Predicate Gradual Logic and Linguistics
This work addresses a foundational problem in formal semantics for linguists and logicians, offering a more generalizable solution than prior approaches.
The paper tackles the problem of donkey anaphora in linguistics by proposing a new logical approach based on predicate gradual logic, which generalizes better than existing theories and also addresses issues with existential import and Aristotle's syllogisms.
There are several major proposals for treating donkey anaphora such as discourse representation theory and the likes, or E-Type theories and the likes. Every one of them works well for a set of specific examples that they use to demonstrate validity of their approaches. As I show in this paper, however, they are not very generalisable and do not account for essentially the same problem that they remedy when it manifests in other examples. I propose another logical approach. I develoop logic that extends a recent, propositional gradual logic, and show that it can treat donkey anaphora generally. I also identify and address a problem around the modern convention on existential import. Furthermore, I show that Aristotle's syllogisms and conversion are realisable in this logic.