EDUCACIÓN AMBIENTAL, SENTANDO LAS BASES PARA UN CAMBIO DE ACTITUD

I follow the view that a proper analysis of natural language semantics needs to unambiguously derive the truth conditions which correspond to certain syntactic terminal nodes and their hierarchical organization. This general approach to natural language semantics is widely adopted in formal linguistics and the system in Heim and Kratzer (1998) is an example of a well known modern implementation. The standard formalism for expressing an analysis of this type is the typed lambda calculus and an analysis must include the following.

(32) a. A denotation is assigned to every syntactic terminal node.

b. Composition principles are stated and they unambiguously derive the truth conditions associated with a syntactic structure, given the deno- tations of the terminal nodes.

An analysis which meets the requirements in (32) makes predictions which can be tested against alternative proposals in a rigorous manner and the conditions under which such an analysis is falsified are fairly well understood. There is no reason to resort to anything less precise and I will therefore spell out explicitly the denotations and composition principles for the proposed structures in this dissertation. Many aspects of my system adopt a standard approach in formal semantics but I will

nevertheless err on the side of overclarifying the formal tools and terminology in order to minimize the risk of misunderstanding.

Semantic composition is assumed to be type-driven and the basic semantic types are (i) truth values and (ii) particulars. A truth value has the type signature t and its value can be either true or false, often written as 1/0, respectively. A particular is any other basic type and it is something that can be picked out in the world and referred to. A particular can be concrete or abstract and the set of particulars includes at least individuals, events and states. Individuals can be humans, animals, or inanimate objects. Events include activities like dancing and walking, and states include the state of someone being cold or something being closed. I will not be concerned with the philosophical implications of such a classification beyond its utility for capturing the distribution of linguistic elements.

The type signature e is used to refer to the subset of particulars which are individuals (entities) and s is used for particulars which are eventualities, including Davidsonian events (Davidson 1967) and states. The type signatures e and s are therefore notational conventions for restricting the domain of particulars.5 _{I will}

use conventional labels for variables of each respective basic type as shown in (33). These conventions mean that whenever I use the variable x, it refers to an individual even if I do not explicitly mention that the type signature is e.

5_{Particular may also be further divided into subdomains like events, states, times, degrees,} humans, animates, etc. and notational conventions can be introduced for any of these if they allow us to capture semantic distinctions which are important for grammatical representation.

(33) Semantic types

type signature variables

truth value t p, q

individual e x, y, z

eventuality s e, e0, e00

For any two types X and Y, which may or may not be the same type, the ordered pairhX,Yiis also a type. A denotation of typehX,Yiis a function from (input) type X to (output) type Y. Type signatures are used to write out such complex types.

For example, he,ti is the type of a function whose domain is the set of individuals

and whose range is the set of truth values. A special function, the interpretation

function, is written out using double brackets _JK. When the syntax is done, the

interpretation function maps each morpheme to a specific denotation and computes the compositional meaning.

The denotation of a morpheme can be of any basic or complex semantic type. If proper names are analyzed as monomorphemic individuals, the denotation of

Cringer is just ‘Cringer’ as in (34). The morpheme √_cat is interpreted as in

(35a), where “∈ Dhe,ti” means that its denotation is a function of type he,ti. The

denotation of √_cat is the function which maps any individual x to ‘true’ (or 1)

if the individual is a cat, but ‘false’ (or 0) otherwise. Rather than writing “true if x is a cat”, predicates will be written out in function notation below, for example “cat(x)” in (35b). The two notations are equivalent.

(35) a. q√_caty ∈ Dhe,ti =λx . true if x is a cat, false otherwise b. q√_caty ∈ Dhe,ti =λx . cat(x)

Under the hood, a function is a set of ordered pairs. If Cringer and Oliver are cats

but Adam is not, then the function q√_caty includes the following.

(36) q√_caty ∈ Dhe,ti = {hCringer, 1i,hOliver, 1i,hAdam, 0i ...}

For the purpose of writing out derivations in the dissertation, the notation in (35b) will be used to express the meaning of predicates. However, the output of cat(x) is mathematically derived by looking the value of x up in the initial elements of a set of ordered pairs as shown in (36) and returning the corresponding second element. Given the state of the world in (36), the following holds.

(37) a. cat(Cringer) = 1

b. cat(Adam) = 0