Combined distributional and logical semantics

Abstract

Understanding natural language sentences requires interpreting words, and combining the meanings of words into the meanings of sentences. Despite much work on lexical and compositional semantics individually, existing approaches are unlikely to offer a complete solution. This thesis introduces a new approach, which combines the benefits of distributional lexical semantics and logical compositional semantics.

Linguistic theories of compositional semantics have shown how logical forms can be built for sentences, and how to represent semantic operators such as negatives, quantifiers and modals. However, computational implementations of such theories have shown poor performance on applications, mainly due to a reliance on incomplete hand-built ontologies for the meanings of content words. Conversely, distributional semantics has been shown to be effective in learning the representations of content words based on collocations in large unlabelled corpora, but there are major outstanding challenges in representing function words and building representations for sentences.

I introduce a new model which captures the main advantages of logical and distributional approaches. The proposal closely follows formal semantics, except for changing the definitions of content words. In traditional formal semantics, each word would express a different symbol. Instead, I allow multiple words to express the same symbol, corresponding to underlying concepts. For example, both the verb write and the noun author can be made to express the same relation. These symbols can be learnt by clustering symbols based on distributional statistics—for example, write and author will share many similar arguments. Crucially, the clustering means that the representations are symbolic, so can easily be incorporated into standard logical approaches.

The simple model proves insufficient, and I develop several extensions. I develop an unsupervised probabilistic model of ambiguity, and show how this model can be built into compositional derivations to produce a distribution over logical forms. The flat clustering approach does not model relations between concepts, for example that buying implies owning. Instead, I show how to build graph structures over the clusters, which allows such inferences. I also explore if the abstract concepts can be generalized cross-lingually, for example mapping French verb ecrire to the same cluster as the English verb write. The systems developed show good performance on question answering and entailment tasks, and are capable of both sophisticated multi-sentence inferences involving quantifiers, and subtle reasoning about lexical semantics.

These results show that distributional and formal logical semantics are not mutually exclusive, and that a combined model can be built that captures the advantages of each.