150 6 Modality
someone’ (Cambridge). To reduce this to the core system, we first note that-ness, a clear deverbal and deadjectival noun-forming suffix (ignoring lexicalized cases likebusiness) is not essential. We can usesad, already defined asemotion, bad in the definition sad
ofgriefassad, <{=agt love person die} cause>. For the ‘extreme, very great’ part 4lang actually offers sorrow, emotion, ER sad, suggesting a better sorrow
definition such as sorrow, <{=agt love person die} cause>. The naive theory of emotions embedded in4langis not very sophisticated, but the links between sorrow ‘dolor’ and badnesscause_ hurtare laid bare.
As in other semantic fields (Buck, 1949devotes an entire chapter to emotions), we resist the temptation to offer a full taxonomy. Many words that Buck considered key are removed during the uroboros search, for examplepity has the following definition:
pity
sorrow, {other(person) suffer} cause_, but we see no reason to trace these exhaustively, let alone to trace all emotionally loaded words one may wish to con-sider. Broadly speaking, the naive theory treats feelings along the Hippocrates/Galenus lines as vapors or liquids (humors) flowing through the body, and we see traces of this in the free use of several motion verbs with emotions as subjectsjoy flooded him, orhis blood boiledetc. We offer a mechanism for uncovering such taxonomies by tracing the definitions to the core, but we do not offer apolicy.
6.4 Defaults 151
person<profession>, think stem_[important], "_-ist" mark_
stem_.
In many cases, we are not sure whether the person is professional: arsonist,
bal-loonist, philanthropist, . . .. That the default isprofession job, before(educate profession for_)is clear from the fact that in these cases we tend to treat them as such, e.g. we
assume that the arsonist is a career criminal, the balloonist has undergone rigorous train-ing and flies balloons for a livtrain-ing, etc. We even have a word,amateurwhose main use is to defease this implication. In the cases where it is hard to distinguish professionals from amateurs, the defaultprofessiontakes precedence over the more generalperson.
Profession descriptors are a subset of person descriptors (as long as we don’t in-sist on strict InstanceOf typing, see 4.5), so the lexical rule for -ist-suffixation oper-ates the same way as the more static entries we quoted from LDOCE above. More challenging are those cases where there are two, seemingly disjunct defaults, as in
bake <cake, bread>; drink <water, alcohol>; or can/1427 cylinder, metal, can/1427 contain [<food>,<drink>]. Such entries resist the kind of analysis based on
is_a, since neithercake/breadnorfood/drinkhas a superordinate member that the sub-ordinate (more specific) member could override.
To compare this to the P¯an.inian idea of “habitual, professional, or skilled” actors noted in2.2, we need to analyze what the three-way disjunction betweenhabitual, pro-fessional,andskilledamounts to. Forhabitual, LDOCE offers ‘usual or typical’ in one sense, and ‘as a habit that you cannot stop’ in another. The distinction is carried back to habit‘something that you do regularly or usually, often without thinking about it because you have done it so many times before’ versus ‘a strong physical need to keep taking a drug regularly’. It appears we can do away with the compulsive sense, especially as the formations where it is most prevalent (chain-smoker, pill-popper) are synthetic to begin with. This leaves something like ‘usual, typical, regular, done without thinking, done may times before’ forhabitual. Forprofessional LDOCE offers ‘doing a job for money rather than just for fun’ and ‘a job that needs special education and training, such as a doctor, lawyer, or architect’. Finally, for skilled it provides ‘has the training and experience’.
It seems quite hard to disentangle the senses of professional and skilled as both require the before(educate for_)aspect that we used in the definition of pro-fession. In modern society, ‘need special education and training’ really means educa-tion/training that provides a license: practicing law, medicine, or architecture without a license is criminalized, no matter how skilled the practitioner. This means we can col-lapse the second and third terms of the P¯an.inian disjunction (no doubt distinguishable back in his day) to justhabitualorprofessional, perhaps adding to the latter an optional default clause <licensed> which must be omitted foremployer, farmer, manager, ruler, waiter,etc. at least until regulations are further tightened.
It is clear that the range of the remaining two options overlaps greatly, but perhaps differently for nominals obtained by deverbal zero-suffixation (a device we have no need for, given the type-free nature of4lang); by deverbal-ersuffixation; and by
denomi-152 6 Modality
nal-istsuffixation. More important, the identification of these sub-meanings ispost hoc, relying on the subdirection (see2.2) rather than on the parts themselves. Ahabitual of-fenderis simply a person who has offended many times before, there is no implication that they get paid for it, or that offending required any education or training, let alone licensing. Iffor our next outing, Jim will be the cook, this does not make him a profes-sional cook, or even a skilled one, just one who assumes the role, quite possibly without the benefit of special education or training. It is precisely because of the post hoc na-ture of the choice between the habitual and the professional reading that the rule lacks productivity: we don’t have a notion of the??habitual sleepernot because nobody is trained in sleeping (some people with disorders actually are, but we don’t consider them professionals for that) but because everybody is on the habitual branch of the definition ofsleeper, eater, breather,. . . to begin with.
Returning to dual defaults, it is intuitively quite clear that we would want to follow P¯an.ini and permit disjunction e.g. inbake cook/825, =pat[<bread>, <cake>], bake
=agt cause_ =pat[hard] whose default object is either bread or cake, but not both. One way to resolve the issue would be the introduction of some abstract supercate-gory such as ‘dough-based baked food’ or ‘victuals’. We call this the KR-style solution, as it is seen quite often in systems of Knowledge Representation. This is unattractive for most languages (cf. 5.3 for ‘doors and windows’ in Hungarian), especially as the first paraphrase sneaks in bakeon the right-hand side of the definition, and the latter (together with its less current synonym ‘aliments’) defaults to food, whereas ‘refresh-ments’, at least in current usage, defaults to drinks. The KR-style solution also goes against the lexicographic principle of reductivity (see1.2) that the definiens should be simpler than the definiendum.
The key to the treatment of defaults is to see them as triggers for spreading activation.
We will discuss the activation process in greater detail in 7.4, but the general picture should already be clear: if a default is present in a lexical entry, it is active unless it gets defeased. At the discourse level, such activity is easily tested by the immediate, felicitous availability of definite descriptions. CompareI went to a wedding. The minister spoke harshly (Kálmán, 1990) to I went to a restaurant. #The minister spoke harshly. The wedding script comes fully equipped with a slot forminister, but the restaurant script does not. In fact, one need not resort to the full conceptual apparatus ofSchankian scripts orFillmorean frames to see this, the lexical entry forwedding ‘a marriage ceremony, especially one with a religious service’ (LDOCE) already carries the religious service and its officator by default, whereas the entry forrestaurantdoes not.
Under the view presented here, a restaurant is not fully defined by ‘a place where you can buy and eat a meal’ (LDOCE) because the same testI went to a restaurant. The waiter spoke harshlyshowswaiterto be available by definite description. The existence of a specific negative,self-service restaurantalso points at the conclusion that waiters are present in restaurants by default, as are chefs, maître d’s, busboys, tables, etc. The Oxford definition, ‘a place where people pay to sit and eat meals that are cooked and served on the premises’ shows the slots for cooks/chefs and servers/waiters, andsit and eatdoes
6.4 Defaults 153
seem to imply the presence of a chair and a table. Whether the maître d’ hôtel is a default feature of a restaurant seems very much culture-dependent, but areal restaurant, as we shall see in7.2, can hardly do without.
Let us return to conjoined defaults. Considerash powder[<grey>, <white>, ash
<black>], {<wood> burn} make. What is the default color of ash? The word ashen suggests ‘pale gray’ but an ashen face ‘looking very pale because you are ill, shocked, or frightened’ (LDOCE) is actually not grey, just pale. The larger encyclopedia, https://en.wikipedia.org/wiki/Shades_of_gray is already overwhelming, and a broader search leads to sites such ashttps://simplicable.com/new/ash-colorwhich call into ques-tion even the Knowledge Representaques-tion-style soluques-tion relying on some technical term (in this case,grayscale).
There are cases like broadcast signal, <radio,television> receive broadcast where a KR-style solution is easy. Unlikealimentsdiscussed above, where the defining
word is lexicographically unreasonable, here we could useantenna, not just as some-thing common to TVs and radios, but also as the instrument of both broadcasting and
reception. But there remain cases likeopponent person, oppose, <compete>, opponent
<in battle> where the defaults are rather contradictory between friendly compe-tition and adversarial battle. In the spreading activation model we don’t have to make early choices between polysemous senses or pretend that these involve a single abstract sense. Rather, the system can resolve later on which of the adjacent polytopes is meant.
We beganS19:1.1with two Fregean principles, the better known Compositionality, and that ofContextuality:
Never ask for the meaning of a word in isolation, but only in the context of a sentence.
In computational linguistics, relating word senses to contexts is known as the problem ofWord-Sense Disambiguation, see Agirre and Edmonds (2007) for the state of the art before 2010. Perhaps the greatest step forward in solving the WSD problem was the introduction ofdynamicembeddings that produce a word vector based on context. Un-fortunately, this is a black box solution, and part of our goal here is to understand the mechanism of disambiguation. Defaults, contradictory defaults in particular, offer an important insight into the structure of lexical entries: while the basic structure is con-junctive, their joint activation, by spreading, is disjunctive. The broad agentive -er -er stem_-er is_a =agt, "_ -er" mark_ stem_ is simply ‘one who stem-s’
(cf.buyer, sleeper, . . . rather than ‘one who habitually stem-s’, so there is no disjunction to consider. The more narrow agentive -er, and-ist are, perhaps just like in Sanskrit, ambiguous between the habitual and the professional readings (cf.smoker, exhibitionist for the former andplumber, pianistfor the latter) but we see no supercategory that con-nects these two: rather, we see these as disjunctive by virtue of being defaults. The work is done by the person[<profession>] clause which defaults to profession.
We have to do extra work to escape this conclusion in order to fall back on the default person, and this extra work is unrelated to any notion of habituality, since the pros
154 6 Modality
obviously ‘do stem’ habitually. In synthetic compounds teetotaler, navelgazer, . . . we assume the work is done during the formation of the compound, in other cases we may have to bring in the compulsive aspect we chose to ignore above.
The entire network of lexical entries is remarkably tight. We have seen that from the uroboros core every word can be reached in three steps via the LDV and LDOCE. Three is the maximum: those familiar with the use of4langcan often write a one-step defini-tion that relies only on the uroboros core. (By now, most readers will have seen enough examples and will understand the principles well enough to try themselves.) Since the average number of clauses within the V2 uroboros set is 2.66, if we let spreading proceed through any undirected ‘associative’ path, we may activate the entire vocabulary in 5-6 steps starting from the words of any sentence. Considercolorless green ideas sleep furi-ously. Colorimmediately activatessensation, light, red, green, blue;
-less activates lack; green activates has, plant, and the already active color;
ideaactivatesin, mind, think, make;-sactivatesmore;sleepactivatesrest, conscious, and the already active lack; furious activates angry, er_, gen.
Only-ly, a pure category-changing affix, does not activate any element, as it is seman-tically empty. This is not to say that it entirely lacks a categorial signature: for English, -lyis clearly [AN]\D, but in4lang we wish to avoid the claim that operators turning adjectives or nouns into adverbs are universal.
In one step we have already activated 20 elements (2.86 per morpheme), and only four of these,er_, gen, andlackare primitives that resist further spreading, while inwill invoke the entireplaceconceptual scheme (3.1). In fact, the morpheme count is somewhat arbitrary, as we should clearly add a nominative and an accusative marker, 3rd person singular, present, and perhaps other unmarked operators such asI declare to you.
To limit combinatorial explosion we need to constrain spreading activation in various ways. First, it is clear that permitting activation in the other direction would be unwise, since one in seven words involve spatial in, almost one in three involve possessive has, some 40 involve comparativeer_, some 60 involve negativelack, and the same number involve generic gen. Second, we need to enforce some condition of locality, in that it is cognitively implausible that the negative element explicit incolorlesscould reinforce the negative element implicit insleep rest, lack conscious. We will sleep
return to spreading activation in 7.4, where we discuss how to implement locality by island parsing, but we note in advance that the key building block will be theconstruction in the sense ofBerkeley Construction Grammar.
For the synthetic compounds in-erthis superficially takes the form(N V -er)N, e.g. innavel.gaze.er. Remarkably, the spreading analysis often leads through the unat-tested intermediary that we use use for agentive-er,(V -er)N. Once this pattern is activated, the very frequent noun-noun compounding pattern(N N)N can be spread to.
InS19:6.4we wrote
The algebraic approach (...) largely leaves open the actual contents of the lexicon. Consider the semantics of noun–noun compounds. As Kiparsky (1982) notes, ropeladder is ‘ladder made of rope’,manslaughter is ‘slaughter
under-6.4 Defaults 155
gone byman’, and testtubeis ‘tubeused fortest’, so the overall semantics can only specify thatN1N2 is ‘N2 that is V-ed by N1’, i.e. the decomposition is subdirect (yields a superset of the target) rather than direct, as it would be in a fully compositional generative system.
This applies to entries liketeetotalerwhich we analyze with an unattested agent noun totalerwho totals (does always) the V-ing oftee(tea). Unsurprisingly (though not ex-actly predictably) the verb in question is drink, so we obtain ‘one who always drinks tea’. While still a bit off the actual target ‘one who abstains from drinking alcohol’, this is close enough for memorization, and offers considerable economy relative to memo-rizing the entire definition.
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7
Adjectives, gradience, implicature
Contents
7.1 Adjectives . . . 158 7.2 Gradience . . . 160 7.3 Implicature. . . 163 7.4 Spreading activation. . . 168
Adjectives are present in most, though not necessarily all, natural languages. In7.1 we begin by discussing the major properties of adjectival roots and the vector semantics associated to the base, comparative, and superlative forms. We discuss the logic associ-ated to these, and extend the analysis to intensifiers.
Starting with Bloomfield (1926), semantics relies not just on the idea of identity (equality) of meanings, but also their similarity. Logical semantics offersimplicational equivalencefor defining identity of meaning, and vectorial semantics offers cosine simi-larity for defining meaning simisimi-larity. But there is a third notion,strength, which remains somewhat elusive in both frameworks. In logical semantics, we speak ofimplicational strengthe.g. that ‘run fast’ implies ‘run’, but not the other way around. In7.2we discuss how this kind of scalar intensification can be implemented both for adjectival and for verbal predication using voronoids.
In7.3we turn to implicature in a broader sense. From the vantage point of algebraic semantics, implicature is also a kind of intensification process, except what gets intensi-fied is not some direct aspect of the meaning but rather the degree of indirection (number of substitutions) we need to carry out. We will present implicatives as satisfying simple inequalities imposed on their agents and patients, and show how theforce dynamics-like analysis offered by Karttunen (2014) can be taken on board in vector semantics.
Finally in7.4we summarize how substitution or, what is the same, spreading activa-tion, is operating during parsing and generation. This puts in a new light the perplexing lack of transitivity in implicature, that we may conclude BfromA, and CfromB, yet we are often reluctant to get fromAtoC. When someone tells usIt can hardly be dis-puted that X, what this means that it is hard to dispute X, which only happens if X is obviously true. From this it follows that X is true, self-evidently so. Yet once our
sus-© The Author(s) 2023 157
A. Kornai, Vector Semantics, Cognitive Technologies, https://doi.org/10.1007/978-981-19-5607-2_7
158 7 Adjectives, gradience, implicature
picions are aroused, we are reluctant to draw this conclusion. What needs to be made explicit in this regard is that sentences whose meaning cannot be tied to truth conditions (other than truth conditions pertaining to the mind-state of the speaker and the hearer) actually demonstrate that truth-conditional semantics is a blunt instrument, incapable of assigning meaning to sentences.