Hanoch Ben-Yami (CEU)

The Quantified Argument Calculus

Abstract:

I present the principles of a logic I have developed, in which quantified arguments occur in argument position. That is, while the natural language sentence 'Alice is polite' is formalised P(a), the sentence 'Some students are polite' is formalised P(ES). In several ways, this logic is closer to Natural Language more than is any version of Frege's Predicate Calculus (PC). 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 about its meta-logical properties. I then extend the Quarc to modal logic and show how its versions of the Barcan formulas and of their converses come out invalid, which is arguably an advantage of modal Quarc over modal PC. Finally, I mention directions for further work.  

The Quarc might be relevant to linguists working on quantification, as it arguably incorporates an improved representation of quantification in natural language.