Traditionally logic has studied the properties of operators corresponding to restricted classes of words, mainly connectives and quantifiers, while nouns, verbs, adjectives and prepositions are represented as relations with no particular properties. However, also words in these classes, in particular verbs and prepositions, obey regular inferential patterns. For example, if “Mary ate a cake” then “Mary ate”, and if “She ate two cakes” we may conclude that “She ate each of the cakes”. But it does not follow from “Two girls ate the cake” that “Each of the girls ate the cake”.
This project will study more systematically inferential patterns of various verb classes. In the semantic literature there are several proposals for classification of verbs semantics, e.g. Levin’s classes and Fillmore’s frame semantics. Verbs have been encoded according to such classifications in various computational resources like various WordNets, PropBank, FrameNet, VerbNet. In this project we will try to uncover systematic relationships between verb classes and inferential patterns and exploit it for inference.
The exact content of the project and which of the questions above it will address will depend on the background of the student. It will be useful with some knowledge in semantics or logic beyond the obligatory courses.