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.
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