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Free Logic and the Quantified Argument Calculus

Edi Pavlović & Norbert Gratzl

In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 105-116 (2018)

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The Quantified Argument Calculus with Two- and Three-valued Truth-valuational Semantics.Hongkai Yin & Hanoch Ben-Yami - 2022 - Studia Logica 111 (2):281-320.details We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of (...) Download Export citation Bookmark 2 citations
The Barcan formulas and necessary existence: the view from Quarc.Hanoch Ben-Yami - 2020 - Synthese 198 (11):11029-11064.details The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus, a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan formulas and their converses is (...) Download Export citation Bookmark 5 citations
Decidable Fragments of the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - 2024 - Review of Symbolic Logic 17 (3):736-761.details This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s assertoric (...) Download Export citation Bookmark
Abstract Forms of Quantification in the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - 2023 - Review of Symbolic Logic 16 (2):449-479.details The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...) Download Export citation Bookmark 4 citations

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