University of Bucharest Faculty of Mathematics and Computer Science
Extending the continuations-based semantics from sentence to discourse
Download 0.74 Mb.
|
- Navigate this page:
- Handling negation
Extending the continuations-based semantics from sentence to discourseWe propose here the semantics of cross-sentential punctuation marks “.” and “;”. We do not give the semantics of other cross-sentential punctuation marks such as the imperative “!” or the question mark “?”, with controversial truth values. We only treat assertive (affirmative or negative) sentences, considering “.” and “;” as functions that take two sentence denotations and return a sentence denotation (the conjunction of original sentence denotation):  
We only take the left context into consideration when interpreting a current sentence, and not both the left and the right context as in de (de Groote’s (2006)). Our approach is supported by the empirical observation that the default order of interpretation is left to right. There are some linguistic data (such as cataphora, i.e. an instance of an expression referring to another one located in following utterances) that suggest this default order may be sometimes broken, but we consider them marginal. For two affirmative sentences with no anaphoric relations and no quantifiers, such as John came. Mary left, the derivation trivially proceeds as follows: 
As one sees above, there is no need in this simple case to resort to type shifting at all. Nevertheless, type shifting and the powerful mechanism of continuations are employed when dealing with linguistic side effects such as quantifier scope or binding. Thus, to transmit quantificational or anaphoric information, the denotation lifts accordantly, for example like this: 
To derive the denotation of “A man came. He whistled”, type lifting, type lowering and the Bind rule become necessary: 
 
Note that the denotations of came and whistled were also lifted so as to match the ones of a and he, both being scope-takers. The last equality sign is due to routine lambda conversion. The picture of relating two sentences is of course much more complex than this. Dot and semicolon are the most simple means of relating two sentences, which leave implicit the specific rhetorical relation between the two (such as Narration, Result, Background, Elaboration, Explanation, Contrast, Parallel, etc). There are a number of explicit discourse connectors, such as but, also, on the one hand, on the other, so, because, when, nevertheless, etc. that determine the possible rhetorical relations between the two sentences they relate. In turn, each rhetorical relation has linguistic side effects such as constraining the possible antecedent for pronominal anaphora. We will deal with some of these phenomena in Handling Hierarchical Discourse Structure section.
Negation generally cannot take scope outside the verb phrase it modifies. We give not the following denotation: 
This means that negation functions in local context as a verb modifier and takes scope at a sentence to give a sentence. Now, one obtains the following denotation of John does not own a car: 
which means that there is no car that John owns, a fair approximation of the denotation of the intended meaning. If we do not restrict the possible scope of negation, continuing the discourse with the sentence “*It is red”, could result in the following wrong derivation: 
 =
which means that it can refer back to a car. In fact, if we do not restrict the possible scope of negation, any following sentence may be wrongly interpreted inside the scope of negation. Thus, one needs to force the scope closing of not immediately after the interpretation of its minimal clause, by applying Lower. This also closes the scope of any other DP inside the scope of negation, so it becomes impossible for it to bind (transmit its value to) subsequent anaphoric expressions. Thus, the interpretation followed by “It is red” crashes. This also has the pleasant effect of allowing the subject of the sentence to bind subsequent anaphora. To exemplify, we give the derivations of “John does not own a car. *It is red“ and “A student did not knocked. He entered”: 
To obtain the above derivation, as soon as the verb phrase under negation was interpreted, we closed the scope of negation by applying Lower, then we lifted the denotation of not knocked to match the levels of a student. Negation takes wide scope over other possible scope takers in the verb phrase it negates (like a man or every man in direct object position). The interpretation of “John does not own a car” in which the existential quantifier takes wide scope over the negation (there is a car that John does not own) is impossible in natural language, possibly because it is pragmatically ruled out by the fact that it is too uninformative. The right (preferred) interpretation is obviously the one in which negation takes scope over the existential quantifier. There are nevertheless lexical entries like definite descriptions (such as John, the men, the man who entered) that, when in direct object position of a negated verb phrase, may take wide scope over negation and thus bind subsequent anaphora. For instance, here it is the derivation of “Mary does not like John. He is rude”:
|
