The driving idea in categorial grammars is that we can assign types to elements of our language and then perform mathematical operations on those types to check the grammaticality of strings of those elements. Pregroup grammars are different from the original categorial grammars as their types are simply concatenations of basic types and adjoints of those, and this makes the framework less complex and more flexible, as fewer restrictions are put on the way types can combine. Another difference is that, mainly because the types are associative, no λ-calculus semantics can be done for those systems without the addition of multiple constraints. Our aim is to come up with a sound variant of the λ-calculus that takes into account the directionality of argument passing, while treating both directions independently. Our goals are to 1) redefine pregroups as a logical system 2) lay down what we think is the right term-calculus, that we will then use to extract the logical representation of a sentence in parallel to doing the grammaticality check 3) make sure that this semantic layer does not add any weight on the complexity of the system.
School of Informatics and Computing, Indiana University.