Semantics of Gradable Modal Expressions
|[The following is from
the NSF proposal BCS-1053038]
The focus of this project is the semantic analysis of expressions such as probable, permissible and likelihood, which we call Gradable Modal Expressions (or GMEs). Like tall and tasty, these predicates are gradable:
(1) a. It is barely permissible to cancel class for a conference.
b. There’s a 60% probability that she’ll be late.
c. John is more able to swim than to fly.
Note that all semantic categories of modality (including deontic, epistemic, and ability) exhibit gradability. The gradability of modal expressions raises such questions as: What is the compositional semantics of GMEs? How is gradability represented? How are the
existing results of the theory of modality to preserved? Our project will have two main strands: (i) a formal semantic component, and (ii) a corpus-based annotation component.
As a point of departure, we build on previous work on graded modality within possible worlds semantics (Lewis 1973, Kratzer 1981). We note, however, that this analysis, while producing important insights, is not adequate as it stands: more likely than, for instance, is treated as a lexical item whose meaning is not composed out of its parts, in particular out of the meaning of more and likely. Clearly, a compositional analysis is needed, and should be integrated into a broader analysis of gradability.
The semantic analysis of gradable expressions has been the subject of intensive study. Most current work builds on the idea that gradable expressions involve scales of degrees (Kennedy 2007, among many others), with recent work showing that these expressions can be classified in terms of the properties of their scale; these properties are indicated by patterns of modification. We will apply this approach to the analysis of GMEs. GMEs differ in terms of their scale structure, as evidenced by the fact that they show differing patterns of modification (parallel to Kennedy and McNally 2005).
(2) a. *It is more possible that Spain will win than that Germany will.
b. It is more likely that Spain will win than that Germany will.
We hypothesize that, in the case of GMEs, degrees are constructed using the resources of modal semantics (possible worlds, accessibility, ordering, etc.); we aim to show that the scales constructed in this way have the appropriate properties. A particular problem arises in the case of probability expressions like probable or likely. It has been observed that Kratzer's ordering-based semantics is not adequate for these (Yalcin 2010 Lassiter 2010), and it has been argued that their scales must have the metric structure of probability theory. We investigate how to embed probability scales into the general account of GMEs.
The key data for our investigation concerns constructions like those in (1)-(2). Because the patterns of acceptability of various GMEs in these constructions in not simple or categorical, we will investigate them through study of the distribution of GMEs in texts. We will develop annotated corpora in which GMEs are identified and coded for semantically relevant information. To this end, we will develop an annotation language for probability information analogous to other semantic annotation schemes such as TimeML and SpatialML. This work will allow us both to better understand the range of syntactic, semantic, and pragmatic contexts in which GMEs occur, and to investigate how context affects their meanings. Longer term, we expect the corpus investigation to serve as a catalyst for more work on the computational semantics of GMEs. We envision applications to such areas as automatic reasoning under partial information and risk management.