Predicate Gradual Logic and Linguistics

TL;DR

This paper introduces an extended propositional gradual logic that effectively handles donkey anaphora in linguistics, addresses existential import issues, and models Aristotle's syllogisms and conversion.

Contribution

It develops a new logical framework extending recent gradual logic to generalize donkey anaphora treatment and incorporate classical syllogistic reasoning.

Findings

Successfully models donkey anaphora generally

Addresses and resolves issues with existential import conventions

Reproduces Aristotle's syllogisms and conversion within the logic

Abstract

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.