Hapax Legomena and the Productivity of the Old English Weak Verb Suffixes

The aim of this article is to measure the productiv ity of the Old English weak verb suffixes -ettan, -læcan, -sian, -nian, -lian, -erian and -cian from a synchronic point of view by taking into account the role played by hapa x legomena. Productivity in the narrow sense P and global productivity P* are measured and frequency is calculated in terms of type and token. Three types of hapax legom ena are distinguished, namely absolute hapaxes (unique formations that appear in one text), relative hapaxes (formations that appear in different texts, but onl y once in each text) and mixed hapaxes (a subsumption of both types). This typology of hap axes puts the focus on sian, -erian, -lian and -cian, which range between very low and zero productivit y.


Introduction
This article engages in Old English word-formation.More precisely, it focuses on the weak verb suffixes -ettan, -laecan, -sian, -nian, -lian, -erian and -cian and aims at assessing their morphological productivity from a synchronic point of view.To fulfill this goal, a combined study of dictionary and corpus data is conducted that produces descriptive and methodological conclusions related to the relative and absolute indexes of productivity of the affixes as well as the assessment of productivity in a historical language.
The topics of Old English word-formation and lexical semantics have drawn a remarkable amount of attention recently.Kastovsky (1986Kastovsky ( , 1989Kastovsky ( , 1990Kastovsky ( , 1992Kastovsky ( , 2005Kastovsky ( , 2006) ) describes the main units and processes involved in Old English word-formation and identifies a typological change in the lexicon from stem-based morphology to word-based morphology.In a more theoretical approach, Martín Arista (2008, 2009, 2011a) lays the foundations of a theory of derivational morphology compatible with functional models and applies it to Old English in general and, more specifically, to zero derivation (Martín Arista 2011c), lexical layers (Martín Arista 2011b), morphological recursivity (Martín Arista 2010a, 2010b, 2013a) and derivational paradigms (Martín Arista 2010c, 2012, 2013b).On the specific question of morphological productivity, Author 2 (2011,2012) and Mateo Mendaza (2012Mendaza ( , 2014) ) concur on the necessity of combining textual and lexicographical sources as well as on the importance of checking statistical analyses against qualitative judgements on the grammaticalisation or loss of the affixes at stake.Apart from these works, the question of the quantitative assessment of the morphological productivity of Old English wordformation has been addressed by Trips (2009) and Haselow (2010), who do not discuss the lexical category of the verb and, moreover, opt for a more absolute approach than the one adopted in this research.
Considering this background, the article is organised as follows.Section 2 raises the question of how to measure productivity in a historical language, with special emphasis on low indexes.Section 3 establishes the methodological and theoretical underpinnings of this work, including the relevant sources, the treatment of the data and the formulae of productivity.Then, section 4 presents the results of the frequency and productivity analysis and discusses the different accounts of productivity obtained on the basis of a typology of hapaxes that distinguishes absolute, relative and mixed hapax legomena.Finally, section 5 offers a summary and the main methodological and descriptive conclusions.

Measuring productivity in a historical language
The topic of productivity has recently been debated within the area of morphological theory.This is probably the case because productivity constitutes, in several respects, the meeting point of lexicology, inflectional morphology and derivational morphology.Indeed, the studies on productivity by Bauer (2004Bauer ( , 2005)), Baayen (1992Baayen ( , 1993Baayen ( , 1994Baayen ( , 2009)), Plag (1999Plag ( , 2003) ) and Rainer (2005), among others, highlight the complex character of this phenomenon, which comprises, at least, the following aspects: (1) the relationship between the likelihood that a certain morphological process becomes operational and the establishment and spread of neologisms; (2) the limits between derivation and inflection as reflected by the use of two types of sources, namely lexicographical (dictionaries containing lemmatised forms) and textual (corpora displaying unlemmatised forms); (3) the relative and absolute measure of the productivity of a certain process; and (4) the impact of the number of hapax legomena or unique formations on the overall index of productivity.
While the assessment of productivity in natural languages constitutes a challenging exercise, historical languages face further problems related to the fragmentary nature of the written records, which often results in a lack of sufficient representative data or reliable linguistic material.Moreover, as linguists like Kastovsky (1992) and Lass (1994) have put forward, an account of the productivity of a historical language poses three main problems.First, there is no direct way of testing productivity; we have to rely on indirect evidence such as the number of occurrences in a text or the continuity of a given process of word-formation.Second, productivity and transparency can vary diachronically.In Kastovsky's (1992: 357) words, "when one has to deal with a linguistic period such as Old English, stretching over some 600 years, there are bound to have been many changes.Only the output of the patterns recorded in the later documents is available for study."This goes in the line of Lass (1994: 193), who remarks that it is difficult to determine whether a given occurrence of a derived form represents an institutionalised lexical item or not, or whether it is a new formation.And third, when a given wordformation process loses its productivity, it may leave at least some of its output as part of the vocabulary.
In recent times, new approaches have tried to overcome the first problem recognized by Kastovsky.Säily and Suomela have developed a series of software programs that allow the direct observation of types and hapaxes.By using Suomela's (2007) Types 1 tool, random permutations of the elements under study can be done, thus identifying the upper and lower bounds for each significance level.This software, and its second version (Types 2) have been successfully applied in studies by Säily andSuomela (2009), Säily (2011) and Gardner (fc.)In the framework of a historical language, the morphological productivity of a word-formation process has to make reference to the number of attested types and tokens produced by the process in question.This calls for a reflection on the relative character of the concepts of type and token, which, moreover, refers us to the relationship between inflectional and derivational morphology.It has to be determined, in other words, if lemmatised types can be distinguished from unlemmatised types, in such a way that a given lemmatised type in the dictionary corresponds to a number of unlemmatised types (forms from the inflectional paradigm of the type) each of which has a number of occurrences (tokens) in texts.
As part of the effort to enlarge and improve the methodology for the assessment of productivity in a historical language, it is also necessary to pay special attention to low productivity indexes, that some of the affixes under analysis happen to display, and to reconsider the role played by hapax legomena in the calculation of the indexes.Beginning with the former question, Fernández-Domínguez et al. (2007) hold that there is a tendency in word-formation research to focus on high productivity measures to the exclusion of low indexes of productivity.Fernández-Domínguez et al. (2007: 35) distinguish three major models of productivity assessment: (1) frequency models, which centre on type frequency, token frequency and relative frequency; (2) probabilistic models, which concentrate on productivity in the narrow sense, global productivity and the degree of productivity based on the count of hapax legomena; and (3) Štekauer's (2005) onomasiological model, in which word-formation patterns are regular, predictable and productive.Fernández-Domínguez et al. (2007) identify a number of shortcomings of these models of productivity assessment.In the first place, frequency models are restricted to affixation measurement, which excludes other morphogical processes of lexical creation.Secondly, probabilistic models rely almost exclusively on figures to interpret the data.Finally, the onomasiological model is hardly compatible with the others because it considers non-quantitative aspects of word-formation processes, such as the need of the speech community for a given neologism.Whatever model of productivity assessment is implemented, Fernández-Domínguez et al. (2007: 51) note that "high figures unequivocally correspond to high productivity, it is not entirely clear whether low figures correspondingly match low productivity or whether they imply a decrease in measurement accuracy."It is necessary, therefore, to take additional perspectives on processes with low productivity indexes.This has to be done with respect to the question of the role played by hapax legomena in the assessment of productivity.It is generally accepted (thus Bauer 2004, for instance) that the higher the figure of tokens the lower the index of productivity and, conversely, the lower the figure of tokens, the higher the index of productivity.Consequently, processes with one instance represent the maximal degree of productivity.This is reflected by the formula that calculates productivity (Baayen 1992(Baayen , 1993)), in which the index of productivity results from dividing the number of hapaxes by the number of tokens.The figure of hapaxes, therefore, is in direct proportion to the index of productivity.
Productivity, as put forward by Bauer (2004: 87), is a matter of availability and profitability.Availability makes reference to whether a given process can be used for producing new words, whereas profitability refers to the frequency of use of a morphological process.For assessing the productivity of the processes of a historical language, the assessment of productivity cannot be restricted to availability.On the contrary, the question of profitability, or how much a process is used, has to be central to the analysis.In this respect, carrying out several accounts of productivity relative to three types of hapax legomena offers a more faithful description of the situation of a certain morphological process and is more compatible with qualitative judgements on loss of semantic analysability, lexicalisation and loss.
Given these considerations, the main point made by this article is that if hapaxes are considered in a relative way, based on a type-token continuum, and a distinction can be drawn between absolute hapaxes and relative hapaxes (as well as mixed hapaxes, which subsume both types), the index of productivity can be calculated in a more accurate way and, moreover, the qualitative aspects of the analysis are reinfored.

Sources, data and formulae
To recapitulate, this research aims at gauging the productivity of the seven suffixes that form weak verbs in Old English (-ettan, -laecan, -sian, -nian, -lian, -erian and -cian) from a synchronic point of view, as well discussing the role that the different types of unique formations play in the measure of productivity.
The sources of this study are both textual and lexicographical.For token analysis, the source is The Dictionary of Old English Corpus, which comprises around 3 million words corresponding to approximately 3,000 texts, divided into prose, poetry and glosses.For the calculation of types, the source is the lexical database of Old English Nerthus (www.nerthusproject.com,consulted on May 2011), which contains approximately 30,000 headwords based on the information provided by standard dictionaries of Old English like Bosworth-Toller (1973), Sweet (1976) and Clark Hall (1996).
Turning to the data, a preliminary question arises regarding the inventory of the suffixes that form weak verbs in Old English, given that, as Figure 1 shows, there is no consensus in the literature.
Figure 1 The Old English weak verb suffixes in the literature.
Whereas there is agreement on the suffixes -ettan and -sian, whose bound and derivational character is unanimously acknowledged, the other affixes analysed in this article are not listed in all secondary sources.For this reason, in the remainder of this section we will argue and provide evidence in favour of the derivational status of -laecan, -nian, -lian, -erian and -cian.
The suffix -ettan, as in lāþettan 'to loathe' or ōnorrettan 'to perform with effort', is considered a derivational morpheme without exception (Marckwardt 1942: 275;Kastovsky 1992: 391;Quirk and Wrenn 1994: 116-118;Lass 1994: 203).The case with -laecan is different.For Kastovsky (1992: 391), the verbal suffix -laec(an) forms deadjectival verbs with the meaning 'be, become, make' (dyrstlaecan 'to dare', geanlaecan 'to make one, join', rihtlaecan 'to put right') and denominal verbs with the meaning 'produce, grow, become' (aefenlaecan 'to become evening', loflaecan 'to promise', sumorlaecan 'to become summer').Quirk and Wrenn (1994) describe the suffix -laecan as being used to form verbs, usually from adjectives and nouns, as in gēanlaecan 'to unite' or nēalaecan 'to approach'.Along with these formations, the affix -laecan coexists with the weak class 1 verb lǣcan 'to spring up, rise, flare up', a zero derivative of the class VIIa strong verb lācan 'to move up and down, leap, jump, swing, fly; play (instrument); play upon, delude; fight, contend'.Such a coexistence of a lexeme and a morpheme in the lexicon indicates that grammaticalisation is underway. 2The data available indicate that, from the semantic point of view, the derivation of lǣcan from lācan is motivated by meaning specialisation.Indeed, a change has taken place from a literal meaning of movement 'to spring' to a figurative meaning 'beginning a state or an action'.There is also a change from a more specific lexical meaning to a more general grammatical meaning, to code inchoative internal aspect (beginning of an action or state) and causative internal aspect (with a secondary predication as second argument).When the affix is attached to nouns, its function is usually to convey an inchoative internal aspect as in the example fālǣcan 'to be hostile to' <fāh 'enemy', except in the causative formations such as gewundorlǣcan 'to make wonderful' <wundor 'wonder' and gehīwlǣcan 'to form' <hīw 'form'.When the affix is attached to adjectives, it conveys a causative meaning, as in (ge)cūðlǣcan 'to make known' <(ge)cūð 'known'.It can be concluded then that -laecan results from grammaticalisation lexeme > derivational morpheme that can be identified on the grounds of a change from specific to general meaning and from literal to figurative meaning. 3 As for the suffix -ian, a decision has to be made regarding the question whether it is simply an inflectional ending or it takes part of larger morphemes with derivational function, namely, -sian, -nian, -lian, -erian and -cian.As shown in figure 2, -sian is considered a derivational suffix in the literature.However, Kastovsky (1992: 392), who lists -ettan, -laecan, -sian and -nian, remarks that "the suffix-n(ian) results from misanalysis of zero-derived verbs such as faegenian 'rejoice'< faegen, openian 'open'< open, tacenian 'make a sign'< tacen, and leads to a few analogical formations, such as berhtnian 'glorify', laecnian 'heal', þreatnian 'threaten'".Lass (1994: 203) also distinguishes between the suffix -s-ian and a formative -n-.The suffix -s-ian appertains to class II 2 Grammaticalisation is a change from lexical into grammatical status (Hopper and Traugott 2003: 18).According to Lehmann (2002: 15) grammaticalisation reduces the autonomy of a unit, shifting it to a lower, more strictly regulated grammatical level.Givón (2009: 301) lays the emphasis on the desemanticisation of lexical forms, which gain more abstract meanings. 3At the same time, some derivatives displaying this suffix undergo lexicalisation, throughout which the meaning of the derivative is not predictable from the meanings of the base of derivation and the affix.
Regarding the formulae of productivity, we aim, first of all, at calculating the type-frequency and the token-frequency of the suffixes under analysis, for which we resort to Bauer's (2004Bauer's ( , 2005) ) distinction.According to Bauer (2004: 102-104), type-frequency refers to the number of items of a particular word-formation process found in the dictionary, while token-frequency expresses the number of occurrences of a given word-formation process in a certain corpus or a text.A high type-frequency corresponds to productive processes, while a high tokenfrequency indicates less productive processes.
As for the index of productivity, there is a distinction between productivity in the narrow sense and global productivity.Beginning with productivity in the narrow sense, Baayen (1989) develops a statistical measure of productivity based on Aronoff's (1976) formula for measuring the degree of productivity of a certain word-formation process.Baayen's formula can draw a distinction between productive and non-productive processes by establishing a degree of productivity among them.The formula is given in Figure 2: (Baayen and Lieber 1991: 809).
The productivity P of a given word-formation process is defined as the quotient of the number of hapax legomena n 1 or unique formations and the total number of tokens N of all the words resulting from a given word-formation process.In Baayen and Lieber's words (1991: 809) productivity "P expresses the rate at which new types are to be expected to appear when N tokens have been sampled, n 1 expresses the number of types of a given affix which only occurs once on the corpus (the socalled hapax legomena), and the total number of tokens of that given affix in a given corpus".Baayen and Lieber (1991: 124) also propose the measure of global productivity P* of a word-formation process, which expresses the relation between the index of productivity P and the number of types V.This measure is innovative for two reasons.In the first place, global productivity is not a numerical calculation but a visual representation in which P appears on the horizontal axis and V on the vertical one.Secondly, this measure requires textual analysis, given that it relates narrow productivity to the number of types in a corpus.This means that whereas the index of narrow productivity P tends to calculate already productive processes, the index of global productivity P* deals with both productive and unproductive processes.Baayen and Lieber (1991: 124) propose global productivity in order to reduce the relative weight of hapaxes in productivity measures.Indeed, if the number of hapaxes is high, then the index of narrow productivity will increase, whereas if the number of types is high, it will decrease.In this way, the number of hapax legomena is directly proportional to the index of productivity.For this and other reasons, there is a certain degree of controversy among scholars on the importance of unique formations.Lass (1994: 193), for instance, remarks that it is not clear if the existence of a hapax legomenon represents a piece of solid linguistic evidence or is simply a question of language survival.Plag (2006: 542), on the other hand, holds that "the number of hapaxes of a given morphological category should correlate with the number of neologisms of that category, and that the number of hapaxes can be seen as an indicator of productivity."Plag (2006: 544) also states that, when measuring productivity by counting the neologisms in a given period, "the greater the number of neologisms in that period, the higher the productivity of a given affix in that period." Although the role played by hapaxes in the assessment of productivity is not uncontroversial, it is true that hapaxes are taken into account by most authors.In a recent study in the diachrony of the English affixes -hood, -dom and -ship, Trips ( 2009) "puts forward the following criterion of productivity: a productive set of formations is defined as the occurrence of formations with a morphological category with at least [emphasis in original] two hapaxes where a hapax is a new type built by a new rule and a new type exploiting that new rule."The criterion of productivity, as stipulated by Trips, has the advantage of marking a cut-off point, under which no morphological productivity can be found.On the other hand, Trips's criterion does not allow for gradation, since it divides processes into unproductive and productive thus leaving aside the question of the different degrees of productivity.
To summarise, Plag's (2006) position on the importance of hapaxes for determining productivity constitutes one of the main guidelines of this research, although global productivity and frequency are also assessed in order to check the results of measures directly based on hapaxes.Moreover, the criterion of productivity as defined by Trips (2009) adds an extra perspective and contributes to a more accurate measure on the productivity of morphological processes of wordformation.This is the reason why several measures have been taken into account, in such a way that the following formulae are required.To calculate type-frequency we make use of the formula shown in Figure 3 For the calculation of token-frequency, the formula presented in Figure 4  Finally, to calculate the productivity of a given affix, we have used the formula displayed in Figure 5  The different measures of productivity as well as the discussion of the types of hapaxes follow in the next section.

Results of the analysis. 4.1. Frequency and productivity.
Overall, there are 186 weak verbs derived by means of the suffixes displayed in Figure 2. The inflected forms of these verbs are considered (relative) types when repetitions of the same form are discarded, and tokens when all repetitions of a given inflectional form are taken into account.With these definitions of type and token, there are 1,498 types and 6,737 tokens in the texts from The Dictionary of Old English Corpus.The figures of the synchronic analysis of the suffixes are presented in Table 1 The resulting indexes can be displayed in a number of hierarchies.By type-frequency, that is, the ratio of derivatives in the lexicographical source to the total number of types, the following hierarchy of suffixes can be established (> means is more type-frequent than): By token-frequency, that is, the ratio of occurrences of the derivatives in the textual source against the total number of tokens in the textual source, the hierarchy in Figure 7 can be established (> means is more token-frequent than):

-ettan > -laecan > -sian > -nian > -lian > -erian > -cian
-sian > -nian > -laecan > -ettan > -lian > -erian > -cian The index of productivity has been calculated by dividing the number of hapaxes by the number of tokens.The hierarchy of productivity is as follows in Figure 8 (> means is more productive in the narrow sense than): By applying productivity we get the graphic presented in Figure 9 Figure 9: Global productivity of the Old English weak verb suffixes.

-ettan > -lian > -cian > -erian > -laecan > -nian > -sian
In Figure 9, The horizontal axis axis P is the index of productivity of has the highest number of types whereas -ettan does not have a high number of types but enjoys the highest index of productivity.In general, the suffixes with a higher number of types have a lower index of productivity, whereas the suffixes with fewer types have higher indexes of productivity.Regarding this question, Plag (2006), -ity, -ist, -less, -ish of having very low rates of tokens and types, has a very high index of productivity.Plag unknown words among all the suffix's potential to be easily used for the coinage of new forms (...) The OED ranking reflects the fact that derivable, not often used place in many different words that are not very frequ Roberto Torre Alonso and Gema Maíz Villalta By applying Baayen and Lieber's (1991) concept of g we get the graphic presented in Figure 9: : Global productivity of the Old English weak verb suffixes.
In Figure 9, The horizontal axis V refers to types while the vertical is the index of productivity of each suffix.Notice that while has the highest number of types V, its index of productivity is very low, does not have a high number of types but enjoys the highest index of productivity.In general, the suffixes with a higher of types have a lower index of productivity, whereas the suffixes with fewer types have higher indexes of productivity.Regarding this question, Plag (2006), in his analysis of the English suffixes -ness ish and -wise, demonstrates that the suffix -wise, in spite of having very low rates of tokens and types, has a very high index of productivity.Plag (2006: 545) points out that "the proportion of unknown words among all the -wise derivatives is high, indicating the ntial to be easily used for the coinage of new forms (...) The OED ranking reflects the fact that -wise words are, though easily derivable, not often used."In other words, when the suffix does not take place in many different words that are not very frequent in the texts, the concept of global refers to types while the vertical each suffix.Notice that while -sian , its index of productivity is very low, does not have a high number of types but enjoys the highest index of productivity.In general, the suffixes with a higher of types have a lower index of productivity, whereas the suffixes with fewer types have higher indexes of productivity.Regarding this ness, -ion, , in spite of having very low rates of tokens and types, has a very high index of the proportion of wise derivatives is high, indicating the ntial to be easily used for the coinage of new forms (...) The wise words are, though easily In other words, when the suffix does not take ent in the texts, the rates of the number of tokens and hapaxes and token-frequency are very low, but the fact that an affix would be used easily to coin new forms makes the index of P very high.That is, suffixes with high frequency, number of tokens and hapaxes, but with a low index of P, are used on stable combiantions root-suffix, but seldom to coin new words.

Absolute and relative hapax legomena.
Despite Baayen and Lieber's (1991) attempt to restrict the relative importance of hapaxes for calculating productivity, productivity indexes crucially depend on the number of hapaxes.For this reason, the concept of hapax legomena requires some further attention at this point.The analysis carried out so far is based on an absolute definition of this concept according to which one type is realized by one token in one text.Defined in relative terms, a hapax legomenon is one type that is realized by the same inflectional form in two or more texts.That is to say, an absolute hapax legomenon is a unique formation that appears in one text whereas a relative hapax legomenon remains a unique formation but it appears in more than one text.Ultimately, this definition is based on the distinction between type and token, which is not absolute but relative.Indeed, the inflected forms of a dictionary form constitute tokens of the dictionary form in question, but when they appear in more than one text, the abstract inflective form becomes a type with respect to the concrete inflective forms as they can be found in the texts.Put in other words, the absolute hapax is a purely derivational concept whereas the relative hapax has more to do with the textual realizations of the abstract morphological paradigm.Finally, mixed hapax legomena represent the sum of the absolute and relative hapaxes of a word and offer comprehensive view of the hapaxes identified.The application of these types of hapaxes to the affixes that form weak verbs in Old English is the following.Begining with -ettan, this suffix presents 27 absolute hapax legomena and 6 relative hapax legomena.They appear in Figure 10:  The hapaxes of the suffix -laecan can be seen in Figure 11:  The hapaxes of the suffix -sian appear in Figure 12: Absolute hapax legomena (6): dwelsode (dwelsian, PsGlI), frecelsod (frecēlsian, ClGl), gedyrsod (gedȳrsian, Jud), hrywsode (hrȳwsian, PsGlC), hwinsianne (hwinsian, LS), wraensiaþ (wrǣnsian, HomU).
Figure 14: The absolute, relative and mixed hapax legomena of -lian.
The hapax legomena of -erian verbs as found in The Dictionary of Old English Corpus are given in Figure 15 Absolute hapax legomenon (1): woperiende (wōperian, LS).Relative hapax legomenon (0).Mixed hapax legomenon: 1.Finally, the hapax legomena of the suffix -cian can be seen in Figure 16: Absolute hapax legomena (1): tamcyan (tamcian, ChrodR).Relative hapax legomena (0).Mixed hapax legomenon: 1.If productivity is measured on the basis of mixed hapaxes, -ettan is the most productive, followed, in this order, by -lian, -cian, -erian, -laecan, -nian and -sian, which qualifies as the least productive.The figures are shown in Table 2.If the account of productivity is based on the figure of relative hapaxes, it turns out that the productivity of -sian, -lian, -erian and -cian is zero.As for the rest of the suffixes, -ettan is the most productive, followed by -laecan and -nian.This is shown in  Although the indexes of productivity based on the different types of hapaxes vary, the relative productivity of the affixes calculated on the grounds of mixed and absolute hapaxes coincide: -ettan is the most productive, followed, in this order, by -lian, -cian, -erian, -laecan, -nian and -sian.However, the productivity indexes based on relative hapaxes bring about an interesting change in perspective: -ettan remains the most productive suffix, which is in keeping with its low number of types and tokens and high figure of hapaxes; since they have no relative hapaxes, the productivity of the suffixes -sian, -lian, -erian and -cian is zero, which is consistent with their high number of tokens (-sian) or low number of types (-lian, -erian and -cian); and the productivity of -laecan and -nian is clearly lower than that of -ettan, which is in agreement with its lower number of types and hapaxes.In sum, the greatest advantage of the measure on productivity based on relative hapaxes is that it considers -laecan and -nian more productive than -lian, -erian and -cian.In this respect, if Trip's (2009) criterion of productivity requiring a minimum of hapaxes is applied, -lian, -erian and -cian cannot be productive, while the productivity of -laecan and -nian is questionable.Leaving aside hapaxes, it is hardly compatible with the concept of productivity as has been discussed in section 2 that an affix with a higher type:token ratio that results from a low number of types (like -lian, -erian and -cian) is more productive than an affix with a lower type:token ratio due to a relatively high number of types (as is the case with -laecan and -nian).Therefore, the measure based on relative hapaxes is more accurate than the one based on absolute hapaxes, the reason being that considering hapaxes in their relative version reduces the relative weight of hapax legomena in the statistical measure on productivity.

Summary and conclusions
The previous discussion has shown that the combination of a lexicographical and a textual source allows us to gauge the morphological productivity of the Old English weak verb suffixes in a principled way.Given the central role played by hapaxes in the quantitative assessment of productivity, two new types of hapax legomena have been distinguished, namely relative hapax legomena and mixed hapax legomena.An absolute hapax legomenon occurs when one type is realised by one token in one text.A relative hapax legomenon occurs when one type that is realised by the same inflectional form appears in two or more texts.In other words, the difference between an absolute and a relative hapax legomenon is that the former appears in one whereas the latter turns up in two or more texts (mixed hapaxes constitute a combination of the other two types).
If productivity is assessed on the grounds of absolute hapaxes, the suffix -ettan enjoys the highest index of productivity, followed by the suffix -laecan, while the suffixes -lian, -erian and -cian display the lowest indexes.In the formula used for calculating productivity, the index of productivity is in direct proportion to the number of hapax legomena (or unique formations) and in inverse proportion to the number of tokens (or textual occurrences in all texts).Thus, the comparatively high productivity of -ettan is a consequence of the high number of hapax legomena containing this suffix while the comparatively low productivity of -nian and -sian results from the low figures of hapaxes shown by these affixes.Additionally, affixes with a high number of tokens, such as -sian, -nian and -laecan are less productive than affixes with a low figure of tokens such as -lian, -cian and -erian.
If the account of productivity is based on the relative hapaxes, -ettan remains the most productive suffix, the productivity of the suffixes -sian, -lian, -erian and -cian is zero and the productivity of -laecan and -nian is lower than that of -ettan.The indexes of productivity calculated on the grounds of relative hapaxes have the advantage over absolute hapaxes in considering -laecan and -nian more productive than -lian, -erian and -cian.Given that an affix with a higher type:token ratio that results from a low number of types cannot be more productive than an affix with a lower type:token ratio due to a relatively high number of types, the measure based on relative hapaxes is more accurate because it lessens the importance of hapax legomena.
Regarding the relationship between absolute and relative hapax legomena, it seems to be the case that lemmatised types in the dictionary correspond to more than one unlemmatised type in the corpus, which, in turn, are reflected by a given number of tokens in the corpus.The opposite is less frequent.That is, a correspondence between one lemmatised type in the dictionary and one unlemmatised type in the corpus reflected by two or more tokens in the corpus (as the concept of relative hapax legomenon requires) occurs very infrequently.Actually, this happens less often than absolute hapax legomena arise, which comprise one lemmatised type in the dictionary and one unlemmatised type in the corpus reflected by one token in the corpus.The conclusion can be drawn, therefore, that, absolute hapaxes are more frequent than relative hapaxes.
Finally, it can be concluded that a high token frequency has resulted in a low productivity index.This is coincidental with the view, already stated by Stanley (in Amos 1980: 141) that the generalised derivation of weak verbs with -ian is characteristic of the end of the Old English period.On the diachronic axis, the loss of the affixes for derivational or inflectional reasons due to the decline of inflections also points to a low level of productivity of the weak verb suffixes.Against this background, the typology of hapaxes allows more fine-grained distinctions to be drawn because it puts the focus on -sian, -erian, -lian and -cian, which range between very low and zero productivity.

:
Index of productivity P = Number of hapax legomena of suffixNumber of tokens of derivatives of suffix

Figure 6 :
Figure 6: The hierarchy of type-frequency.

Figure 8 :
Figure 8: The hierarchy of the index of productivity.

Table 1 :
: Frequency and productivity indexes of the Old English weak verb suffixes.

Table 2 :
Index of productivity with mixed hapaxes.

Table 3 :
Index of productivity with relative hapaxes.

Table 4
provides an account of the index of productivity considering the number of absolute hapaxes.Given that -sian, -lian, -erian and -cian do not have any relative hapaxes, their figures coincide with those based on mixed hapaxes.

Table 4 :
Index of productivity with absolute hapaxes