The Quantified Argument Calculus

Hanoch Ben-Yami

Abstract. I present the principles of a logic I have developed, 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(ES). In this and several other respects, this logic is closer to Natural Language than is any version of Frege’s Predicate Calculus. I proceed to discuss further features of this logic, the Quantified Argument Calculus (Quarc). For instance, the Quarc incorporates both sentential negation and predication negation. The use of anaphors vis-à-vis variables is also discussed. I then concisely introduce the proof system and semantics, and describe the system’s power and its metalogical properties. The possible interest for mathematics and possibilities for further formal research and extensions are then addressed.