INFORMACION COMPLEMENTARIA PARA LOS LEVANTAMIENTOS DE VEGETACIÓN

Mainstream formal semantics does not decompose bare LIs but lets them denote single semantic objects; for example, the bare noun board as a whole denotes 𝜆𝑥∶entity . Board(𝑥) (a first-order predicate). This convention is retained in more recent studies that otherwise do use lexical de- composition. In the neo-Davidsonian representation in (21), for example, the bare verb butter denotes BUTTER(𝑒), which integrates an idiosyncratic tag “BUTTER” and an event variable “e.” (21) a. Jones buttered the toast slowly in the bathroom with a knife.

b. ∃e[BUTTER(e) ∧ AGENT(e) = j ∧ THEME(e) = t ∧ SLOWLY(e) ∧ LOCATION(e) =

b ∧ INSTRUMENT(e) = k] (Landman 2000: 1–2)

The same is true in Ramchand’s first-phase syntax (22a) and quotational semantics (22b). I have abbreviated Ramchand’s denotations and only kept the bare verb parts.

(22) a. JpushK = … 𝜆e[… push(e) … ] (Ramchand 2008: 61)

b. JrunK = … 𝜆e[run(e)] … (Ramchand 2018: 15)

Here too the idiosyncratic and compositional parts of a bare verb are integrated into a single expression. The examples in (21)–(22) show that the root/categorizer-oriented thinking—or the idea of separating compositional and idiosyncratic content in meaning representation—has not had much influence in formal semantics. Despite this state of affairs, a root-level semantics is not too difficult to implement. Kelly (2013) adopts a conjunctivist approach (as in event semantics) and lets the root and the categorizer both denote first-order predicates, though he assigns the former a more general argument type than the latter. Thus, when the two compose—by argu- ment identification—the argument of the overall predicate is restricted to the categorizer’s type. Kelly takes eventuality to be a generic type covering all of nouns, verbs, and adjectives. He then divides eventuality into two subtypes, event (for verbs) and state (for nouns and adjectives),28 and assigns these to the DM categorizers. Meanwhile, the generic type eventuality is assigned to roots under the assumption that roots are “all underlyingly properties of eventualities, but are vague between properties of events and properties of states” (Kelly 2013: 81). Kelly illustrates the root-categorizer composition with the following examples:

(23) Root Categorizer Composition

J√redK = 𝜆𝑒 . red′_{(𝑒) Ja0K = 𝜆𝑒 . state(𝑒) 𝜆𝑒 . state(𝑒) ∧ red}′_(𝑒)

J√doorK = 𝜆𝑒 . door′

(𝑒) Jn0_{K = 𝜆𝑒 . state(𝑒) 𝜆𝑒 . state(𝑒) ∧ door}′_(𝑒)

J√breakK = 𝜆𝑒 . break′_{(𝑒) Jv0K = 𝜆𝑒 . event(𝑒) 𝜆𝑒 . event(𝑒) ∧ break}′_(𝑒)

(Kelly 2013: 82, 95) 28_{Kelly (2013: 78) assumes that n and a are “semantically equivalent” and that their difference is “purely syntactic,”}

Throughout (23) 𝑒 is implicitly typed as eventuality, and the more specific types (i.e., those in the categorizers) are expressed by first-order predicates. As such, Kelly treats (nongeneric) types and roots as the same sort of semantic object, though he presumably gives them different the- oretical status, as reflected in his use of two different typefaces (roman and italic). To facilitate comparison with the alternative possibilities to be introduced, I adapt Kelly’s idea into a more familiar type system (i.e., that in Kratzer & Heim 1998, with a Davidsonian extension), where nouns denote predicates over entities rather than eventualities. I also propose a truly generic type u, defined as the most general supertype in the heterogeneous universe of discourse introduced in §2.2.3.1. All the conventional types are thus subtypes of u.29 Below I illustrate this ontology with a HPSG-style type hierarchy (I have kept Kelly’s subtyping of eventuality).

(24) u

entity eventuality

event state

truth value ⋯

The root-categorizer composition proceeds as in Kelly’s model. I simply replace eventuality by u as the type of roots and state by entity as the type of the nominalizer. Accordingly, I update Kelly’s examples in (23) to (25). I change Kelly’s eventuality variable 𝑒 to the type-neutral 𝑥 and mark its background type u explicitly. I also adapt the notation to my own style and mark types in the 𝑣𝑎𝑟∶type format in the composition column to highlight the different theoretical status between type declarations and root predicates.

(25) Root Categorizer Composition

J√redK = 𝜆𝑥∶u . Red(𝑥) JAK = 𝜆𝑥∶u . State(𝑥) 𝜆𝑥∶state . Red(𝑥) J√doorK = 𝜆𝑥∶u . Door(𝑥) JNK = 𝜆𝑥∶u . Entity(𝑥) 𝜆𝑥∶entity . Door(𝑥) J√breakK = 𝜆𝑥∶u . Break(𝑥) JVK = 𝜆𝑥∶u . Event(𝑥) 𝜆𝑥∶event . Break(𝑥)

How does the Kellyan approach fare in the composition of MHCs? It correctly composes X and 𝜔2; for instance,J{N, √board}K = JNK∧J√boardK = 𝜆𝑥∶u . Entity(𝑥)∧𝜆𝑥∶u . Board(𝑥) =

𝜆𝑥∶u . Entity(𝑥) ∧ Board(𝑥) = 𝜆𝑥∶entity . Board(𝑥). Besides, upon the Cat-X agreement, the Cat-𝜔₁merger also gets a computed denotation, as in (26).

(26) J{Cat_{⟨cat∶n, pos∶1⟩}, black}K = 𝜆𝑥∶entity . Black(𝑥)

Note that a nominally valued Cat is not the same as a nominalizer; that is, the (re)categorization in (26) does not yield the independently lexicalized nominal meaning for black (i.e., a color name). 29_{The conventional basic types are all sort-types; hence, the logical metalanguage they are part of is essentially many-}

This is because (i) black is not a root (so the categorization is not that needed for the lexical noun black, which is presumably {N, √black}), and (ii) in the course of derivation Cat and N are categorially unified (with N becoming a two-segment category) and come to share a single label (N); hence, {Cat, black} is not interpreted alone at the C-I interface but in conjunction with {N, √board}. In other words, the valued Cat in (26) does not categorize black into a noun but categorizes it into part of a bigger noun. The ultimate compositional representation of blackboard is given in (27a), and the same information is displayed in tree format in (27b).

(27) a. J{{Cat, black}, {N, √board}}K = 𝜆𝑥∶entity . Black(𝑥) ∧ Board(𝑥) b. N_{[𝜆𝑥∶entity . Black(𝑥) ∧ Board(𝑥)]}

N_{[𝜆𝑥∶entity . Black(𝑥)]}

√board

[𝜆𝑥∶u . Board(𝑥)]

N_{⟨cat: n, pos: 1⟩}

[𝜆𝑥∶u . Entity(𝑥)]

Cat[? ∧ 𝜆𝑥∶u . Black(𝑥)]

black

[𝜆𝑥∶u . Black(𝑥)]

Cat_{⟨cat: , pos: ⟩}

[?]

Agree

However, there are two problems in the above composition. First, it does not really give us the meaning of blackboard but merely gives us that of Cat-N, which denotes an entity-typed semantic category. As to the definition of that category, all (27) tells us is that it is somehow related with “Black” and “Board.” Thus, we are brought back to our point of departure; namely, the mean-

ing of an MHC is only compositional in its categorial facet but not in its lexical-encyclopedic facet. The latter’s noncompositional nature leads us to ask what benefit having root denotations in the semantic model really gives us on the one hand and makes it inappropriate to represent the integration of root interpretations by logical conjunction on the other.

Second, the above composition is tailored for lexical categories; that is, it only works for DM- style categorizers and lexical-purpose roots, which we know a priori would compose into first- order predicates (i.e., the denotations of bare lexical categories). Thus, Kellyan root semantics is bundled with the presupposition that roots can only ever be used for lexical categories. While this is an established assumption in most root-based theories, it makes the peculiar prediction that the lexical/functional division is black-and-white; yet half-lexical–half-functional items are widely attested in world languages (e.g., the numerous classifiers in East Asian languages; such items will be investigated in Chapter 4), and a proper theory for such items requires a principled mechanism to integrate functional categories and idiosyncratic-information-bearing units (i.e., roots in our terminology). In short, the lexical-category-specific nature of possibility I makes its applicability and explanation power unduly limited.