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Advances in the Quantified Argument Calculus

Thursday, September 9, 2021, 10:00 am – 6:00 pm

This online conference will bring together researchers who are currently working on the Quantified Argument Calculus, to present their most recent results and work-in-progress.

(link to timetable and abstracts)

The Quantified Argument Calculus (Quarc) is a new logic system, developed by Hanoch Ben-Yami and other philosophers and logicians. Its basic departure from Frege’s logic is in its treatment of quantification: quantifiers are not sentential operators but connect to one‑place predicates to form arguments – quantified arguments – of other predicates. Quarc is closer to natural language in its syntax and the inferences it validates than the first-order Predicate Calculus, while being at least as strong as the latter.

By now, Quarc comprises a family of closely related systems. On all or some of its versions, Quarc has been shown to be sound and complete; to contain and validate Aristotle’s assertoric logic; it separates quantification from existence, shedding new light on logic’s ontological commitments, and lack thereof; it has been extended to modality, invalidating its analogues of the Barcan formulas; three-valued versions of it have been developed, capturing presupposition failure; additional quantifiers have been incorporated in it, such as ‘most’ and ‘more’; several Quarc proof systems have been developed, including sequent calculi, and its metalogical properties have been researched in depth; the image of the Predicate Calculus it contains shows in what sense quantification in the latter is restricted relative to Quarc’s; and more. Further research is currently being conducted, and there’s much potential in additional directions.

A recording of an introductory talk on Quarc, by Ben-Yami, delivered as a World Logic Day event, is available here. A Quarc publications page is found here.


(link to timetable and abstracts)

Hanoch Ben-Yami (Central European University, Vienna)
On ‘There Is’: Logical Investigations into Instantial Sentences

Norbert Gratzl (MCMP, LMU Munich)
Edi Pavlovic (MCMP, LMU Munich)
Proof Theory of Modal Quantified Argument Calculus

Ran Lanzet (The University of Haifa; Edelstein Center, Hebrew University of Jerusalem)
Quantification, Ontology, and Quarc

Elio La Rosa (MCMP, LMU Munich)
Edi Pavlović (MCMP, LMU Munich)
A Nested Sequent Calculus for Quarc

Matteo Pascucci (Slovak Academy of Sciences, Bratislava; Central European University, Vienna)
Jonas Raab (University of Manchester)
A Geometrical Analysis of Modalities in Quarc

Hongkai Yin (Central European University, Vienna)
Quarc and a Decidable Fragment of Predicate Logic


Registration is free but required. To register and obtain a link to the conference talks, please write to


Hanoch Ben-Yami
Hongkai Yin