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THE QUANTIFIED ARGUMENT CALCULUS

Published online by Cambridge University Press:  22 January 2014

HANOCH BEN-YAMI
HANOCH BEN-YAMI*
Affiliation:
Department of Philosophy, Central European University
*
*DEPARTMENT OF PHILOSOPHY CENTRAL EUROPEAN UNIVERSITY, 9 NÁDOR STREET 1051 BUDAPEST, HUNGARY
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Abstract

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 1 , March 2014 , pp. 120 - 146
Copyright
Copyright © Association for Symbolic Logic 2013 

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