  Non-sentential utterances (NSUs) are utterances that lack a complete
sentential form but whose meaning can be inferred from the dialogue context,
such as "OK", "where?", "probably at his apartment". The interpretation of
non-sentential utterances is an important problem in computational linguistics
since they constitute a frequent phenomena in dialogue and they are
intrinsically context-dependent. The interpretation of NSUs is the task of
retrieving their full semantic content from their form and the dialogue
context. The first half of this thesis is devoted to the NSU classification
task. Our work builds upon Fern\'andez et al. (2007) which present a series of
machine-learning experiments on the classification of NSUs. We extended their
approach with a combination of new features and semi-supervised learning
techniques. The empirical results presented in this thesis show a modest but
significant improvement over the state-of-the-art classification performance.
The consecutive, yet independent, problem is how to infer an appropriate
semantic representation of such NSUs on the basis of the dialogue context.
Fern\'andez (2006) formalizes this task in terms of "resolution rules" built on
top of the Type Theory with Records (TTR). Our work is focused on the
reimplementation of the resolution rules from Fern\'andez (2006) with a
probabilistic account of the dialogue state. The probabilistic rules formalism
Lison (2014) is particularly suited for this task because, similarly to the
framework developed by Ginzburg (2012) and Fern\'andez (2006), it involves the
specification of update rules on the variables of the dialogue state to capture
the dynamics of the conversation. However, the probabilistic rules can also
encode probabilistic knowledge, thereby providing a principled account of
ambiguities in the NSU resolution process.
