Phrase Structure Grammar
2.5 Rules, principles, constraints
2.5.2 Lexical rules
In comparison to constraints postulated in lexical entries and resulting from the inheritance along the type hierarchy, which are called vertical generalisations, lex-ical rules43 represent horizontal generalisations. They state abstract and “[. . . ] systematic relationship[s] holding between two word classes, or more precisely, be-tween the members of one class and the members of another class” (Flickinger, 1987: 101). For instance, at the beginning of Section 2.5.1, it was postulated that some parts of the information in the AVM (26) was contributed by the affix -t, stated now more accurately by the lexical rule which inserts -t. Taking the quote of Flickinger (1987: 101), we can describe the relation between the verb stem putz-and the verb form putzt as a systematic relationship between the members of the class “verb stems” and the members of the class “verb form in 3rdperson, singular, in present tense” in general, and not only between the specific forms putz- and putzt. This relationship represents a generalisation which can be captured through a constraint in form of a lexical rule (cf. AVM (30)).
Lexical rules in general state relationships between two linguistic objects of type stem or word, i.e. between two words, two stems, or between a word and a stem.
The lexical rule in (30) in particular states the relationship between the AVM of a stem to the left – the input of the rule, and the AVM of a word to the right – the output of the rule. This relation is expressed by the symbol ↦ (cf. Meurers, 2001: 168ff).44 To be more precise, (30) states a relation between all elements
43Lexical rules are also called lexical redundancy rules.
44Please remember that the symbol for lexical rules (↦) is different from the operator which will
sign root strict-trans-verb-root
mal- ess-
schlag-pos-sign h headposi verb-sign h headverbinoun-sign h headnouni
pos-sem h cont|relslisti verb-sem h indeventi ag-rel h relsag-reli ag-th-rel h relsag-th-reli
th-rel h relsth-reliexp-rel h relsexp-reli
noun-sem h indindi
unsaturated-sign sprlist subjlist compslist nom-arg h subjhNP[nom]iinom-acc-arg subjhNP[nom]i compshNP[acc]i
Figure 2.7: Example of vertical generalisations (based on Müller 2013a: 94)
satisfying the constraints posited by the AVM to the left hand of the arrow and all elements satisfying the constraints posited by the AVM on the right hand. Further attribute-value pairs not mentioned in the AVM to the right are carried over to the output as far as they are compatible with the output.
(30) Lexical Rule (MLR): Verb inflection for 3rd person, singular, present
⎡
The AVM to the left states that the element must be of type stem, and that it has to be a verb (cf.synsem∣loc∣cat∣head verb). The output must be of type word, and the values of the attributes vform, tense, per and num must be specified as fin, present, 3, and sg, respectively, that is yielding some finite verb in third person, singular, in present tense that agrees in person and number with its subject (cf. subj). Take into account that not constraining the input AVM for vform, tense,subj, etc. as in (30) is in this case equivalent to give the maximalunspecific constraints as in the following AVM in (31).
be used forimplicational constraints(→), cf. Section 2.5.3. In the literature, one can sometimes find the double arrow (Ô⇒) instead of↦, see for instance Pollard (2000).
(31) ⎡⎢⎢
synsem | loc
⎡⎢
The function f under phon in the output AVM of the lexical rule 30 calculates the suitable result of the phonological form. f takes two lists as arguments. The first one is represented by 1 which is a variable for any list of phonemes that constitutes thephon value of the verb stem in the input AVM. The second one is the list built by the endingt. Then, f concatenates its arguments into one single list, deriving e.g.⟨/p, U,>
ts, t/⟩out of the list of the stem⟨/p, U,>
ts/⟩and the list of the affix ⟨/t/⟩.45 All further attribute-value pairs not explicitly mentioned in the lexical rule are meant to be carried over from the input structure into the output structure. To put it in the words of Pollard (2000: 2): “change the input entry only in the ways that the right-hand side of the rule tells us to change it, and leave everything else the same”.46
A different formalisation of processes below the syntactic level, i.e. of lexical processes, has been proposed in order to formalise them as one single description, integrating them into the general HPSG theoretical framework. The two related AVMs in (30) represent a so-called Meta Level Lexical Rule (MLR) which deal with lexical rules and the lexicon as external to the theory, i.e. on a meta level, separating the lexicon and its generalisations from the grammatical component
45According to Müller (2013a: 378f), the functionf would make the necessary changes if we are dealing with verb stems needing more than only ⟨t⟩as the ending of the respective verb form.
For instance, the verb stemarbeit-‘work’ gets concatenated with the affix-etin order to derive the verb form in 3rd person, singular, in present tense arbeit-et ‘works’. In other words, it is f which chooses which allomorph has to be used, according to the phonological information of the stem.
46Pollard (2000) mentions also that this kind of interpretation of the formalisation conflicts with the fact that lexical rules are not algorithms, but descriptions. See also Calcagno and Pollard (1995).
(cf. e.g. modularisation in MGG). In contrast to MLR, Description Level Lexical Rules (DLR) integrate lexicon and lexical rules into the HPSG theory, getting rid of the extra meta-system needed in MLR.47
The AVM in (33) shows the DLR formalisation of the lexical rule presented in (30) in MLR format. The DLR format, as already mentioned and as can be seen in (33), is formalised as a single description, without using the ↦symbol to relate two descriptions. The AVM of the new lexical rule is an object of type fin-verb-infl-lr that stands for “lexical rule for inflected finite verb forms”. fin-verb-infl-lr is a subtype of word, therefore all objects licensed by this rule are elements of type word. This is important, since this rule cannot apply recursively, i.e. only elements of type stem can be inflected through this rule, resulting in an element of type word (cf. (32a)). But elements of type word – i.e. the result of the rule – cannot be input for this rule again (cf. (32b)), as the following example may illustrate.
(32) a. putz-cleanstem
+ -t
3.sg.prs = putzt
clean.3.sg.prsword
b. putzt cleanword
+ -t3.sg.prs = * putztt
clean.3.sg.prs.3.sg.prs
Just as the MLR format, the DLR format in AVM (33) can be divided into an input and an output. The new attributes lexical-daughter (lex-dtr) and affixrepresent the inputs of the rule,48 similar to the left side of the rule in (30).
lex-dtr is constrained to be of type stem. The output of the lexical rule is, as already mentioned, an object of type fin-verb-infl-lr – a subtype of word. The relations between input and output of the rule are represented in (33) only by means of structure sharing (cf. cat, cont, and phon), thereby getting rid of the relation represented by the ↦ symbol.
The lexical rule in (33) can be thought of as a unary tree whose daughter is the sign in the lex-dtr and whose mother node is the whole structure. Thereby, the phon value oflex-dtr and thephon value of the affix are concatenated into the phon value of the whole structure. In comparison to phrase structure trees,
47A more detailed comparison of DLR and MLR can be found in Meurers (2001: 170ff). Further-more, the MLR format does not necessarily need to be interpreted as external to the theory.
An attempt to use the MLR format including lexicon and lexical rules into the theory has been made in Pollard (2000).
48Sometimes, instead oflex-dtrandaffix, only the attribute stemwith the output are used.
The latter representation reflects better the idea of a unary rule (cf. Wechsler, 2015: 207).
(33) Lexical Rule (DLR): Verb inflection for 3rd person, singular, present
cat|val|subj ⟨3 NP
⎡
cont [ind|tense 5 present]
⎤⎥
ind 6 event rels 7
mother and daughter nodes are lexical.49
The most important difference between MLR and DLR concerns the idea that MLR relates elements contained in the lexicon. Namely, MLR states that if there is an element satisfying the constraints in the input, there must be also an element in the lexicon satisfying the constraints of the output. The rule itself which states the relation between input and output does not belong to the description language, but is a meta-rule. On the other hand, DLR states also a relation between objects, but the rule itself is an object of the description language, loosely speaking, the rule itself represents the output and to do so it embeds the input (cf. Wechsler, 2015: 206).