Formal semantics meets distributional vectors
The goal of this project is to study two different approaches related to linguistic meaning, formal sentence semantics and vectors derived from distributional patterns (sometimes called "distributional semantics").
Formal semantics has its roots in logic. Its goal is to model inferential patterns, like the classical from All men are mortal and Socrates is a man it follows Socrates is mortal. Formal semantics success is in modelling predicate-argument structure, sentential connectives and quantification. It has less to say about the relationship between words; house and building are not more similar than house and alligator.
Distributional representations (sometimes called "distributional semantics") represent words in terms of vectors. These vectors are based on the distributional patterns of the words. Words with similar patterns will appear close together in the vector space. Words with more distinct distributional patterns will appear further apart. It is observed that words that are distributional similar are also similar in meaning, e.g. that house is similar to building but less similar to alligator. This adds a dimension compared to the pure formal semantics. But the relationship to inferential patterns is not straightforward; a house is also a building - but not the other way around - and a tiger is not a lion even though they are similar.
The goal of this project is first to conceptually clarify the goals and ambitions of the two approaches and the relationships between them. It is then to study the actual vector representations of a set of words and to which degree these representations support inferences. Further questions will depend on the initial results and the interests of the student. One possibility is to consider vagueness, approximate truths or probabilities. Another possibility is to consider the geometric structure of the vector space and decomposition.
Suitable background is some familiarity with vector representations and interest in logically-based formal semantics.