Speaker
Affilliation
Sussex
Abstract
Techniques such as latent semantic analysis and measures of distributional similarity are based around the idea that meanings of words may be represented as elements of a vector space. Such representations often provide clear advantages in many applications, but many questions relating to these representations remain unanswered. How do such representations relate to ontological representations of meaning, and is it possible to combine the two? How are representations of words to be combined into representations of phrases and sentences, and what role may syntax play in this? How can notions such as entailment and contradiction be described between such representations?
In this talk I will motivate the use of algebra as a means towards answering these questions. Several observations point towards a particular area of mathematics that has been neglected in the computational linguistics literature -- that of vector lattices -- structures that combine a vector nature with a lattice structure. Our thesis is that meanings may be represented as 'positive' elements of such a structure, and words may then be considered as positive operators on a vector lattice.