7# UFJNNN^*"466^x ,]*n*]D]]B]]]]]]Extending lattice theory into new domains LSoRB, Tulane University Jan. 10, 1995 I. Introduction Spanish grammar has several constructions that come in two versions, such as count vs. mass nouns, the copula verbs ser vs. estar, and the position of an adnominal adjective before or after the noun it modifies. In this paper, a common semantics is proposed for these pairings, based informally on a mathematical framework called lattice theory, which lets us talk about the parts of an entity in terms of the relations that bind those parts together. II. Countable vs. uncountable or mass nouns II.1. Preliminary data and terminology Those interested in natural language, especially in the Indo-European languages spoken in Western Europe, have long noticed that noun stems can be classified according to their privileges of occurrence with quantificational determiners. In Spanish, for instance, some quantificational determiners are simply excluded from modifying a noun like harina, flour, though they are fine with a noun like mesa, table: 1QuantifierCount (mesa table)Mass (harina flour)a)la segunda the second [ordinals]la segunda mesa*la segunda harinab)uno a/one [indefinite/cardinal]una mesa*una harinac)un(os) someunas mesas*unas harinasd)dos two [cardinals]dos mesas*dos harinase)dos N ms/menos dos mesas ms/menos*dos harinas ms/menostwo N more/less f)ms/menos de diez N ms de diez mesas *ms de diez harinasmore/less than ten Ng)ambos bothambas mesas*ambas harinash)varios severalvarias mesas*varias harinasi)cada eachcada mesa*cada harinaj)todo everytoda mesa*toda harinaOther quantificational determiners can modify uncountables, as long as they agree with them in the singular: 2QuantifierCount (mesa table)Mass (harina flour)a)cunto(s) how much/manycuntas mesascunta harinab)ninguno(s) noningunas mesasninguna harinac)alguno(s) somealgunas mesasalguna harinad)poco(s) few/littlepocas mesaspoca harinae)mucho(s) many/muchmuchas mesasmucha harinaf)tanto(s) so many/muchtantas mesastanta harinag)demasiado(s) too many/muchdemasiadas mesasdemasiada harinah)todo(s) alltodas las mesastoda la harinai)ms morems mesasms harinaj)menos fewer/lessmenos mesasmenos harinaSince one of the distinctive characteristics of the mesa/harina pair is that tables can be counted while flour cannot, mesa-type nouns have come to be called countable, and harina-type nouns have come to be called mass or uncountable. There does not seem to be a commonly-accepted term for the countable-uncountable distinction itself, but it is referred to in this paper as countability. The grammatical repercussions of countability go beyond determiner co-occurrences. Certain classes of nouns take nominal complements according to their countability. Group nouns can take de plus a plural countable as illustrated in (3a), while measure nouns take de plus an uncountableor plural countable as illustrated in (3b): 3 a) un grupo de estudiantes a group of students b) un kilo de salmn a kilogram of salmon Countable nouns are more easily modified in terms of spatial dimensions: 4. La {mesa/??harina} mide un metro y medio de largo. the {table/flour} measures a meter and half in length Some verbal contexts also have countability restrictions. Existential contexts prefer bare singular uncountables: 5. Hay {harina/??mesa} en el saco. There are also verbs in Spanish which govern a partitive complement, introduced by de or con: 6 a) Llen el saco con/de {harina/??mesa} b) El suelo estaba salpicado/manchado de {harina/??mesa} It is safe to conclude that for these and other constructions, the value for countability of a noun is crucial for grammaticality. Moreover, it is tempting to lump this data under a morphological prohibition against using harina in the plural, but the judgments for the ordinal numbers and the indefinite article un(a) in (1a, b), as well as for cada and todo in (1i, j) show this to be inaccurate. There must be some factor more subtle than a simple feature [plural]. This is indeed the case. This preceding introduction has been misleading in its implicit assumption that a given noun stem has a fixed value for countability. It is currently assumed that practically any noun which the preceding constructions diagnose as countable can be used uncountably with a change in meaning. Consider the putatively countable stems perro, dog and misionero, missionary in the following sentences: 7 a) La calle estaba salpicada de perro. the street was splattered of dog b) Mucho misionero se comi en ese rito. much missionary was eaten in that ritual In (7a), perro refers to dog as a substance the flesh and bone, blood and guts of which dogs are composed rather than as an articulated whole. Likewise in (7b): misionero denotes the edible portions of a missionary - or missionaries - rather than to a countable totality thereof. This process of a putatively countable noun taking on uncountable properties has been dubbed the Universal Grinder, after Pelletiers (1979) report of David Lewis delightful coinage. The converse phenomenon, of an uncountable noun be used countably, is also attested in Spanish: 8 a) caf > un caf coffee > a cup of coffee b) Han sacado una cerveza nueva. They have come out with a new beer. c) agua > las aguas del mar water > the waters of the sea, i.e. ocean currents (8a, c) are instances of Lewis Universal Packager, which creates a count usage of a mass noun by associating it with a characteristic container. Given this mutability of noun categorization, the rest of this paper speaks of countability in terms of noun usages and occurrences or readings and interpretations, rather than ascribing nouns univocally to one sort or the other. However, this approach may be overly generous in attributing ambiguity to all noun tokens, whereas in many cases the most salient usage is consistently of one sort or the other. For such cases, the terms primary and secondary are reserved for the sake of empirical accuracy. II.2. The analysis in pictures Since the early Eighties, the approach to formalizing the difference between count terms/events and mass terms/processes is to propose structures for the former which have minimal elements and structures for the latter which do not. It will be convenient to have a specific instantiation for the purposes of illustration, so let us assume that the intension, i.e. the lexical entry, for the noun snake includes the information that a snake consists of the three parts labeled below as head, body and tail: 9. Snake1.GIF The next step is to imagine how the three parts of the snake are put together. The diagram in (10) illustrates the two paths from the parts at the bottom to the whole at the top, or vice versa: 10. Snake2.GIF This diagram is meant to be read in the following way. The three minimal parts are given nearly at the bottom. Above each one, there is a line leading to a larger piece of the snake. The bottom of the line gives the part, and the top of the line gives what it is part of. The tail, for instance, is a part of two larger groupings tail plus body and tail plus body plus head. The comment at the very bottom, no shared part indicates that at this level of magnification, there is no part which any pair of minimal parts shares. Turning to the mass domain, let us call the following blotch an instance of sugar:. If we put it together with another blotch of sugar, we still get sugar: 11.  If we add a third blotch, it can be combined with the other two , and the result is still an instance of sugar: 12.  In fact, any of these parts can be put together in any order, and the result is still sugar: 13.  Obviously, we could keep adding together quantities of sugar until the end of time, and we would still get a valid instance of it. And it does not matter which blotch we pick to start with and which one we pick to add next. Any way the combination is effected, the outcome is always sugar. (10) and (13) are so big and clumsy that they are difficult to reason about. We can make them more manageable by substituting letters for the parts, as in (14): 14.   0 symbolizes the lack of a smaller part; 1 is as above: it represents the totality; the part that contains all of the other parts. At this level of abstraction, two differences between the count and mass structures stand out. The first is that the count structure has a zero, while the mass structure does not. This is the proposal which has informed the recent theories of the count-mass distinction. This proposal runs into the problem of fruitcake. Fruitcake has a noncountable usage in which it denotes a mass of fruits and nuts in a sweet batter. It is easy to pick out some of the minimal parts of this mass: they are the individual fruits and nuts. It follows that noncountable fruitcake does have at least some minimal parts, so basing the count/mass distinction on the minimal/no-minimal part distinction leads to incorrect predictions. Hinrichs (1985:167-8) and Verkuyl (1993: 219-221) draw a similar conclusion for the event/process domain. The solution adopted within the confines of the structures of (14) lies in a partial recognition of the second difference between (14a) and (14b): the mass whole is the sum of its parts and nothing else; the count whole is the sum of its parts and specific instructions for how they are composed. For instance, the count diagram is not drawn with the part t+h filling the gap in the middle of the diagram, in contrast to (15): 15)  It is excluded for an empirical reason: there is no physical decomposition of the snake into a part that consists only of the head and tail. In every case, the head and tail are combined into larger parts through the mediation of the body. In other words, the steps which go into creating the snake from its parts proceed in a monotonic fashion, with one step only adding on to the structure created in the previous step: to make a snake, you start with the head, add a body and then a tail, or vice versa. If you start with the head and then add the tail, you have to undo this join in order to add the body. It follows that the t+h part has no empirical motivation in a monotonic composition of the snake and so should not be included. I would like to make the rather radical proposal that the parts of countables select for one another in a highly idiosyncratic way, much as lexical items select for specific categories in an idiosyncratic way. (16) summarizes the requirements of the three parts of our snake: 16 a) h: [+b], i.e. the head selects for a body. b) b: [+h, +t], i.e. the body selects for a head and a tail. c) t: [+b], i.e. the tail selects for a body. This lexicon accounts for the structure of (15) exactly. Both the head and the tail combine with the body, because both select for a body via the [+b] feature. Once the body is added to either of the two extremities, the extremitys requirement is satisfied and it becomes inert, or saturated. However, the body still has one more feature active, so it must combine with the remaining extremity - and vice versa - to form the whole. The result is a tiny grammar of the snake, composed of a lexicon of minimal elements and a set of rules for their combination by means of +. The crucial difference between this and the mass structure in (14b) is that in (14b), the part consisting of a and c is formed. What this means is that any part can be combined with any other part, which indicates that no part a has a particular stipulation of the form a:[+x]. Being unmarked for a such preferences, no part is prevented from joining with any other. This is exactly what is represented in diagram (14b). The next step is to see whether this characterization of the count/mass generalizes to the other binary distinctions in Spanish grammar. III. Ser vs. estar Spanish has two verbs meaning to be, whose specific usages are summarized in the examples below: 17 Estar a) Initial-state: La luna est deshabitada. the moon is uninhabited b) Progressive: Mara est leyendo. Mary is reading c) Result-state: El profesor est aburrido. the professor is bored d) Contrary-to-expectation: Qu alto est el nio! how tall the boy is! e) Evidential: La sopa est rica. the soup tastes good 18 Ser a) Classificatory: El libro es aburrido. the book is boring b) Identificational: Mara es la que buscan. Mary is the one they are looking for c) Abstract subject: La fiesta fue en mi casa. the party was at my house d) Activity: Mara fue amable conmigo. Mary was nice to me e) Passive: El Presidente fue asesinado. the President was murdered We turn directly to their analysis. III.1. Aspectual estar The first three usages of estar in (17) can be grouped under the label aspectual. These are the ones that most theories of copula selection in Spanish try to account for. They can be described naturally by a single countable part structure that Gerstl & Pribbenow (1995) calls the segment. Gerstl & Pribbenow defines it as a part that results from the application of an external scheme. The simplest external scheme is that of segmenting an entity into beginning, middle, and end parts. The only requirement on the internal structure of the whole is its one-dimensional boundedness, as in (?): 19.  Each part can occur as a point or an extended phase, though Gerstl & Pribbenow do not appear to have a temporal extension in mind for this latter possibility. The scheme in (19) can be used to segment a street, a rope, a queue of people, or, after projection onto an abstract entity, a story, a cinema play or even a career. Another obvious instance of this scheme is the snake discussed above. The segment part structure can be called upon to name the three parts of aspectual estar in lattice-theoretic terms as in (20): 20.  That is, the initial state includes the beginning but not the middle and end, the progressive includes the middle but not the beginning or end, and the result state includes the end but not the beginning and middle. Note that there is a fourth, unattested possibility: 21.  In this lattice, both M and E are instances of the predicate. Since the join M+E does not exist in this lattice, the predicate must be assigned to each subpart separately, so that it holds at two discontinuous moments. An E-copularization like Mara est contenta, would be interpreted as Mary being happy at two different intervals and not being happy in the intervening interval. This is not an implausible meaning. It could be understood either as Mary is happy again or perhaps Mary resumed being happy, since to resume implies that the activity was interrupted at an earlier moment. Nevertheless, neither again or resume is a reading available for an E-copularization. The reason for this lacuna may be systematic, rather than accidental. It may be conjectured that this meaning is actually resolved into two smaller ones: 22.  In prose, what happens is that the first result state is asserted, and then the second, identical to the first. Continuing with the example, the sequence is that of (23): 23. contenta + contenta + contenta + contenta It can be proposed that (23) is too complex to be resolved as a single temporal whole and so can only be resolved as two separate temporal entities. In other words, there is a principle of aspectual individuation at work in Spanish and presumably all natural languages which limits functional meanings to a single whole: 24. Conjecture of functional individuation: A functional morpheme F that imposes an aspectual interpretation on some lexical constituent L can only denote the smallest maximal unit in F(L), i.e. the lowest 1 in the lattice. There is presumably some relation between this restriction and the restriction on the formation of the missing part b+e, but it escapes me at the moment. III.2. Contrary-to-expectation estar Many researchers have noted that E-copularizations are used to convey a deviation from an expected, usual or normative state. Bull (1965:294) describes this usage quite perceptively: Thus a person who expects mountains to be high, but not as high as they really are, may say Qu altas estn las montaas! [How high the mountains areE!] The mountains, obviously, have not changed. The use of estar simply indicates the speakers observation that they do not conform to his norm. A short passage from Franco & Steinmetz (1986:380) makes a similar point: Let us suppose that a worker in a steel mill believes or otherwise anticipates that because of its present location in the production line the steel in question should be (relatively) soft and finds these beliefs or anticipations contradicted by that [sic] fact that the steel in question is, in fact, hard. This person would say Este acero est duro [This steel isE hard.] More generally, this type of E-copularization can be said to signal an implicit comparison or contrast between ones expectations and the evidence of the situation. Let us refer to this as the contrary-to-expectation usage, since it depends on the speaker having immediate evidence for an otherwise unusual condition. As with the result-state usage, grammarians in general and researchers into copula selection in particular have adduced many examples. The next few paragraphs review some of these examples, to fix the idea in the readers mind. Contrary-to-expectation E-copularizations often take the form of exclamations: 25 a) Qu ancha est la carretera ahora! (Falk 1979:73) how wide isE the highway now! b) Pepe, qu alto ests! (Va-Cerd 1982:158) Pepe, how tall you-areE! The salient reading of these exclamations is not the inchoative one that the highway or Pepe were subject to an inchoative event which changed their prior condition of narrowness or shortness to their present condition of wideness or tallness, respectively, but rather the contrary-to-expectation one in which the speaker was expecting narrowness or shortness and found the opposite. In support of this hypothesis of a contrary-to-expectation unit of meaning, it can be noted that if this sememe is removed from the E-copularization, the notion is preferentially expressed by an S-copularization, as can be appreciated in the contrast between the unprimed and primed sentences of (26): 26 a) La nieve est negra! The snow isE black [specific snow] a) La nieve es blanca. (the) snow isS white [specific or generic snow] b) El acero est blando! The steel isE soft [specific steel] b) El acero es duro. (the) steel isS hard [specific or generic steel] c) Hoy est muy discretito. Today [he] isE very discrete-DIM (en el vestimiento) (in the clothing) c) Es discreto. [he] isS discrete The S-copularizations in the primed examples view the property characteristically and without reference to any particular aspect of the context. The E-copularizations, on the other hand, are unavoidably dependent on the context to explain why the expected S-copularization is not used. In both cases, one must imagine situations in which the subject was expected to be other than it is asserted to be. That is, the snow in (26a) is expected to be other than white and the steel in (26b) is expected to be other than hard. An interesting addition to these data comes from Porroche Ballesteros (1988:105ff), where it is observed that even predicate nominals can be used in E-copularization, if they have an emphatic or ironic shade of meaning: 27. Buen mdico eres t! Buen mdico ests t (hecho)! good doctor areS you good doctor areE you (become [lit. done]) The E-copularization of (27) without exclamation qualifies as a result-state usage, since the past participle hecho, which comes from the inchoative hacerse mdico become a doctor, is optional. But it can also be understood as an exclamation of how counter to ones expectations about doctors the addressee behaves. In the contrary-to-expectation usage, an asserted predicate is at odds with a norm for that situation. For the sake of illustration, let us analyze Qu alto est Juanito! how tall Johnny is!. Bierwisch (1988) takes the semantics of a dimensional adjective like alto or its complement bajo short to consist of adding or subtracting a constant to or from a contextually-given norm, as in (28): 28 a) j is tall f(j, Height) = Norm + c b) j is short f(j, Height) = Norm c However, from the point of view of lattice theory, Bierwischs format can be translated as a three part segment structure with the form of (29): 29.  With these parts, there are two contrary-to-expectation lattices: 30.  The missing progressive version in which the norm is asserted would be equivalent to the assertion of the expected, which is redundant. III.3. Evidential estar The usage of estar for personal reactions presents an interesting challenge to the analysis developed so far. At first glance, it would seem to follow naturally from the contrary-to-expectation usage, by generalizing the norm as some body of generic observations, which is contrasted to ones immediate perception of the situation. The problem is that one can have a personal reaction that includes the middle-of-the-road value, e. g. La sopa est regular, The soup is OK/so-so. Reserving this part for estar leaves no room for the putative intermediate part consisting of impersonal or common knowledge. In other words, the lattice-theoretic analysis would need at least four parts to account for the personal reaction reading, as sketched in (31): 31.  The three values in the outer circle correspond to the three main personal reactions. These four parts can of course be used to construct a lattice, in which 1 = general knowledge + less + average + more. However, if we want to assert one, say more, then it must be contrasted to general knowledge + less + average. The lumping together of general knowledge with the other two personal reactions does not seem to be a natural part. In fact, it seems to be a contradiction. The only alternative that occurs to us is to lump all three values for personal reactions together into a single part: 32.  The result is a bipartite structure in which there is only one immediate reaction, though it can have several sorts or degrees. We forego designing lattices for this simple structure in the interests of brevity. III.4. Ser From the lattice-theoretic perspective, ser turns out to be rather dull. The essential claim of the structure of (14b) is that, although one can discern parts and subparts to ser, they are all interchangeable. It follows that there is no way to define beginnings or ends, or greater or lesser extents. Such interchangability frees ser from explicit reference to a specific temporal structure, placing it in the realm of the atemporal. This property accounts straightforwardly for the well-known usages of ser for states of characterization and identity. This also accounts for the abstract subject usage, though a little imagination is necessary to see it. The relativization of aspectual E-copularization to specific temporal parts often attaches it to specific temporal locations as well. The clearest examples come from result-state clauses like Mara estuvo en mi casa, Mary was at my house, in which Mary must have been somewhere else before she was there. Now, if temporal specificity is excised from the copular relation as it is for ser, it follows that locational specificity can be excised also. The outcome is that in __ fue en mi casa, the blank can only be filled in for something that does not need to have been anywhere else before it was at my house. This is impossible for physical objects, but perfectly understandable for abstract objects, and especially for events, which do not have any location anywhere while they are not taking place. This abstraction effect for ser can be extended to account for the activity usage by claiming that in a clause such as Mara fue amable conmigo, Mary was nice to me, the subject Mara is understood more abstractly as something along the lines of Maras behavior, an event that comes into existence for a certain time and then disappears, without having to have existed anywhere else beforehand. With the background of these proposals, it is an easy step to the prediction that there should be a usage of ser in which the predicate is an entire event, without reference to any temporal parts. Such usages are indeed attested abundantly as the passive voice. In summary, the lattice-theoretic account of countability generalizes quite naturally to copula selection in Spanish, with the result that E-copularization patterns as a count structure, while S-copularization patterns as a mass structure. IV. Indicative vs. subjunctive mood Spanish also has two moods for subordinate clauses, the indicate and the subjunctive. Farkas (1992) classifies the predicates which govern either mood in the following way: 33. Indicative governors: a) Categorial epistemics: saber to know, pensar to think, creer to believe b) Declaratives: decir to say, escribir to write, declarar to declare c) Predicates of certainty: estar {seguro/convencido} to be {sure/convinced} d) Commissives: prometer to promise e) Fiction verbs: soar to dream, imaginar to imagine, mentir to lie 34. Subjunctive governors: a) Desideratives: querer to want b) Directives: ordenar, mandar to order c) Predicates of likelihood:1 es probable it is probable d) Modals: ser {posible/necesario} it is {possible/necessary} e) Epistemic predicates expressing neutral/negative commitment: no creer to not believe, dudar to doubt Farkas treats indicatives as denoting in a singular possible world and subjunctives as denoting in a plurality of possible worlds. (35) provides a pair of examples: 35 a) Juan so que Mara estaba enferma. John dreamed that Mary wasind sick b) Juan mand que Mara se fuera. John ordered that Mary leavesubj (35a) is true in the fiction world of Johns dream, whereas (35b) is true in many possible worlds, distinguished by how and when Mary leaves. Howard (1994) discusses some minor drawbacks of Farkas analysis, but there is one area of facts that Farkas does not mention that makes the analysis contemplated here much easier to pursue. It has to do with the fact that Spanish also has a distinction in mood in adjectival complements, illustrated in (36): 36 a) Mara busca a un secretario que habla yucateco. Mary is looking for a secretary that speaksind Yucatec. b) Mara busca un secretario que hable yucateco. Mary is looking for a secretary that speakssubj Yucatec. In the indicative clause of the (36a) example, Mary is understood to have a specific secretary in mind. Not so in the subjunctive clause of (36b), in which Mary is understood to be searching for any secretary at all that speaks Yucatek. We have not said anything about plurality yet, but it patterns against count meanings and with mass meanings. Thus we predict that indicative clauses should have a countable lattice structure and subjunctives, a mass lattice structure. The challenge is to describe exactly what a count structure looks like in the context of mood. Consider the two diagrams below, which represent the total field of secretaries that speak Yucatek: 37.  In the left-hand diagram, a secretary is foregrounded from the background field. This represents the indicative reading, in which a specific person is under consideration by Mary to the exclusion of anyone else. It can be converted into lattice structure by gloming all of the rejected candidates together as a single point, producing a binary structure such as (22) or (32). In the right-hand diagram, in contrast, no individual is foregrounded to the exclusion of the others: they are all equally foregrounded. This represents the subjunctive reading, in which all of the candidates qualify for consideration by Mary. It answers to the mass characteristic of presenting all parts as interchangeable that is, each one is equally viable for satisfying the predicate in question and can be reduced to a mass lattice without problem. V. Adjective placement The final construction to be examined here concerns the placement of an adjective before or after the noun it modifies. There is a robust meaning associated with either position in Spanish. Restrictive adjectives follow the noun, while appositive adjectives precede it: 38. los chinos trabajadores los trabajadores chinos the Chinese hard-working the hard-working Chinese RESTRICTIVE APPOSITIVE There are several facts that support this conclusion. The most obvious one comes from the intuitions which informants have about how many entities the head nouns denote in phrases like the following: 39. RESTRICTIVE APPOSITIVE a) las palmeras verdes del Caribe las verdes palmeras del Caribe the palms green of-the Caribbean. the green palms of-the Caribbean b) la mujer hermosa del general la hermosa mujer del general the wife pretty of-the general the pretty wife of-the general c) el rector amigable de Penn el amigable rector de Penn the president friendly of Penn the friendly pres. of Penn d) mi leal amigo mi amigo leal my loyal friend my friend loyal In (39a), palmeras verdes implies that there are palm trees in the Caribbean which are not green. The reverse order lacks any such implication of non-green Caribbean palm trees. A similar contrast is brought out even more sharply in (39b, c). In our society, a general tends to have one wife and a university one president, so the restrictive versions have the odd implication that others are excluded. Pedagogical grammars of Spanish for English-speakers generally echo these intuitions in their explanations. One particularly clear statement is found in Stockwell, Bowen & Martin (1965:89): In un famoso hroe, the order indicates that we expect heroes to be well-known. But in un hroe famoso, we are differentiating the hero who is famous from others who have not been acclaimed. The item in final position carries more information. In a similar vein, Rojo (1975:201) notes that the post-nominal adjective implies the existence of other objects, while the prenominal adjective does not: 40 a) Trajo un vaso amarillo (no un vaso blanco, o verde) s/he-brought a glass yellow (not a glass white, or green) b) Trajo un hermoso vaso (el vaso era hermoso, no feo.) s/he-brought a pretty glass (the glass was pretty, not ugly) Un vaso amarillo excludes glasses which are white, green or any other color. Un hermoso vaso does not exclude other glasses, but rather other properties which this glass could have. In addition to intuitions about meaning, one can point to two other differences between the two positionings of the adjective. Rojo observes that the prenominal adjective may repeat some of the intension of the noun: 41. RESTRICTIVE APPOSITIVE a) los animales mansos las mansas ovejas the animals tame the tame sheep b) la piedra verde la verde esmeralda the stone green the green stone c) la nieve negra de Nueva York la blanca nieve the black snow of NY the white snow The appositive adjectives all recapitulate some well-known property of the noun sheep are tame, emeralds are green while the same adjectives in the postnominal position sit best with nouns which do not include this property as part of their meaning. Rojo (1975:201) goes on to note that the lessened informative content of the appositive adjective is reflected in the fact that they do not sound well as answers to questions, though no such limitation is found with restrictive adjectives: 42 a) Qu novelas te interesan? - Me interesan las novelas policiacas. what novels you interest? - me interest the police novels b) Qu dinero os domina? - #Nos domina el maldito dinero. what money yall dominates? - us dominates the damn money In this case, the general outline of the lattice-theoretic approach should be clear. The left side of (43) shows how the restrictive meaning can be reduced to a binary included vs. excluded structure for las palmeras verdes, while the right side shows how the appositive meaning of las verdes palmeras is mass-like in that all of the palm trees have the same interchangeable status: 43.  Again, we do not draw the lattices for the sake of brevity. VI. Summary This paper argues for a common structure to several disparate pairings of grammatical constructions in Spanish. We have not gone very deep either into the data or into alternative analyses for these constructions, but rather have sketched the essence of a lattice-theoretic approach. Many other constructions come to mind as possible instantiations of the two sorts of lattices postulated above, such as the preterite-imperfect distinction, por vs. para, the -illo/ito distinction in diminutives, the verbal-adjectival distinction in past participles, and the appositive-restrictive distinction in adverbial modifiers. We hope to extend the lattice-theoretic approach even further, to cover these cases as well, in the future. VII. References Bull, W. 1965. Spanish for teachers. Applied Linguistics. New York: The Ronald Press Company. Contreras, Heles (1981) The Case for Base-generated Attributive Adjectives in Spanish in William Cressey & Donna Jo Napoli, eds. Linguistic Symposium on Romance Languages 9 . Georgetown University Press, Washington, D.C. Farkas, Donka (1992), On the semantics of subjunctive complements in P. Hirschbhler and K. Koerner (eds.), Romance Languages and Modern Linguistic Theory, John Benjamins, Amsterdam, pp. 69-104. Franco, Fabiola & Donald Steinmetz. 1986. Taming ser and estar with Predicative Adjectives. Hispania. 69:377-386. Gerstl, Peter & Simone Pribbenow. 1995. Midwinters, End Games and Bodyparts: a classification of part-whole relations. International Journal of Human-Computer Studies. 43:847-864. Hinrichs, Erhard. 1985. A Compositional Semantics for Aktionsarten and NP Reference in English. Doctoral dissertation, Ohio State University, Columbus, Ohio. Howard, Harry. 1994. Mood Selection in Spanish and Lattice Structure. In Lenguajes Naturales y Lenguajes Formales X, ed. Carlos Martn Vide, 435-442. Barcelona, Spain: Promociones y Publicaciones Universitarias. Landman, Fred (1991), Structures for Semantics, Kluwer Academic Publishers, Dordrecht, The Netherlands. Lujn, Marta (1980) Sintaxis y Semntica del Adjetivo. Ediciones Ctedra, Madrid, Spain. Pelletier, Francis Jeffry. 1979. Non-singular reference: some preliminaries. In Mass Terms: Some Philosophical Problems, ed. Francis Pelletier, 1-14. Boston, Massachusetts: D. Reidel Publishing. Porroche Ballesteros, Margarita. 1988. Ser, estar y verbos de cambio. Madrid: Arco/Libros, S.A.. Rojo, Guillermo (1975) Sobre la coordinacin de adjetivos en la frase nominal y cuestiones conexas Verba 2:191-224. Siegel, Muffy E. A. (1980) Capturing the Adjective. Garland Publishing, Inc. New York. Originally 1976 University of Massachusetts at Amherst dissertation. Stockwell, Robert P., J. Donald Bowen & John W. Martin (1965) The Grammatical Structures of English and Spanish . The University of Chicago Press, Chicago. Terker, Andrew (1985) On Spanish adjective position Hispania 68:505-509. Verkuyl, Henk. 1993. A theory of aspectuality: the interaction between temporal and atemporal structure. Cambridge, New York, Melbourne: Cambridge University Press.  An alternative way of reading the diagram is by means of the plus signs: tail combined with body gives the complex part tail + body, and tail + body combined with tail + head gives the complex part tail + body + head.  Rojo actually claims that the affirmations do not give rise to felicitous questions. I have altered this claim to avoid interpreting the follow-up question as an echo question. This alteration is more in accord with contemporary linguistic theory, which investigates questions in terms of the answers they license, and not the other way around. 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Y|UEHEH @@UU17"B*2d7@P+@MP@>P"@Pv@+IL;ZC&ijklm: r=5[{Unopqrstu IZ ((()9:R HH(EG(HH(d'@=/RH-:LaserWriter 8 PalatinoTimesAAA+$(.BLattice morphology - LSoRB Harry Howardlattice Harry Howard