(6.3)} tit+waddé‘ ⟶_{(6.6)} titwaddé‘ ⟶_{(4.3)} titwadda‘

And finally, let us do one calculation where both the first and last radicals are gutturals. V = ‘lhaa “to ascend”.

C_{3f,1,3}(V) ⟶ ⋯ ⟶ tha‘l[ey]h ⟶_{(6.3)} ta‘l[ey]h ⟶_{(10.5)} ta‘^{a}l[ey]h ⟶_{(6.7)} ta‘^{a}liyh. But Weingreen has this as ta‘^{a}läh. So, what is wrong here? According to Section 14, the final h should presumably be replaced by y; but this won’t help. One solution is to suppliment (6.7) by

[ey] ⟶ ä before h. (16.2)

There are many more examples that can be easily calculated. However there is not much to gain from going on. We have not found any great surprises. There are two reasons why doubly weak verbs do not seem so hard. First, all the examples that Weingreen describes have a weakness in the first radical and the third radical. Not the second radical. Hence, the second radical separates the two weak radicals. This separation ensures that the different rules do not effect each other. Second, all the examples that Weingreen deals with have the last radical as a guttural. As we have seen, since the last radical is never doubled, there are not many rules that apply to that guttural.

17 Conclusion and a comparison with Arabic

We have shown how the finite forms of the regular verbs can be calculated with the help of certain rewriting rules, embedded in the conjugation formula of Section 6 and tables I and II, together with a few phonological rules. We have also shown how the finite forms of the so-called “weak” verbs can be calculated in the same way, using additional phonological rules. We are not entirely satisfied with our effort, for the following reasons.

• We have ignored the non-finite forms of the verb and the modifications necessary when pronominal suffixes are added.

• The ultimate phonological rules should apply not only to the verb, but to other aspects of biblical Hebrew morphology as well.

• We had started ignoring stress, but were forced to incorporate it into two of our rules, namely (6.8) and (9.3), and to mention it parenthetically after (10.3) and after (15.2).

• The final modifications contained in (15.2) and (16.1) suggest that there are still gaps in our account.

Hebrew resembles Arabic [2] even more closely than English resembles German. For example, a typical verb in both Semitic languages is completely described by three consonants and two vowels. Although classical Hebrew was written down about a thousand years before classical Arabic, its inflectional grammar is much simpler. Like English, it has replaced the cases of the nouns by prepositions and has undergone erosion of many conjugational forms.

Where modern standard Arabic has potentially 18 different patterns, 10 active and 8 passive for each verb, standard Hebrew has only seven^{17}. We would therefore expect the computational treatment of Hebrew verbs to be much simpler then that of Arabic ones. Unfortunately, this is not the case, because written Arabic presumably records only phonemes, whereas written Hebrew records either no vowel phonemes or, according to the Masoretic tradition, numerous vowel allophones, which we found difficult to ignore. Hopefully, our approach can also be applied to the pre-Masoretic text, if one starts with the three vowel phonemes a, i and u.

18 Appendix: Waw Conjunctions

Many of the verbs in the Bible start with “and”. To write “and” in Hebrew, one prefixes a verb (most of the rules below work for nouns also) with a w. Biblical Hebrew makes use of a strange convention^{18}: if two sentences in a continuous narrative both refer to the past (future), then only the first verb is expressed in this tense, while the second is expressed in the future (past) tense preceded by a waw. This works for more than two verbs by continually switching back and forth. The waw switches the tenses.

w + C_{i,j,k}(V) ⟶ wC_{i,3−j,k}(V) (18.1)

Such a waw is called a “waw consecutive” (also called “waw conversive”).

Punctuating a verb with a w prefix conforms to the following rules:

w + C ⟶ \{ \begin{matrix}w^{e}C & If the verb is past \\ waCC & If the verb is future where C ≠ ’ \\ wāC & If the verb is future where C = ’ \end{matrix} (18.2)

The third case is actually a specialization of rule (10.3) that deals with gutturals.^{19}

For the first rule we have further changes. If the first letter of the word has a shewa, then we change the first shewa into a shuriq:

w^{e}C^{e} ⟶ wuC^{e} where C ≠ b, m, p, y. (18.3)

Before labials b, m, p, the w also takes a shuriq:

w^{e}L ⟶ wuL where L = b, m, p. (18.4)

Before a y^{e}, the w takes the h.ireq and the y loses its shewa:

w^{e}y^{e} ⟶ wiy. (18.5)

Before a composite shewa, the w takes the corresponding short vowel:

w^{e}Cä ⟶ wäCä. (18.6)

w^{e}Cā ⟶ wāCā. (18.7)

w^{e}C^{a} ⟶ waC^{a}. (18.8)

Notes

1 With some stretch of the imagination, the connection between these two concepts can be seen in English also. A man who demands honor does “not take himself lightly.”

2Judges 12. As far as we know, the distinction between š and ś is not explained by any phonetic rule, but that between b and b^{h} is.

3See Gesenius Section 7a.

4According to [3], the main reason for the Masoretic enterprise was to ensure that these attached consonants do not make their way into the sacred texts. They are used to represent vowels in written Yiddish.

5There are two other Masoretic traditions: Babylonian and Yemenite. They have different symbols and different conventions. For example, they make no distinction between a (patach) and ä (segol). We shall only deal with the more commonly used Tiberian system.

6There has been much variation in pronunciation even after the introduction of the Masoretic symbols. Within the last two centuries, the Hasidic pronunciation has varied widely from the “standard” Ashkenazi pronunciation from which it sprang. Hasidim are in the habit of effectively adding a consonant y after every e (\begin{matrix}S \\ . \end{matrix}ere). So they go from sefär to seyfär. Their pronunciation of T orāh is T oyrāh.

7Within classical Rabbinic Judaism, there is some discussion about the Talmud not having the exact (consonant) spelling of certain words (e.g., Babylonian Talmud Kiddushin 30a). Furthermore, Rabbi Akiva Eiger Guenz (1761-1835) gives a list of places where the Rabbinic tradition of the Bible text conflicts with our accepted text op. cit. Babylonian Talmud Saabath 55b. See also Nedarim 38a. There is much discussion on the varieties of “the” Masoretic text and the elasticity of the text in the passing millennia. One imagines that this uncertainty would extend from written consonants to the unwritten vowel pronunciation. c.f. Nehemiah 8:8. We shall not go into this.

8 The traditional names of the short vowels are:

pata\begin{matrix}h \\ . \end{matrix}

segol  qāme\begin{matrix}s \\ . \end{matrix} − katan
\begin{matrix}s \\ . \end{matrix}ere  \begin{matrix}h \\ . \end{matrix}olem
\begin{matrix}h \\ . \end{matrix}ireq  qibbus

The names of the long vowels are:

qāmes. − gadol
\begin{matrix}s \\ . \end{matrix}ere − yud  \begin{matrix}h \\ . \end{matrix}olem
\begin{matrix}h \\ . \end{matrix}ireq − yud  šureq

9Denoting the silent shewa as ^{s} and the mobile/vocalic shewa as ^{m}, we might write some of the easier rules as follows: A. In the middle of a word, when there are two shewas in a row, the first one is a silent shewa and the second one is a mobile one:

CV X^{e}X^{′e}C′ ⟶ CV X^{s}X^{′m}C′.

B. When a shewa is under a doubled letter(usually indicated by a dot=dagesh), then the above rule applies:

X^{e}· = X^{e}X^{e} ⟶ X^{s}X^{m}.

C. After a long vowel, the syllable is over and the following shewa is a mobile/vocalic shewa starting the next syllable. In contrast, after a short vowel, the following shewa is finishing that syllable and hence is a silent shewa:

CV̄ X^{e} ⟶ CV̄ X^{m} where V̄ = ā, ey, iy, uw, ow
CV X^{e} ⟶ CV X^{s} where V = a, ä, ȧ, i

10One of the most surprising facts about Hebrew grammar is how late the triliteralness of Hebrew words was recognized. Although this seems obvious to us, it was not known until Yehuda ibn David Hayyuj (940 - 1010) wrote of it. It seems Rashi (1040 - 1105), the “first of the commentators”, was not aware of this or not convinced of it. For Rashi, words might have three literal roots (e.g., Exodus 23:27, Deuteronomy 12:30, Deuteronomy 32:26), but more commonly two letter roots (e.g., Genesis 2:19, Genesis 3:15, Numbers 22:32) and even one letter roots (e.g., Numbers 21:11).

11This categorization exists in Arabic also.

12There are actually many other less common patterns found in the Bible. Some are more common in Mishnaic, medieval, and modern Hebrew. There are: po‘el, hitpo‘el; pa‘lel, hitpa‘lel; p^{e}‘al‘al; pilpel, hitpilpel; tiph‘el; šaph‘el as well as several others.

13The only exception to the first case we have found is w^{e}hitšo\begin{matrix}t \\ . \end{matrix}a\begin{matrix}t \\ . \end{matrix}nāh (Jeremiah 49:3) avoiding three t-sounds in close proximity.

14Weingreen is following a long tradition of using this word. K .imh.i uses the more peaceful verb pqdoa “to visit”; but q\begin{matrix}t \\ . \end{matrix}loa has the advantage of being similar in other Semitic languages and so is used in comparative linguistics. It has the disadvantage of not being found that often in the Hebrew Bible (only Psalms 139:14; Job 13:15; Job 24:14 c.f. Obadiah 1:9.). Its Aramaic equivalent occurs seven times in Daniel.

15Some of the more interesting five-letter nouns are:

• šalhābät “flame” (Job 15:30 and Canticles 8:6). Most scholars take this to be a case of a conjugation of the word lāb by a very strange šaph‘el pattern.

• \begin{matrix}s \\ . \end{matrix}^{e}pardde‘a “frog” (Exodus Chaps 7 and 8, Psalms 78:45, 105:30).

• \begin{matrix}h \\ . \end{matrix}^{a}ba\begin{matrix}s \\ . \end{matrix}\begin{matrix}s \\ . \end{matrix}älät “a lily” or “a meadow saffron” (Canticles 2:1, Isaiah 35:1)

• \begin{matrix}s \\ . \end{matrix}almāwät “shadow of death” (e.g. Psalms 23:4, Amos 5:8, Job 12:22). This is usually seen as a composite word.

16In contrast, Arabic does allow a doubling of a guttural which makes the language significantly harder for a non-native speaker to pronounce.

17See however footnote 12.

18According to Gesenius [7] page 132, this is one of the most “striking peculiarities” even within the family of Semitic languages. Phoenician is one of the only other Semitic languages that has anything similar.

19Some exceptions to the third case are wa’^{a}gāreš (in fact, some bibles do have it as wā’^{a}gāreš) (Judges 6:9), wa’^{a}mottehuw (2Samuel 1:10), and wa’^{a}kasek (Ezekiel 16:10).

References

[1] Bargelli, D. and Lambek, J. “A Computational View of Turkish Conjugation.” Lingustic Analysis 29 (1999), 248-256.

[2] Bargelli, D. and Lambek, J. “A Computational Approach to Arabic Conjugation.” Lingustic Analysis 30 (2001/2002), 1-22.

[3] Chomsky, William. “The history of our vowel-system in Hebrew,”Jewish Quarterly Review, 32,(1941), 27-49.

[4] Chomsky, William. Hebrew: The Eternal Language, Jewish Publication Society of America (1958).

[5] Chomsky, William. “The pronunciation of the shewa,”Jewish Quartely Review, 62, (1971), 88-94.

[6] Chomsky, William. David K .imh.i’s Hebrew Grammar (Mikhlol), Bloch Publishing Company, (2001 edition).

[7] Gesenius, William and Kautzsch, Emil (ed.), Gesenius’ Hebrew Grammar, translated from German by A. E. Cowley, Oxford, Oxford University Press, 1985.

[8] Halkin, Abraham S. 201 Hebrew Verbs. Barron’s Educational Series, Woodbury, N.Y. 1970.

[9] Lambek, J, “A Mathematician Looks at Latin Conjugation.” Theoretical Linguistics 6 (1979), 221-234.

[10] Sáenz-Badillos, Angel. A History of the Hebrew Language (Translated by John Elwolde), Cambridge University Press (1993).

[11] Weingreen, J, A Practical Grammar for Classical Hebrew, Second Edition, Oxford, Oxford University Press, 1959.

19 Postscript

After we completed this article in March 2005, two recent articles dealing with Hebrew morphology were brought to our attention:

[12] R. Finkel and G. Stump, “Generating Hebrew verb morphology by default inheritance hierarchies”, University of Kentucky, preprint.

[13] S. Yona and S. Wintner, “A finite-state morphological grammar of Hebrew”, to appear in Natural Language Engineering 1, received May 2006.

Both papers offer interesting but different computational approaches to Hebrew verb morphology, although to a smaller extent and in less details than ours, which ultimately goes back to Panini and incorporates insights of medieval grammarians.

J. Lambek Department of Mathematics and Statistics McGill University 805 Sherbrooke Street West Montreal, QC, Canada H3A 2K6 email: lambek@math.mcgill.ca

Noson S. Yanofsky Department of Computer and Information Science Brooklyn College, CUNY Brooklyn, N.Y., U.S.A. 11210 email: noson@sci.brooklyn.cuny.edu