The Quantified Argument Calculus

Speakers Abstract:

I first present the principles of a logic I have developed over the years, in which quantified arguments occur in the argument position of predicates. That is, while the natural language sentence ‘Alice is polite’ is formalised P(a), the sentence ‘Some students are polite’ is formalised P(?S). In several ways, this logic is closer to Natural Language more than is any version of Frege’s Predicate Calculus. I proceed to discuss further features of this new logic, the Quantified Argument Calculus (Quarc). For instance, the Quarc incorporates, like Natural Language, both sentential negation and predication negation, as well as converse relation-terms: it sheds light on the necessity for expressive completeness of these devices, absent from the PC. The use of anaphors vis-à-vis variables is also discussed. I next describe the system’s power and say a few words on its meta-logical properties. I then extend the Quarc to modal logic and show how its versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which is arguably an advantage of modal Quarc over modal PC. Finally, I mention directions for further work. 

The talk’s intended audience are people interested in philosophy of language, logic or linguistics.