Hanoch Ben-Yami, Central European University
The Quantified Argument Calculus: Introduction, Current Achievements, New Directions.
I present a logic system I recently developed (RSL 2014), the Quantified Argument Calculus or Quarc. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, on any of its versions, yet it is no less powerful than the first-order Predicate Calculus. Its basic departure from Fregean logic is in its incorporation of quantification: quantifiers are not sentential operators but join one-place predicates to form a quantified argument. Various other departures follow, which also make Quarc closer to Natural Language (negative predication, converse relation terms…). After presenting the principles of the system, I show how it can be extended in several ways, focusing in this talk on modal Quarc. I describe other extensions and applications of Quarc by myself and others, and mention a few additional promising directions of research, to be further explored in a research group I shall convene at the Edelstein Center.